ABSTRACT. We present a class of model-based reinforcement learning algorithms based on the reward-biasing (RB) principle. Unlike the Upper Confidence Bound (UCB) approach, which selects the most optimistic model within a high-confidence set, the RB approach adopts a tempered approach to optimism by regulating the trade-off between a model's average reward and empirical fitting error. This algorithm enjoys state-of-the-art instance-dependent regret guarantees. This tempered approach to optimism in the face of uncertainty (OFU) yields better performance in comparative simulation experiments than state-of-the-art approaches, including the UCRL2 and Thompson Sampling algorithms.

ABSTRACT. Motivated by robust and quantile regression problems, we investigate the stochastic gradient descent (SGD) algorithm for minimizing an objective function that is locally strongly convex with a sub--quadratic tail. This setting covers many widely used online statistical methods. We introduce a novel piecewise Lyapunov function that enables us to handle functions with only first-order differentiability, which includes a wide range of popular loss functions such as Huber loss. Leveraging our proposed Lyapunov function, we derive finite-time moment bounds under general diminishing stepsizes, as well as constant stepsizes. We further establish the weak convergence, central limit theorem and bias characterization under constant stepsize, providing the first geometrical convergence result for sub--quadratic SGD. Our results have wide applications, especially in online statistical methods. In particular, we discuss two applications of our results. 1) Online robust regression: We consider a corrupted linear model with sub--exponential covariates and heavy--tailed noise. Our analysis provides convergence rates comparable to those for corrupted models with Gaussian covariates and noise. 2) Online quantile regression: Importantly, our results relax the common assumption in prior work that the conditional density is continuous and provide a more fine-grained analysis for the moment bounds.

ABSTRACT. The meta-task of obtaining and aligning representations through contrastive pre-training is steadily gaining importance since its introduction in CLIP and ALIGN. In this paper we theoretically explain the advantages of synchronizing with trainable inverse temperature and bias under the sigmoid loss, as implemented in the recent SigLIP models of Google DeepMind. Temperature and bias can drive the loss function to zero for a rich class of configurations that we call (m,b)-Constellations. (m,b)-Constellations are a novel combinatorial object related to spherical codes and are parametrized by a margin m and relative bias b. We use our characterization of constellations to theoretically justify the success of SigLIP on retrieval, to explain the modality gap present in SigLIP, and to identify the necessary dimension for producing high-quality representations. We also propose a reparameterization of the sigmoid loss with explicit relative bias, which appears to improve training dynamics.

ABSTRACT. Diffusion bridges are random processes obtained by conditioning a diffusion process on its values at two times. We use diffusion bridges to explore adversarial robustness of machine learning classifiers in a few ways. Distances on the example space related to bridges make movement through denser parts of the example distribution cheaper, thus making "realistic" examples closer to an original example. By constraining an adversary's modifications to a test example using this distance, we get a definition of test-time adversarial robustness that better captures desired classifier behavior. We develop new algorithms to efficiently compute bridge distances and search for adversarial examples subject to bridge distance constraints.

ABSTRACT. Link functions, which characterize how human preferences are generated from the value function of an RL problem, are a crucial component in designing RLHF algorithms. Almost all RLHF algorithms, including state-of-the-art ones in empirical studies such as DPO and PPO, assume the link function is known to the agent (e.g., a logistic function according to the Bradley-Terry model), which is arguably unrealistic considering the complex nature of human preferences. To avoid link function mis-specification, we study general RLHF problems with unknown link functions. We propose a novel policy optimization algorithm called ZSPO based on a new zeroth-order policy optimization method, where the key is to use human preference to construct a parameter update direction that is positively correlated with the true policy gradient direction. ZSPO achieves it by estimating the sign of the value function difference instead of estimating the gradient from the value function difference, so it does not require knowing the link function. Under mild conditions, ZSPO converges to a stationary policy with a polynomial convergence rate depending on the number of policy iterations and trajectories per iteration. Numerical results also show the superiority of ZSPO under link function mismatch.

ABSTRACT. Federated learning (FL) is a distributed machine learning (ML) approach that allows multiple clients to collaboratively train ML model without exchanging their original training data, offering a solution that is particularly valuable in sensitive domains such as biomedicine. However, training robust FL models often requires substantial computing resources from participating clients, such as GPUs, which may not be readily available at institutions such as hospitals. While cloud platforms (e.g., AWS) offer on-demand access to such resources, their usage can incur significant costs, particularly in distributed training scenarios where poor coordination strategies can lead to substantial resource wastage. To address this, we introduce FedCostAware, a cost-aware scheduling algorithm designed to optimize synchronous FL on cloud spot instances. FedCostAware addresses the challenges of training on spot instances and different client budgets by employing intelligent management of the lifecycle of spot instances. This approach minimizes resource idle time and overall expenses. Comprehensive experiments across multiple datasets demonstrate that FedCostAware significantly reduces cloud computing costs compared to conventional spot and on-demand schemes, enhancing the accessibility and affordability of FL.

ABSTRACT. This works presents a modular federated suite of four methods—LoRA-SilverBullet (LoRA-SB), ABBA, Fed-SilverBullet, and FedEx-LoRA that together enable low-rank, expressive, and resource-efficient fine-tuning of large language models (LLMs). LoRA-SB approximates full fine-tuning within low-rank subspaces via a principled initialization strategy, provably preserving gradient directions and reducing trainable parameters by 27–90× without any additional hyperparameter tuning. ABBA reparameterizes weight updates as the Hadamard product of two low-rank matrices, and formally increasing expressivity under a fixed parameter budget. FedEx-LoRA introduces a lightweight residual correction to recover exact LoRA adapter updates under standard federated averaging, preserving efficiency with minimal overhead. Fed-SB leverages the LoRA-SB’s low-rank update with FedEx-LoRA's exact aggregation in differentially private federated learning, and cuts communication costs by up to 230x. We will detail theoretical results on convergence, reconstruction bounds, communication complexity, and privacy loss, alongside empirical evaluations on reasoning and language benchmarks. This suite offers a principled path to deploy LLM fine-tuning in resource-constrained and privacy-sensitive federated environments.

ABSTRACT. The high communication cost between the server and the clients is a significant bottleneck in scaling distributed learning for overparametrized deep models. One popular approach for reducing this communication overhead is randomized sketching. However, existing theoretical analyses for sketching-based distributed learning (sketch-DL) either incur a prohibitive dependence on the ambient dimension or need additional restrictive assumptions such as heavy-hitters. Nevertheless, despite existing pessimistic analyses, empirical evidence suggests that sketch-DL is competitive with its uncompressed counterpart, thus motivating a sharper analysis. In this work, we introduce a sharper ambient dimension-independent convergence analysis for sketch-DL using the second-order geometry specified by the loss Hessian. Our results imply ambient dimension-independent communication complexity for sketch-DL. We present empirical results both on the loss Hessian and overall accuracy of sketch-DL supporting our theoretical results. Taken together, our results provide theoretical justification for the observed empirical success of sketch-DL.

ABSTRACT. Federated learning (FL) has long been the dominant paradigm for training machine learning (ML) models from distributed, private data. However, recent work has shown that training centrally on differentially-private synthetic data can have better model quality and training cost than FL. This finding relies heavily on a recent differentially-private synthetic data algorithm known as Private Evolution (PE). PE turns out to be somewhat brittle; its performance depends heavily on initialization, and it does not always work well on domain-specific tasks. In this talk, we will discuss two works that deepen our understanding of PE and improve its performance on federated tasks. First, we will discuss our recent theoretical analysis of the utility of PE. To our knowledge, this is the first analysis of PE literature that holds for all privacy settings and does not making simplifying assumptions about the algorithm. Our analysis explicitly shows the effect of poor initialization, and also explains other practical aspects of the PE algorithm. Next, we discuss algorithmic improvements to PE to improve its performance. Our proposed improvement, POPri, recasts the private synthetic data generation problem as a preference optimization problem and significantly outperforms vanilla PE in collaborative learning tasks.

Based on work with Tomas Gonzalez Lara, Aditya Ramdas, Charlie Hou, Mei-Yu Wang, Yige Zhu, and Daniel Lazar.

ABSTRACT. This talk introduces a novel methodology for constructing stochastic bridges in control-affine systems, effectively steering the system state from an initial condition to a desired target state within a finite time horizon. The proposed approach utilizes the time-reversal of diffusion processes to derive the required feedback control law. Subsequently, these stochastic bridges enable the design of feedback control laws that transition the system from an initial probability distribution to a specified target probability distribution, thereby addressing a Schrödinger-bridge-type problem. Preliminary numerical experiments on several benchmark scenarios are presented to demonstrate the applicability of the proposed approach.

ABSTRACT. Markov decision processes (MDPs) is viewed as an optimization of an objective function over certain linear operators over general function spaces. Using the well-established perturbation theory of linear operators, this viewpoint allows one to identify derivatives of the objective function as a function of the linear operators. This leads to generalization of many well-known results in reinforcement learning to cases with generate state and action spaces. Prior results of this type were only established in the finite-state finite-action MDP settings and in settings with certain linear function approximations. The framework also leads to new low-complexity PPO-type reinforcement learning algorithms for general state and action space MDPs.

ABSTRACT. Diffusion models and autoregressive models are the two dominant approaches to generative modeling. While both are powerful tools for modeling complex distributions, they represent opposite ends of the spectrum in terms of generation dynamics—parallel vs. sequential. Using an information-theoretic perspective, we explore a continuous spectrum of generation dynamics that interpolate between these two extremes. The I-MMSE identity connects probability estimation with denoising in a Gaussian channel and has recently been used to illuminate the structure of diffusion models. Building on stochastic localization, we construct a family of noising paths that interpolate between classical diffusion and autoregressive dynamics. Our key result is a path-generalized I-MMSE identity that holds across this spectrum, recovering autoregressive probability decomposition at one end and the classical I-MMSE of diffusion at the other. We present preliminary results demonstrating the benefits of hybrid diffusion-autoregressive generation in language modeling tasks.

ABSTRACT. Modern generative AI pipelines -- from autoregressive transformers through score-based diffusion samplers to reinforcement-learning agents -- can be reframed as special cases of stochastic optimal control and/or transport. In this talk I will review how by treating generative modelling, inference and decision-making within a single stochastic-variational scaffold allows to design algorithms that seamlessly span data-driven and physics-aware regimes and promises improvements in sample efficiency and stability in complex, uncertain and dynamical systems. I will review recent case studies – path-integral diffusion for rapid sample synthesis, physics-guided reinforcement learning, and the sampling decisions framework, and then outline open problems at the intersection of non-equilibrium statistical physics, stochastic control/transport and machine learning.

ABSTRACT. We reformulate the DiffusionNet architecture, widely used for surface learning tasks, as a geometry-informed neural operator for inductive learning across multiple surfaces. We then propose Probabilistic DiffusionNet (PDN), a generative extension which introduces latent random variables derived from a stochastic modification of the underlying diffusion process. The resulting probabilistic neural operator can be used as a resolution-invariant and uncertainty-aware surrogate for the trace solution map of PDEs whose boundary conditions are determined by surface geometry. Such a surrogate can expedite typical engineering design and optimization processes that require computationally burdensome computational fluid dynamics (CFD) analysis pipelines. We demonstrate that PDN produces state-of-the-art uncertainty quantification (UQ) performance on standard CFD datasets without sacrificing predictive accuracy, while enjoying lower computational cost compared to other prevalent geometry-informed PDE surrogates endowed with UQ capabilities.

ABSTRACT. We investigate the service-rate region (SRR) of distributed storage systems that employ linear codes. We focus on systems where each server stores one code symbol, and a user recovers a data symbol by accessing any of its recovery groups, subject to per-server capacity limits. The SRR--the convex polytope of simultaneously achievable request rates--captures system throughput and scalability. We first derive upper and lower bounds on the maximum request rate of each data object. These bounds hold for all linear codes and depend only on the number of parity checks orthogonal to a particular set of codeword coordinates associated with that object, i.e., the equations used in majority-logic decoding, and on code parameters. We then check the bound saturation for 1) all non-systematic codes whose SRRs are already known and 2) systematic codes. For the former, we prove the bounds are tight. For systematic codes, we show that the upper bound is achieved whenever the supports of minimum-weight dual codewords form a 2-design. As an application, we determine the exact per-object demand limits for Hamming codes. Our framework provides a new lens to address the SRR problem through combinatorial design theory.

ABSTRACT. Design of the optimal encoder and decoder for a discrete memoryless channel is a well-studied problem in classic information theory. However, there exists important systems which operate with components (encoder and decoders) that are prebuilt and possibly mismatched, limiting the achievable performance metrics. In this paper, we propose a model that takes into account such constraints. Using this model, we develop an understanding of the source coding problem in this context and introduce two new functions -transitory and restricted rate distortion- and analyze certain properties of them. In addition, one important application of this model for developing a comprehensive theory of semantic communication is discussed. Finally, some numerical examples are provided to illustrate the concepts mentioned in the paper.

ABSTRACT. We study interactive error-correcting codes (iECCs) in the binary communication model with separate corruption budgets for both the directions of communication. Interactive error-correcting codes (iECCs) allow two parties, Alice and Bob, to communicate over a noisy channel through an interactive protocol, with the goal of communicating a message from Alice to Bob even when a bounded fraction of the communication is adversarially corrupted. In the standard one-way communication setting, previous works show that an error fraction \alpha of bit flips can be corrected to recover the original message if and only if \alpha is bounded by 1/4. Berlekamp showed that this fraction improves to 1/3 with interaction using noiseless feedback. Elfremenko, Kol, Saxena and Zhang further construct interactive error-correcting codes (iECCs) that can uniquely decode from an error fraction of 1/4 + 10^{-5} even in the presence of noisy feedback while the best known impossibility upper bound for this setting is 13/47. In order to better understand this gap, we study the communication model with independent corruption budgets for both sides of communication and show that no iECC can be resilient to more than 7/24 fraction of errors in this model.

ABSTRACT. Side channels have become an essential component of some modern information-theoretic schemes. The emerging field of cross technology communications (CTC) provides practical methods for creating intentional side channels using existing communication technologies. This paper describes a theoretical foundation for one such recently proposed CTC scheme: Ghost Modulation (GM). Designed to modulate a low-data-rate message atop an existing network stream, GM is particularly suited for transmitting identification or covert information. The implementation only requires firmware updates to existing hardware, making it a cost-effective solution. However, GM provides an interesting technical challenge due to an asymmetric binary crossover erasure channel (BCEC) that results from packet drops and network delays. In this work, we provide a mathematical description of the signal and channel models for GM. A heuristic decision rule based on maximum-likelihood principles for simplified channel models is proposed. We describe an algorithm for GM packet acquisition and timing synchronization, supported by simulation results. Several well known short block codes are applied, and bit error rate (BER) results are presented.

ABSTRACT. Hardware Trojans are malicious modifications to communication circuitry that leak information by altering the transmitted signal. This paper models certain classes of hardware Trojans via the cascading of a Z channel. We use the Z-channel to capture the asymmetric on-off behavior of certain Trojans---such as amplitude-based Trojans---that selectively reduce the power (and hence signal-to-noise ratio) of some legitimate symbols while leaving other symbols unaffected. For convenience and tractability of cascaded channels, the legitimate and the rogue channels are also modeled as Z channels in this initial study. We characterize the tradeoff between information leakage to the rogue receiver and rate loss at the legitimate receiver and analyze Trojan detectability under varying assumptions about the legitimate receiver’s knowledge of the rogue codebook. Numerical results illuminate our findings.

ABSTRACT. Dynamic max-min fair allocation (DMMF) is a simple and popular mechanism for the repeated allocation of a shared resource among competing agents: in each round, each agent can choose to request or not for the resource, which is then allocated to the requesting agent with the least number of allocations received till then. Despite its widespread use in practice, its theoretical properties are less well understood. I will summarize some of our recent work, where we show that in large markets when an agent has i.i.d. values across rounds, under mild distributional assumptions (e.g., bounded PDF function), the DMMF mechanism allows each agent to realize a 1−o(1) fraction of her ideal utility -- her highest achievable utility given her nominal share of resources. This guarantee holds under arbitrary behavior by other agents, and our techniques also allow us to handle settings where an agent's values are correlated across rounds, and also the case of reusable resources, where an agent might need to hold the item over multiple rounds to receive utility. On the negative side, we show that despite these strong robustness guarantees, the associated strategies admit no Nash equilibrium. However, we show this can be remedied in the symmetric case by a simple data-driven request policy, wherein agents aim to match the historical allocation rate with a vanishing drift towards the rate optimizing overall welfare for all users. Furthermore, the resulting equilibrium outcome can be significantly better compared to what follows from the robustness guarantees.

ABSTRACT. Multi-agent reinforcement learning (MARL) is emerging as a key tool in application areas as varied as robotics, the distributed control of networked systems, and the fine-tuning of language models. While MARL algorithms are actively being deployed across domains---often to great effect--- they are not well understood theoretically outside of highly structured regimes like zero-sum games, cooperative games, and finite-horizon Markov games where the structure renders the underlying problem of equilibrium computation tractable by e.g., dynamic programming. In infinite horizon general-sum Markov games, however, even generalizations of Nash equilibria can be hard to compute which has resulted in a lack of algorithms with convergence guarantees to stationary equilibrium concepts.

In this work, we show that bringing in structures from behavioral economics into MARL can help us address this challenge. In particular, we show that bounded rational agents who are risk-averse to their opponents' strategies give rise to a new equilibrium concept: stationary Markov strategically risk-averse quantal response equilibria (MSRQE)--- a class of which is computable across all general-sum Markov games. We show that the equilibrium concept smoothly interpolates between stationary Nash equilibria of the underlying Markov games and players' security strategies as the degree of strategic robustness increases. Furthermore we present a simple, independent Actor-Critic based algorithm that converges to an MSRQE when used by all players in any Markov game. Finally we show that the algorithm can easily be adapted to use function approximation, allowing it to scale to complex MARL problems.

ABSTRACT. Learning-to-communicate (LTC) in partially observable environments has emerged and received increasing attention in deep multi-agent reinforcement learning, where the control and communication strategies are jointly learned. On the other hand, the impact of communication has been extensively studied in control theory. In this paper, we seek to formalize and better understand LTC by bridging these two lines of work, through the lens of information structures (ISs). To this end, we formalize LTC in decentralized partially observable Markov decision processes (Dec-POMDPs) under the common information-based (CIB) framework, and classify LTCs based on the ISs before additional information sharing. We first show that non-classical LTCs are computationally intractable in general, and thus focus on quasi-classical (QC) LTCs. We then propose a series of conditions for QC LTCs, violating which can cause computational hardness in general. Further, we develop provable planning and learning algorithms for QC LTCs, and show that examples of QC LTCs satisfying the above conditions can be solved without computationally intractable oracles. Along the way, we also establish some relationships between (strictly) QC IS and the condition of having strategy-independent CIB beliefs (SI-CIB), as well as solving general Dec-POMDPs without computationally intractable oracles beyond those with the SI-CIB condition, which may be of independent interest.

ABSTRACT. In this talk, we study linear-quadratic leader-follower Stackelberg differential games for jump-diffusion stochastic differential equations. In Stackelberg games, the leader holds a dominant position: the leader chooses and then announces his or her optimal strategy, taking into account the rational behavior of the follower. The follower subsequently determines his or her own optimal solution based on the leader's choice. This setup describes a sequential and hierarchical optimization problem between the leader and the follower, which arises in various applications in finance, engineering, economics, and the sciences.

We first study the case of complete information, where both the leader and the follower have access to the full filtration $\mathbb{F}$ generated by the underlying stochastic processes. We then study the case of asymmetric information, where the leader and the follower have access to partial filtrations $\mathbb{G}_1 \subset \mathbb{F}$ and $\mathbb{G}_2 \subset \mathbb{F}$, respectively, with $\mathbb{G}_2 \subset \mathbb{G}_1$ capturing the asymmetric information structure. In both problems, by the stochastic maximum principle as well as the four-step scheme, we obtain the explicit feedback-type Stackelberg equilibrium for the leader and the follower.

ABSTRACT. An interception problem involving a single interceptor (pursuer) and multiple targets (evaders) is considered. At a prescribed moment, the pursuer chooses a single evader for interception. The probabilities of choosing each of the evaders are assumed to be known. The strategies after the decision time are known, yielding the performance index depending on the state at the decision time. A non-standard linear-quadratic type differential game problem before the decision time is formulated that takes into account the average performance over all decision outcomes for the optimal Norm Bounded Differential Game after-decision strategy. Based on this differential game formulation, we derive guidance algorithm and study its performance by numerical simulations. The game solvability conditions are established. The influence of control effort penalty coefficients on the pursuit strategy performance is investigated. The results of numerical simulation are presented.

ABSTRACT. We sample directed graphs from asymmetric graphons and investigate the probability that the digraph has at least one hamiltonian decomposition. We show that the probability essentially obeys the zero-one law in the asymptotic regime where the order of the digraph goes to infinity. We exhibit an explicit condition that can efficiently decide whether the limiting probability is zero or one.

ABSTRACT. We present an algorithm for the discounted discrete-time Linear Quadratic Regulator (LQR) problem with unknown dynamics that achieves $\varepsilon$-optimality using only $\widetilde{\mathcal{O}}(1/\varepsilon)$ function evaluations. This is made possible by employing a gradient estimation technique inspired by REINFORCE, combined with a time-varying step-size. Our results improve over existing techniques outside the two-point estimation framework—which is impractical in practice—that typically yield $\widetilde{\mathcal{O}}(1/\varepsilon^2)$ sample complexity or impose strong stability assumptions.

ABSTRACT. Flow matching is a method introduced in the generative modeling literature for constructing transport maps between given probability measures. Applications of constructing transport maps between measures range from spatial coverage by robotic swarms to shaping uncertainty and introducing multi-stability in control systems. In this talk, we present a generalization of flow matching to settings where the evolution of the measures is constrained at the path level to be trajectories of a control-affine system. A key advantage of this approach of transport lies in its simplicity. Specifically, it computationally reduces to a regression problem. Classical tools from control theory, such as feedback stabilization and motion planning with oscillatory controls, traditionally used to solve point-to-point control problems, can be directly used to address the more general measure-to-measure transport problem. In cases where the point-to-point control problem is not analytically solvable, we head in the opposite conceptual direction. That is, using the measure-to-measure problem to solve the classical point stabilization problem. In this latter case, using the idea of time-reversals, flow matching also provides new way to approach the stabilization problem from the perspective of transport theory.

ABSTRACT. Given scalar observations of an unknown nonlinear dynamical system, Extended Dynamic Mode Decomposition (eDMD) seeks to model the time-evolution of these observables by a linear dynamical system. To avoid information loss and numerical challenges, one often wants the collection of observables to separate points and be continuous (or smoother). Stacking such observables into a vector-valued function yields a globally linearizing "Koopman embedding" of the nonlinear system, which, conceptually, embeds the nonlinear system as an invariant subset of a linear system of greater or equal dimension. However, Koopman embeddings do not generally exist, posing a fundamental challenge for eDMD and related algorithms. In this talk, I will present necessary and sufficient conditions for the existence of Koopman embeddings for a broad class of nonlinear systems. For cases when exact Koopman embeddings do not exist, I will also discuss the question of approximately "engineering around" this constraint in practice. Aspects of this talk are based on joint work with Philip Arathoon and with Eduardo D. Sontag.

ABSTRACT. Reservoir computing is an efficient gradient-free black-box machine learning method that is highly effective at forecasting systems with complex nonlinear dynamics. Echo state networks (ESNs) are the archetypal neural network architectures used for reservoir computing. Effective initialization of ESNs remains an open problem, despite their widespread utilization. In this work we make progress towards establishing more principled initialization criteria for ESNs and broader classes of reservoirs. It is often suggested that reservoirs operate best near the "edge of criticality", i.e. when their rate of contraction is close to zero. However, reservoirs also fall off in performance "too close" to criticality, suggesting a localized range of time scales for optimal performance. We investigate the role of a reservoir's intrinsic time scale in its forecasting performance, showing empirically that ESNs are ultrasensitive to the choice of time scale relative to that of the input time series. We investigate the origins of this sensitivity with numerical and theoretical tools, and based on these insights suggest several strategies for reservoir initialization to improve forecasting performance.

ABSTRACT. The increasing use of renewable energy presents challenges for utilities managing the dispatch of production resources to meet the variable and uncertain net demand. In previous work, we developed methods for managing unit commitment dispatch in a flexible manner, i.e., without committing resources in advance. In this work, we apply these methods to a network setting with transmission constraints and present results for an example system.

ABSTRACT. The time at which renewable (e.g., solar or wind) energy resources produce electricity cannot generally be controlled. In many settings, however, consumers have some flexibility in their energy consumption needs, and there is growing interest in demand-response programs that leverage this flexibility to shift energy consumption to better match renewable production—thus enabling more efficient utilization of these resources. We study optimal demand response in a setting where consumers use home energy management systems (HEMS) to autonomously adjust their electricity consumption. Our core assumption is that HEMS operationalize flexibility by querying the consumer for their preferences and computing the “indifference set” of all energy consumption profiles that can be used to satisfy these preferences. Then, given an indifference set, HEMS can respond to grid signals while guaranteeing user-defined comfort and functionality; e.g., if a consumer sets a temperature range, a HEMS can precool and preheat to align with peak renewable production, thus improving efficiency without sacrificing comfort. We show that while price-based mechanisms are not generally optimal for demand response, they become asymptotically optimal in large markets under a mean-field limit. Furthermore, we show that optimal dynamic prices can be efficiently computed in large markets by only querying HEMS about their planned consumption under different price signals. Using an OpenDSS-powered grid simulation for Phoenix, Arizona, we demonstrate that our approach enables meaningful demand response without creating grid instability.

ABSTRACT. Electric power systems are evolving to accommodate intermittent renewable sources and storage technologies like batteries. As privately-owned batteries gain prominence, key questions arise: How do they behave in electricity markets, and how does their strategic behavior differ from that of centrally operated batteries? We propose an analytically tractable model that captures salient features of the highly complex electricity market. We derive in closed form the resulting battery behavior and generation cost in three operating regimes: (i) no battery, (ii) centralized battery, and (ii) decentralized profit-maximizing battery. We identify three distortions in decentralized battery behavior: (1) quantity withholding, i.e., discharging less than centrally optimal; (2) shift from day-ahead to real-time, i.e., postponing some discharge from day-ahead to real-time; (3) reduction in real-time responsiveness, i.e., discharging less in response to smoothing real-time demand than centrally optimal. We quantify efficiency loss using the Price of Anarchy metric and show that the cost of strategic behavior is always bounded between $9/8$ and $4/3$. That is, incentive misalignment always exists, but it is bounded even in the worst case. We calibrate our model to real data from Los Angeles and Houston. Lastly, we show that competition is effective at reducing distortions, but many market power mitigation mechanisms backfire, leading to higher total cost. This work offers a framework for analyzing and quantifying market power in battery operations. It underscores that while battery market power does pose a concern, its negative impact is limited compared to the overall system benefits of sufficient battery capacity.

ABSTRACT. We study the optimal placement of an unlimited-capacity battery in power grids under a centralized market model, where the independent system operator (ISO) aims to minimize total generation costs through load shifting. The optimal battery placement is not well understood by the existing literature, especially regarding the influence of network topology on minimizing generation costs. Our work starts with decomposing the Mixed-Integer Linear Programming (MILP) problem into a series of Linear Programming (LP) formulations. For power grids with sufficiently large generation capacity or tree topologies, we derive analytical cost expressions which demonstrate that, under reasonable assumptions, the weighted degree is the only topological factor for optimal battery placement. We also discuss the minor impact of higher-order topological conditions on tree-topology networks. To find the localized nature of a single battery's impact, we establish that the relative cost-saving benefit of a single battery decreases as the network scales. Furthermore, we design a low-complexity algorithm for weakly-cyclic networks. Numerical experiments show that our algorithm is not only approximately 100 times faster than commercial solvers but also maintains high accuracy even when some theoretical assumptions are relaxed.

ABSTRACT. We consider a collection of microgrids (MGs) with renewable generation capability that can operate independent of the main power grid. Such microgrids are increasingly becoming popular for critical services such as hospitals to function during catastrophic failures as well as among local communities. Microgrids must provide high probability guarantees for service over a finite horizon so they invest in battery energy resources (BES) to mitigate the risk of generation or load curtailment arising from the uncertainty in production/demand. With appropriate connectivity and control, the microgrids can share this risk and reduce the BES requirements for the same level of probabilistic guarantee. To study this, we present a chance-constrained BESs sizing methodology combined with power-sharing policy between microgrids (MGs) in a multi-MG power distribution network. In particular, given a power network and stochastic models of the RESs production and load demand, we provide a methodology to decide the minimum required BESs capacity of the MGs and a power transfer policy governing the amount of power transfer between the MGs, to minimize load and generation curtailment over a given time horizon [0, Tf ] with high probability. We further characterize the trade-offs between the BESs capacity and the power line capacity to provide a comprehensive system planning guideline. We find that there is a sharp threshold such that if and only if the power line capacities are above the threshold then the microgrids are able to completely pool their risk. Surprisingly, this threshold decreases with the increase in the time horizon. Our work suggests that it is feasible to design sparse and minimally connected microgrid networks that can operate with high probability service guarantees.

ABSTRACT. Transparency and explainability are two extremely important aspects to be considered when employing black-box machine learning models in high-stake applications. Providing counterfactual explanations is one way of fulfilling this requirement. However, this also poses a threat to the privacy of both the institution that is providing the explanation as well as the user who is requesting it. In this work, we propose multiple schemes inspired by private information retrieval (PIR) techniques which ensure the \emph{user's privacy} when retrieving counterfactual explanations. We present a scheme which retrieves the \emph{exact} nearest neighbor counterfactual explanation from a database of accepted points while achieving perfect (information-theoretic) privacy for the user. While the scheme achieves perfect privacy for the user, some leakage on the database is inevitable which we quantify using a mutual information based metric. Furthermore, we propose strategies to reduce this leakage to achieve an advanced degree of database privacy. We extend these schemes to incorporate user's preference on transforming their attributes, so that a more actionable explanation can be received. Since our schemes rely on finite field arithmetic, we empirically validate our schemes on real datasets to understand the trade-off between the accuracy and the finite field sizes. Finally, we present numerical results to support our theoretical findings, and compare the database leakage of the proposed schemes.

ABSTRACT. We develop an information-theoretic framework for text summarization that formalizes the rate–distortion–perception trade-off for summarizers. This trade-off, originally introduced in lossy compression, quantifies the relationship between the length of a compressed representation (rate), the fidelity of the reconstruction (distortion), and its perceived naturalness (perception). Motivated by the structural similarities between lossy compression and text summarization, we adapt this framework to the summarization setting. We define the summarizer rate–distortion–perception function (SRDPF) and show that it characterizes the fundamental performance limits of any summarizer. We then present an algorithm to compute the SRDPF for a given text source, and a practical method to estimate it from limited data. Experimental results demonstrate that the SRDPF provides a principled basis for evaluating summarizers and can guide the generation of higher-quality summaries. Additionally, we extend classical rate–distortion–perception results to the setting where the reference distribution differs from the source distribution.

ABSTRACT. Today, the vast majority of the world's digital information is represented using the fundamental assumption, introduced by Claude Shannon in 1948, that ``...the semantic aspects of communication are irrelevant to the engineering problem (of the design of communication systems)...''. It is hard to overestimate the extraordinary positive impact of this assumption, which has allowed the design of flexible efficient and reliable communication systems that operate regardless of the intended meaning of our messages.

Consider, nonetheless, the observation that we, individuals, as well as our computing devices, often combine a received message with other information in order to deduce new facts (and hopefully make better decisions), thereby expanding the value of the originally received message. It is noteworthy that to-date, no rigorous theory of communication has been put forth which postulates the existence of deductive capabilities on the receiver's side.

The purpose of this paper is to present a proposal that combines information theory and logic at a fundamental level. We formally model such deductive capabilities using logic reasoning, and present a rigorous theory which covers the following generic scenario: Alice and Bob each have knowledge of some logic sentence, and they wish to communicate as efficiently as possible with the shared goal that, following their communication, Bob should be able to deduce a particular logic sentence that Alice knows to be true, but that Bob currently cannot prove. Many variants of this general setup are considered in this article; in all cases we are able to provide sharp upper and lower bounds phrased in terms of an entropy-like function that we call $\Lambda$, in reference to its apparent connection to problems of communication involving logic. Our contribution includes the identification of the most fundamental requirements that we place on a logic and associated logical language for all of our results to apply; an example is Propositional Logic over a finite number of propositions. Practical algorithms that are in some cases asymptotically optimal are provided, and we illustrate the potential practical value of the design of communication systems that incorporate the assumption of deductive capabilities at the receiver using experimental results that suggest significant possible gains compared to classical systems.

ABSTRACT. In this paper, we explore the rate-distortion theory for semantic communication with zero perception error (ZEPE). By incorporating a ZEPE constraint, the decoder can generate a reconstructed signal that maintains ZEPE while satisfying a given distortion constraint. This approach can be viewed as a special case of the conventional rate-distortion framework. We derive the optimal transition probability and extend the ZEPE rate-distortion framework to include inferred latent variables, which can capture the semantic meaning of the observed signal. For practical implementations, we discuss the use of generative models such as variational autoencoders (VAEs).

ABSTRACT. We address key challenges in transfer reinforcement learning (RL), where the goal is to learn a near-optimal policy in a target environment using limited data and knowledge from related source domains. Existing methods often lack performance guarantees and risk negative transfer from poor sources. To tackle this, we propose a pessimism-based framework that conservatively estimates target performance, which ensures safer decisions and consistent improvements with higher-quality sources. We introduce two estimation methods, analyze their effectiveness, and design distributed algorithms with convergence guarantees, thereby offering a robust and principled approach to transfer in RL.

ABSTRACT. In this paper, we address the challenges of offline reinforcement learning (RL) under model mismatch, where the agent aims to optimize its performance through an offline dataset that may not accurately represent the deployment environment. We identify two primary challenges under the setting: inaccurate model estimation due to limited data and performance degradation caused by the model mismatch between the dataset-collecting environment and the target deployment one. To tackle these issues, we propose a unified principle of pessimism using distributionally robust Markov decision processes. We carefully construct a robust MDP with a single uncertainty set to tackle both data sparsity and model mismatch, and demonstrate that the optimal robust policy enjoys a near-optimal sub-optimality gap under the target environment across three widely used uncertainty models: total variation, $\chi^2$ divergence, and KL divergence. Our results improve upon or match the state-of-the-art performance under the total variation and KL divergence models, and provide the first result for the $\chi^2$ divergence model.

ABSTRACT. Watermarking has emerged as a crucial method to distinguish AI-generated text from human-created text. Current watermarking approaches often lack formal optimality guarantees or address the scheme and detector design separately. In this paper, we introduce a novel, unified theoretical framework for watermarking Large Language Models (LLMs) that jointly optimizes both the watermarking scheme and detector. Our approach aims to maximize detection performance while maintaining control over the worst-case false positive rate (FPR) and distortion on text quality. We derive closed-form optimal solutions for this joint design and characterize the fundamental trade-off between watermark detectability and distortion. Notably, we reveal that the optimal watermarking schemes should be adaptive to the LLM’s generative distribution. Building on our theoretical insights, we propose a distortion-free, distribution-adaptive watermarking algorithm (DAWA) that leverages a surrogate model for model-agnosticism and efficiency. Experiments on Llama2-13B and Mistral-8 7B models confirm the effectiveness of our approach, particularly at ultra-low FPRs.

ABSTRACT. We propose a novel gradient estimation algorithm for training neural stochastic differential equations by combining a weak derivative estimator using the Hahn–Jordan decomposition, together with a Malliavin calculus framework for conditional expectation estimation. Unlike kernel-based methods, this Malliavin framework results in Monte Carlo simulation-based estimators with \sqrt{n} convergence rates even when conditioning on rare events. One of the main advantages of the proposed weak derivative estimator is that it entails uniformly bounded variance scaling with respect to the time horizon. This improves on score function or likelihood ratio methods which suffer from the variance which grows linearly with the time horizon. We illustrate the effectiveness of the proposed estimator in training goal-conditioned diffusion models conditioned on rare events.

ABSTRACT. Robust Markov Decision Processes (RMDPs) have received significant research interest, offering an alternative to standard Markov Decision Processes (MDPs) that often assume fixed transition probabilities. RMDPs address this by optimizing for the worst-case scenarios within ambiguity sets. Existing studies on RMDPs have largely centered on risk-neutral reinforcement learning (RL), with the goal of minimizing expected total discounted costs. In this talk, we analyze the robustness of CVaR-based risk-sensitive RL under RMDP.

ABSTRACT. Solving real-world stochastic optimization problems presents two key challenges: the messiness of real-world data, which can be noisy, biased, or corrupted due to factors like heavy-tailed noise distributions, outliers, distribution shifts, and even adversarial attacks; and the laborious, time-intensive requirement of manually tuning step sizes in many existing algorithms.

I will introduce a simple adaptive optimization framework that avoids the need for manual step size tuning by adaptively adjusting the step size in each iteration based on the progress of the algorithm. To address the issue of messy data, the algorithm only assumes access to function-related information through probabilistic oracles. Crucially, these oracles can return function value and gradient estimates contaminated with noise that is heavy-tailed.

This framework is very general, encompassing a wide range of algorithms for both unconstrained and constrained optimization. It is applicable to multiple problem settings, such as expected loss minimization in machine learning, simulation optimization, and derivative-free optimization. Under reasonable conditions on the oracles, we provide an analytical framework that bounds the iteration complexity with high probability for settings with highly noisy and corrupted inputs.

ABSTRACT. We introduce a new belief-based learning model in which players update their strategies by combining statistical hypothesis testing with utility-driven exploration. In this dynamics, each player forms beliefs about opponents’ strategies and episodically tests these beliefs using empirical observations. Beliefs are resampled either when the hypothesis test is rejected or through exploration, where the probability of exploration decreases with the player's expected utility. In general finite normal-form games, we show that the learning process converges to a set of approximate Nash equilibria and, more importantly, to a refinement that selects equilibria maximizing the minimum utility across all players. This result establishes convergence to equilibrium in general finite games and reveals a novel mechanism for equilibrium selection induced by the structure of the learning dynamics. We extend this result to stochastic and repeated games and discuss how such learning dynamics can support cooperative outcomes that emerge through repeated interactions.

ABSTRACT. Developing prompt-based methods with Large Language Models (LLMs) requires making numerous decisions, which give rise to a combinatorial search problem over hyper-parameters. This exhaustive evaluation can be time-consuming and costly. In this paper, we propose an \textit{adaptive} approach to explore this space. We are exploiting the fact that often only few samples are needed to identify clearly superior or inferior settings, and that many evaluation tests are highly correlated. We lean on multi-armed bandits to sequentially identify the next (method, validation sample)-pair to evaluate and utilize low-rank matrix factorization to fill in missing evaluations. We carefully assess the efficacy of our approach on several competitive benchmark problems and show that it can identify the top-performing method using only 5-15% of the typical resources---resulting in 85-95% LLM cost savings. Our code is available at https://github.com/kilian-group/banditeval.

ABSTRACT. Incorporating prior knowledge or specifications of input-output relationships into machine learning models has attracted significant attention, as it enhances generalization from limited data and leads to conforming outputs. However, most existing approaches use soft constraints by penalizing violations through regularization, which offers no guarantee of constraint satisfaction, especially on inputs far from the training distribution—an essential requirement in safety-critical applications. On the other hand, imposing hard constraints on neural networks may hinder their representational power, adversely affecting performance. To address this, we propose HardNet, a practical framework for constructing neural networks that inherently satisfy hard constraints without sacrificing model capacity. Unlike approaches that modify outputs only at inference time, HardNet enables end-to-end training with hard constraint guarantees, leading to improved performance. To the best of our knowledge, HardNet is the first method with an efficient forward pass to enforce more than one input-dependent inequality constraint. It allows unconstrained optimization of the network parameters using standard algorithms by appending a differentiable closed-form enforcement layer to the network’s output. Furthermore, we show that HardNet is expressive and retains the universal approximation capabilities of neural networks. We demonstrate the versatility and effectiveness of HardNet across various applications: learning with piecewise constraints, learning optimization solvers with guaranteed feasibility, and optimizing control policies in safety-critical systems.

ABSTRACT. It is difficult to design economic mechanisms for markets with discrete decisions. A prominent example is unit commitment in power systems, in which the decision to turn a generator on or off is binary. Because strong duality does not hold, one cannot simply use dual multipliers as prices, as in some other types of electricity markets.

In this talk, we describe a new way of designing market mechanisms for discrete problems. Our approach is based on a fundamental result of Burer (2009), which establishes that a mixed-integer quadratic program can be equivalently represented as a completely positive program (CPP). CPP is a conic optimization class that is both convex and NP-hard. As such, it does not provide a better way to solve MILPs like UC; being more general, CPP is even less tractable. Its convexity does however provide a new notion of duality for discrete problems.

We use the CPP reformulation and its copositive dual to design several new pricing mechanisms for unit commitment. Convexity also brings tools like the Karush-Kuhn-Tucker conditions, which are helpful for establishing properties like efficiency and budget balance. We will also discuss current options for solving CPPs and COPs, and other problems where copositive duality might be useful.

ABSTRACT. In this paper, we review some well-established notions of opacity in discrete event systems, such as current- and initial-state opacity. System opacity has proven important in capturing information flow properties in dynamic systems with respect to a passive observers that can make inferences about system properties and parameters based on available observations and their knowledge of the system model. We then apply these techniques towards the verification/enforcement of different notions of opacity for end users in a smart grid. We also discuss potential implications to privacy and privacy-preserving strategies in such systems.

ABSTRACT. Rapidly growing deployments of distributed energy resources like rooftop solar and electric vehicles have disrupted the status quo of distribution network operations. Power export/import limits that change as network conditions change, also known as operating envelopes, have been proposed as a means of safely operating distribution networks containing distributed energy resources. This talk analyzes the impacts of using convex relaxations, specifically the second-order cone relaxation, for determining the limits required for safe operation. We illustrate the inadequacy of operating envelopes calculated using a second-order cone formulation for ensuring network safety. Then we discuss the complexity in the relationship between the relaxation, the nonlinear formulation, and the network parameters. For the case of purely resistive, radial networks and the case of purely reactive, radial networks, we prove that the second-order cone relaxation is inexact and exact, respectively, for the operating envelope problem. This work illustrates that while using a second-order cone relaxation to determine operating envelopes will not always result in overly large bounds, it often will and with potentially damaging consequences.

ABSTRACT. We develop a mathematical framework to jointly schedule water and electricity in a profit-maximizing water desalination plant that operates both thermal- and membrane-based desalination technologies that are co-located with renewable generation. The price-taking desalination plant sells desalinated water to a water utility at a given price and engages in bi-directional electricity transactions with the grid, purchasing or selling power based on its net electricity demand. We show that the optimal scheduling policy depends on the plant’s internal renewable generation and follows a simple threshold structure. Under the optimal policy, thermal-based water output decreases monotonically with renewable availability, while membrane-based output increases monotonically. We characterize the structure and intuition behind the threshold policy and examine key special properties.

ABSTRACT. Model reduction techniques are routinely used to focus on specific phenomena and features in a representation, typically by reducing the number of variables. In electric circuits where only a subset of nodes may be of interest, Kron reduction is routinely employed to eliminate the other nodes, while preserving the electrical behavior as seen from the retained nodes. While resulting in networks with fewer nodes, Kron reduction has potential drawbacks. By design, the original network's structure is not preserved. Therefore, despite the terminal behavior being equivalent to that of the originating system, practical algorithms may find the ensuing analysis more computationally demanding. For instance, Kron reduction of radial networks yields meshed topologies. Several (optimal) power flow algorithms provide stronger performance guarantees for radial networks. In these cases, having a radial network with a higher number of nodes may be a pertinent choice. In this paper, we pursue a course akin to reverse Kron reduction in which we purposely enlarge a network model to achieve a topology that may have favorable characteristics for downstream analysis. This larger model will preserve the electrical behavior as seen from the original nodes and will revert to the original network when Kron reduction is employed. We consider the question of when it may be possible to convert a meshed network to a larger tree network, and we examine conversion to other structures that may have favorable topologies.

ABSTRACT. Power electronic converter-based resources are becoming ubiquitous in the power system. Unlike rotating machines, these converters are tightly constrained by the current limits imposed by semiconductor devices. The explosive growth of high-power loads, such as electric vehicles and AI data centers, is rapidly reducing the power margins of converters. A common solution is to implement hard current limiters in the converter firmware, but it is not optimal and can destabilize the system.

In this paper, we show how to optimally control the operation of converters under current limits. By characterizing their feasible operating regions, we provide decentralized algorithms that do not require detailed system information and are provably optimal. They generalize and remove some of the limitations found in existing algorithms, such as grid-forming inverter control loops.

ABSTRACT. It is now standard practice to start from a broadly performant pre-trained "foundation" model and further-train or fine-tune it for new tasks or on new data. Doing so, however, often degrades the model for tasks it was previously good at.

We present two independent ways to solve this problem: (1) up-weighting the loss on fine-tuning samples that are "easy" for the existing model, and (2) generating "unconditional" synthetic data, and then training on a mix of this and the new data

We first develop the intuition and theoretical basis behind each of these methods. We then show that both these ideas not only outperform several other existing approaches (L2 regularization, model averaging, etc.), but provide gains that are complimentary and additive to those given by the other methods. We show our results on pre-trained only models, instruction tuned models and reasoning models.

ABSTRACT. Scaling language models to handle longer input sequences typically necessitates large key-value (KV) caches, resulting in substantial memory overhead during inference. In this paper, we propose Tensor Product Attention (TPA), a novel attention mechanism that uses tensor decompositions to represent queries, keys, and values compactly, substantially shrinking the KV cache size at inference time. By factorizing these representations into contextual low-rank components and seamlessly integrating with Rotary Position Embedding (RoPE), TPA achieves improved model quality alongside memory efficiency. Based on TPA, we introduce the Tensor Product Attention Transformer,(T6), a new model architecture for sequence modeling. Through extensive empirical evaluation on language modeling tasks, we demonstrate that T6 surpasses or matches the performance of standard Transformer baselines, including Multi-Head Attention (MHA), Multi-Query Attention (MQA), Grouped-Query Attention (GQA), and Multi-Head Latent Attention (MLA) across various metrics, including perplexity and a range of established evaluation benchmarks. Notably, TPA's memory efficiency and computational efficiency at the decoding stage enable processing longer sequences under fixed resource constraints, addressing a critical scalability challenge in modern language models.

ABSTRACT. In lifelong learning, a learner faces a sequence of tasks with shared structure and aims to identify and leverage it to accelerate learning. We study the setting where such structure is captured by a common representation of data. Unlike multi-task learning or learning-to-learn, where tasks are available upfront to learn the representation, lifelong learning requires the learner to make use of its existing knowledge while continually gathering partial information in an online fashion. In this paper, we consider a generalized framework of lifelong representation learning. We propose a simple algorithm that uses multi-task empirical risk minimization as a subroutine and establish a sample complexity bound based on a new notion we introduce—the task-eluder dimension. Our result applies to a wide range of learning problems involving general function classes. As concrete examples, we instantiate our result on classification and regression tasks under noise.

ABSTRACT. For a simple model of shallow and wide neural networks, we show that the epigraph of its input-output map as a function of the network parameters approximates epigraph of a convex function in a precise sense. This leads to a plausible explanation of their observed good performance.

ABSTRACT. In this work, we present image inversion (transporting an image to noise to enable editing) and subsequently editing of the image, using rectified flow models. Rectified Flow (RF) models are currently the state-of-art for image generation, yet their inversion has been under-explored. We propose RF inversion using dynamic optimal control derived via a linear quadratic regulator. We prove that the resulting vector field is equivalent to a rectified stochastic differential equation. Additionally, we extend our framework to design a stochastic sampler for Flux. Our inversion method allows for state-of-the-art performance in zero-shot inversion and editing, outperforming prior works in stroke-to-image synthesis and semantic image editing, with large-scale human evaluations confirming user preference.

ABSTRACT. Data assimilation (DA) integrates observations with a dynamical model to estimate states of PDE-governed systems. Model-driven methods (e.g., Kalman, particle) presuppose full knowledge of the true dynamics, which is not always satisfied in practice, while purely data-driven solvers learn a deterministic mapping between observations and states and therefore miss the intrinsic stochasticity of real processes. Recently, score-based diffusion models learn a global diffusion prior and provide a good modeling of the stochastic dynamics, showing new potential for DA. However, their all-at-once generation rather than step-by-step transition limits their performance when dealing with highly complex stochastic processes and lacks physical interpretability. To tackle these drawbacks, we introduce FlowDAS, a generative DA framework that uses stochastic interpolants to directly learn state transition dynamics and achieve step-by-step transition to better model the real dynamics. We also improve the framework by combining the observation, better suiting the DA settings. Directly learning the underlying dynamics from collected data removes restrictive dynamical assumptions, and conditioning on observations at each interpolation step yields stable, measurement-consistent forecasts. Experiments on Lorenz-63, Navier-Stokes super-resolution/sparse-observation scenarios, and large-scale weather forecasting -- where dynamics are partly or wholly unknown -- show that FlowDAS surpasses model-driven methods, neural operators, and score-based baselines in accuracy and physical plausibility.

ABSTRACT. Score-based diffusion models have significantly advanced the generation of high-dimensional data across various domains by learning a denoising oracle (or score) from datasets. From a Bayesian perspective, these models offer a realistic approach to modeling data priors and facilitate solving inverse problems through posterior sampling. Despite the development of numerous heuristic methods for this purpose, most lack the quantitative guarantees required for scientific applications. This talk introduces a technique called tilted transport, based on the analysis of SDEs for data generation. We demonstrate that the denoising oracle enables an exact transformation of the original posterior sampling problem into a new `boosted' posterior that is provably easier to sample from. We quantify the conditions under which this boosted posterior is strongly log-concave, highlighting the dependencies on the condition number of the measurement matrix and the signal-to-noise ratio.

ABSTRACT. High-quality photography in extreme low-light conditions is challenging but impactful for digital cameras. With advanced computing hardware, traditional camera image signal processor (ISP) algorithms are gradually being replaced by efficient deep networks that enhance noisy raw images more intelligently. However, existing regression-based models often minimize pixel errors and result in oversmoothing of low-light photos or deep shadows. Recent work has attempted to address this limitation by training a diffusion model from scratch, yet those models still struggle to recover sharp image details and accurate colors. We introduce a novel framework to enhance low-light raw images by retasking pre-trained generative diffusion models with the camera ISP. Extensive experiments demonstrate that our method outperforms the state-of-the-art in perceptual quality across three challenging low-light raw image benchmarks.

ABSTRACT. Deep generative models have demonstrated remarkable success in high-dimensional, high-resolution natural image synthesis. Their capabilities show promise across a wide range of applications, particularly in inverse problems where reconstruction from partial or noisy measurements is crucial. However, their generation performance heavily relies on access to high-quality training data. This limits their application in scientific domains where uncorrupted, noise-free data is either costly or impossible to obtain. In this talk, we present the surprising finding that score distillation — a method primarily used to accelerate diffusion models without sacrificing generation quality — can serve as an effective approach for training high-quality generative models from noisy data. Across varying noise levels and datasets, we show how one can distill a degraded diffusion model to obtain a generative model with enhanced sample quality. This perspective reframes distillation as not only a tool for efficiency but also a mechanism for improving generative models, particularly in low-quality data settings.

ABSTRACT. This paper develops a game-theoretic model and an agent-based model to study group formation driven by resource pooling, spatial cohesion, and heterogeneity. We focus on cross-sector partnerships (CSPs) involving public, private, and nonprofit organizations, each contributing distinct resources. Group formation arises as agents strategically optimize their choices in response to others within a competitive setting. We prove the existence of stable group equilibria and simulate formation dynamics under varying spatial and resource conditions. Results show that limited individual resources lead to groups forming mainly among nearby actors, while abundant resources enable groups across larger distances. Increased resource heterogeneity and spatial proximity promote larger, more diverse groups. These findings reveal key trade-offs shaping group size and composition, guiding strategies for effective cross-sector collaborations and multi-agent systems.

ABSTRACT. This paper presents a framework for analyzing opinion dynamics when agents' opinions are shaped by multiple (social) networks but at different frequencies. Building on an existing baseline single-layer model, we model opinion updates as a coordination game on a multiplex network, where agents adjust their opinions by minimizing a local cost function aiming to maintain opinions close to their neighbors', with the neighbors selected for coordination periodically alternating across different networks. Crucially, we show that even when no individual network converges to a consensus opinion on its own, the combined multiplex structure can still enable global consensus, and also conversely, that networks supporting coordination in isolation may fail to do so when interconnected. We provide insights into when and why cross-network interactions generate emergent coordination or lead to instability. Specifically, using random-walk theory and spectral analysis, we derive sufficient conditions for consensus, characterize convergence rates, and assess stability under network perturbations. Our results shed light on how multilayer interactions shape opinion evolution, and offer insights about how the timing of interactions across multiple interconnected online and/or offline networks may impact consensus.

ABSTRACT. In many human–AI collaborative contexts, a decision maker must sequentially allocate limited attention to acquire information, culminating in a single decision at an exogenously determined time. The overall objective is to minimize a given function of the estimation error covariance at that final decision time. While the decision maker knows the current objective function, future objectives remain unspecified. Extending recent insights from economics on similar dynamic information acquisition problems, we use majorization theory to analyze conditions under which the optimal attention allocation exhibits monotonicity across time stages and remains time consistent. Specifically, we characterize the conditions on the objective and attention functions that guarantee that a strategy chosen without full knowledge of future objectives remains optimal. Our results highlight the robustness of such allocation policies, offering guidelines for human–AI collaborations where partial or evolving knowledge of performance measures often characterizes the decision-making environment.

ABSTRACT. A noncooperative solution for cooperative games is proposed. Recognizing the interdependence between partition of players to form coalitions and payoff negotiations within coalitions, we utilize both to explicitly describe the state of the system and determine their equilibrium values jointly. Being a dynamic game, the model naturally incorporates farsightedness of players. This solution can be readily applied to coalitional games with externalities since the model's state includes the whole partition and therefore has all relevant information.

ABSTRACT. The compression of high-dimensional data is a central problem in information theory, traditionally dominated by two paradigms: compression for reconstruction and compression for utility. This paper introduces and formalizes a third, largely unexplored paradigm: compression for competition. Unlike its predecessors, this approach aims not to preserve the intrinsic content of data but rather its relational integrity, ensuring that a desired ranking or preorder among data points is maintained after compression.

We investigate this concept within the context of mechanism design, where an evaluator incentivizes rational agents based on their performance features. Agents select effort profiles that map to high-dimensional feature vectors. The core challenge is to compress these features into a low-dimensional score without compromising the evaluator's ability to incentivize desired behaviors. We formally define this objective as preserving the set of incentivizable effort profiles. The primary goal of this work is to determine the optimal compression scheme—the scoring function with the lowest possible dimensionality—that satisfies this preservation-of-incentivizability criterion.

ABSTRACT. Safety is a foundational requirement in the deployment of autonomous systems. Control Barrier Functions (CBFs) have emerged as powerful tools for designing safety filters that minimally modify unsafe nominal controllers to enforce safety constraints. However, synthesizing CBFs using correct-by-construction methods remains computationally intractable in high dimensions. To address this, recent work has focused on learning CBFs in the form of neural networks from data. In this talk, I’ll discuss two approaches that integrate methods from the reinforcement learning literature to overcome major challenges facing this direction. First, we introduce a method for learning neural CBFs from safe expert demonstrations using inverse constraint learning (ICL). ICL uses such demonstrations and a simulator that generates unlabeled trajectories to train a classifier that defines a constraint that explains the deviation of the expert from otherwise optimal behavior. Equivalently, the classifier distinguishes states in and out of a safe controlled invariant set, ideally one that delineates the backward reachable set of an unknown failure set. This classifier is then used to label the states and controls of newly sampled trajectories as safe and unsafe, enabling the training of neural CBFs without requiring prior knowledge of the safe set. We show that our method outperforms existing baselines in diverse environments, achieving performance on par with models trained with ground-truth safety labels. Second, we propose a method for learning neural CBFs offline from a fixed dataset of safe and unsafe trajectories, inspired by Conservative Q-Learning from the offline reinforcement learning literature. Our method augments the loss function used in training with a term that penalizes over-estimation of the barrier values, i.e., the safety degree estimate, of the states not seen in the offline dataset. The aim is to obtain neural CBFs which not only prevent violations of safety constraints but prevents over-approximation the safety of out-of-distribution states where the learned filter may be unreliable. This conservative training improves robustness while preserving task performance. We demonstrate the effectiveness of our method across a range of simulated control tasks. Together, these approaches advance the data-driven synthesis of safety filters by addressing key challenges in labeling, generalization, and out-of-distribution robustness.

ABSTRACT. Verifying the behaviors of autonomous systems with learned perception components is a challenging problem due to the complexity of the perception and the uncertainty of operating environments. Probabilistic model checking is a powerful tool for providing guarantees on stochastic models of systems. However, constructing model-checkable models of black-box perception components for system-level mathematical guarantees has been an enduring challenge. In this paper, we propose a method for constructing provably conservative Interval Markov Decision Process (IMDP) models of closed-loop systems with perception components. We prove that our technique results in conservative abstractions with a user-specified probability. We evaluate our approach in an automatic braking case study using the object detector YOLO11 in the CARLA driving simulator.

ABSTRACT. Autonomous systems tackling complex tasks often rely on multiple neural networks that process the sensor data. These neural networks are called perception models. A typical perception model is trained to minimize the loss function, which could capture how well the perception models reconstructs the scene for one step. Given that autonomous systems behaviors are typically multistep, perception models that are optimal for one step are not necessary and sometimes not optimal for the performance of the system at whole. In this paper we propose a solution for model-selection problem --- namely to determine the appropriate perception model given the current state of the autonomous system. Here, the system performance can be considered as a weighted sum of perception costs (computational budget and delay associated with a perception model) and the control cost. We address this by formulating the problem as a multi-objective optimization and provide a provably optimal solution. Using a photo-realistic drone landing task in AirSim, our method reduced control cost by 38.04% and perception time by 79.1% compared to other approaches.

ABSTRACT. Prediction of failures in real-world autonomous systems either requires accurate model information or extensive testing. Partial knowledge of the system model makes simulation-based failure prediction unreliable. Moreover, obtaining such demonstrations is expensive, and could potentially be risky for the autonomous system to repeatedly fail during data collection. This work presents a novel three-step methodology for discovering failures that occur in the true system by using a combination of a limited number of demonstrations from the true system and the failure information processed through sampling-based testing of a model dynamical system. Given a limited budget of demonstrations from true system and a model dynamics (with potentially large modeling errors), the proposed methodology comprises of a) exhaustive simulations for discovering algorithmic failures using the model dynamics; b) design of initial demonstrations of the true system using Bayesian inference to learn a Gaussian process regression (GPR)-based failure predictor; and c) iterative demonstrations of the true system for updating the failure predictor. To illustrate the efficacy of the proposed methodology, we consider: a) the failure discovery for the task of pushing a T block to a fixed target region with UR3E collaborative robot arm using a diffusion policy; and b) the failure discovery for an F1-Tenth racing car tracking a given raceline under an LQR control policy.

ABSTRACT. AI-based components have become integral to Cyber-Physical Systems (CPS), enabling transformative functionalities across various domains. In safety-critical applications such as automotive and aerospace, machine learning components are now widely used for perception, control, and decision-making. This widespread adoption necessitates rigorous verification methods to ensure the safe deployment of these systems in real-world environments.

In this talk, we present a formal approach for verifying the safety of AI-enabled CPS. We focus on closed-loop systems that integrate a dynamical model of the physical system with neural network-based perception and control modules. We explore two verification scenarios: (1) where the controller is implemented as a neural network, and (2) where the perception pipeline includes a camera model coupled with a neural network. A key challenge in both settings lies in the scalability of verification algorithms, particularly due to the large size of neural networks and the complexity introduced by image-based perception.

To address these challenges, we propose abstraction techniques that simplify system representations and make verification tractable. Specifically, we introduce two novel data structures: Interval Neural Networks, which provide abstract representations of neural network behaviors, and Interval Images, which serve as abstract symbolic representations of reachable sets. Our experimental results demonstrate that these abstractions significantly improve the scalability and efficiency of verification, enabling the analysis of complex, large-scale AI-enabled CPS.

ABSTRACT. Providing safety guarantees for autonomous systems is difficult as these systems operate in complex environments that require the use of learning-enabled components, such as deep neural networks (DNNs) for visual perception. DNNs are hard to analyze due to their size (they can have thousands or millions of parameters), lack of formal specifications (DNNs are typically learnt from labeled data, in the absence of any formal requirements), and sensitivity to small changes in the environment. We present compositional techniques for the formal verification of safety properties of such autonomous systems. The main idea is to abstract the hard-to-analyze components of the autonomous system, such as DNN-based perception and environmental dynamics, with either probabilistic or worst-case abstractions. This makes the system amenable to formal analysis using off-the-shelf model checking tools, enabling the derivation of specifications for the behavior of the abstracted components such that system safety is guaranteed. We illustrate the idea in a case study from the autonomous airplane domain.