ABSTRACT. We investigate energy-efficient resource allocation for a RIS-assisted user-centric (UC) cell-free massive MIMO in downlink under spatially correlated Rayleigh fading, imperfect CSI, pilot reuse, and maximum ratio precoding at the APs. Using a closed form SINR bound that captures coherent and non-coherent interference, we formulate an energy efficiency (EE) maximization problem over AP-user association and downlink power allocation. To obtain a tractable solution, we first assign pilots through a scalable Primary-AP-based procedure and then develop an alternating optimization framework. The association stage is modeled as a finite local altruistic game and solved using a Dinkelbach best-response procedure for fixed power allocation, while the power allocation stage is solved using a Dinkelbach-based successive convex approximation method for fixed AP-user association. Simulation results show that the association game consistently improves EE under both orthogonal and reused pilot settings, and that the final association depends on the initial AP serving sets. The power allocation stage further improves EE mainly by reducing total power consumption while maintaining comparable or higher sum rate. The results also show that RIS-assisted gains depend on the pilot-reuse factor, since the RIS affects both desired and pilot-contaminated links. These findings highlight the importance of jointly considering pilot assignment, AP-user association, and power allocation in RIS-assisted UC cell-free networks.

ABSTRACT. State estimation in open client–server networks is challenging because the set of active observation sources changes over time, and active sources need not be valid sensors of the latent state. We study a client-server estimation problem in which a fixed but unknown state-consistent sensing class measures the latent state when active, while nuisance sources may arrive in the active set and generate observations from a different signal class. The server observes active source observations, but it does not know which agents observe valid state measurements. We propose a source-reliability-weighted observer. The state estimate is a standard fixed-prior weighted least-squares update, but the information assigned to each active observation is determined by a source-level reliability score learned from repeated innovation consistency. Numerical results show that the observer, when all-active sources are considered, has a finite bias, while the proposed observer initially learns source reliability and then tracks the desired latent state after a finite learning period.

ABSTRACT. We study the minimax estimation error for distributed covariance matrix estimation in the vertical-split (feature-split) setting, where two agents each observe different coordinates of m i.i.d.\ sub-Gaussian samples and communicate a limited number of bits to a central server. While Rahmani et al. (2025) established nearly tight bounds for dense (unstructured) cross-covariance matrices, we investigate whether imposing elementwise $s$-sparsity on the cross-covariance C_{21} can reduce the required communication and sample complexity. In contrast to the horizontal-split setting, where Braverman et al. (2016) showed that sparsity does not reduce communication cost for mean estimation, we prove that sparsity does help for cross-covariance estimation in the vertical split.

Specifically, we establish minimax lower bounds showing that the communication budget per agent scales as $B_k = \Omega(\sigma^4 d_k\, s' \log(d_1 d_2/s')/\varepsilon^2)$ and the sample complexity for cross-covariance estimation as $m = \Omega(\sigma^4\, s' \log(d_1 d_2/s')/\varepsilon^2)$, where $s' = s \wedge d_{\min}$. For the $1$-sparse case, this yields an exponential improvement from $d_1 d_2$ to $\log(d_1 d_2)$ compared to the dense rate. Our lower bounds are established via Fano's method with an explicit sparse packing using a Varshamov--Gilbert-type argument for signed partial permutation matrices combined with the Conditional Strong Data Processing Inequality of Rahmani et al. (2025). We show the bounds are tight with a matching achievable scheme, based on covering-net quantization and entry-wise hard thresholding, that attains the $s$-sparse lower bound up to polylogarithmic factors.

ABSTRACT. Remote source monitoring is a key use case for Internet of things (IoT) applications, calling on efficient communications protocols to ensure timely data delivery. In this paper we consider a practically inspired scenario in which an IoT device reports sensor readings to a gateway over a lossy channel, receiving feedback on the transmission outcome only after some delay. For this setting, we investigate practical, threshold-based reporting strategies for monitoring a Markov process over a correlated wireless channel. We evaluate two approaches: a reactive strategy where the node awaits feedback after an update, and a proactive strategy that pre-emptively transmits a second update. Leveraging renewal processes, we provide an exact performance analysis in terms of the mean squared error (MSE). Our study characterizes the fundamental trade-off between estimation error and communication rate, revealing that proactive transmissions significantly improve MSE even under strict IoT rate constraints.

ABSTRACT. Emerging physical AI systems require low-latency, task-oriented video communication over unreliable channels. We propose a semantic-aware multi-level neural video coding method for robust low-latency video transmission over unreliable channels that are abstracted as multi-level packet erasure channels. Built upon the real-time DCVC-RT neural video codec, the proposed framework introduces a semantic- and feature-aware coding strategy that partitions encoded representations into packets carrying different levels of semantic and latent-feature importance and assigns these packets to different streams, each associated with a priority level when transmitted over unreliable communication channels. We also developed an error-resilient entropy model that removes inter-packet dependencies, allowing each packet to be decoded independently under packet losses. The complete system is trained end-to-end over the abstracted multi-level packet erasure channels, enabling learning of channel-aware representations together with importance-aware packet assignment while facilitating the network for differentiated packet prioritization. Experiments show that the proposed framework significantly improves robustness over baseline DCVC-RT under packet erasures, achieving graceful degradation in less important regions while better preserving task-relevant visual content.

ABSTRACT. Classical multi-armed bandits typically aim to learn and repeatedly select the arm with the highest average reward. While this expectation-based view is powerful, it overlooks other important features of the reward distribution, such as variability, tail risk, and robustness. This work takes a broader view by replacing average reward with a general preference metric that can reflect different attitudes toward uncertainty, including risk sensitivity or aversion to rare but severe outcomes. Under this perspective, the optimal strategy may no longer be to select a single best arm. Instead, it may require choosing a carefully designed mixture of arms. This leads to a different algorithmic challenge: learning not only which arms are valuable, but also how often each should be selected. This paper develops a framework and algorithms for learning and tracking such mixtures, analyzes their regret guarantees, and establishes lower bounds that clarify the limits of preference-based bandit learning.

ABSTRACT. Sequential change detection is a fundamental problem in statistics and signal processing, with the CUSUM procedure widely used to achieve minimax detection delay under a prescribed false-alarm rate when pre- and post-change distributions are fully known. However, releasing CUSUM statistics and the corresponding stopping time directly can compromise individual data privacy. We therefore introduce a differentially private (DP) variant that injects calibrated Laplace noise into both the vanilla CUSUM statistics and the detection threshold, preserving the recursive simplicity of the classical CUSUM statistics while ensuring per-sample differential privacy. We derive closed-form bounds on the average run length to false alarm and on the worst-case average detection delay, explicitly characterizing the trade-off among privacy level, false alarm rate, and detection efficiency. We also extend the idea to the local differential privacy notions and to multi-stream detection. Numerical simulations are conducted to demonstrate the detection efficiency of our private CUSUM algorithms.

ABSTRACT. Sequential change-point detection aims to identify distributional changes in streaming data while controlling false alarms and detection delay. In modern settings, this problem is often complicated by high dimensionality, small effective sample sizes, heavy tails, contamination, and possible adversarial structure in the change itself. In this talk, I will discuss recent work on robust high-dimensional change-point detection based on angular kernel statistics. The method aggregates bounded one-dimensional angular discrepancies across coordinates, leading to a nonparametric and moment-agnostic scan statistic that remains stable in high-dimensional low-sample-size regimes. I will describe its population structure, null calibration, and a fixed-window sequential monitoring version with average run length calibration and delay guarantees.

I will then discuss a related question: when is a change statistically detectable before it causes too much cumulative damage? This perspective leads to adversarial formulations of sequential change detection, where the post-change signal may vary over time and the onset time is unknown. I will highlight examples showing that large cumulative damage need not imply early detectability, since the information available to the detector may accumulate at a different rate. This suggests a useful distinction between damage accumulation and information accumulation, and points to new lower bounds and stopping-rule designs for adversarial and time-varying changes.

ABSTRACT. We consider fictitious play dynamics in product Markov games, where each player has a local state that only it can directly control. We show that product Markov games are Markov potential games when their instantaneous costs decompose into a global state-dependent cost and a control cost, providing sufficient conditions for a Markov potential structure. We study fictitious play in this setting, where agents compute best responses to other players’ empirical policies using estimated value functions. Empirical policies are updated from realized actions, while value functions are updated using realized costs under best-response actions. We show that empirical frequencies converge to a stationary Nash equilibrium of a product Markov game, provided that value function updates decay faster than empirical policy updates. Our results extend convergence guarantees for fictitious play to product Markov games. Numerical experiments demonstrate convergence of fictitious play with perturbed best responses on a shortest path game with collision avoidance.

ABSTRACT. We study the following repeated non-atomic routing game. In every round, nature chooses a state in an i.i.d. manner according to a publicly known distribution, which influences link latency functions. The system planner makes private route recommendations to the agents according to a signaling strategy. Prior work has provided sufficient condition on private pricing to ensure convergence to a desired Bayes correlated equilibrium. However, a matching necessary condition is missing and extensions to public pricing in general are missing. In this work, we address this gap by casting the steering problem as that of controllability.

ABSTRACT. We study dynamic games where players are uncertain about each other's control policies or goals and consequently seek to be strategically robust. We focus on two fundamental settings: closed-loop information structures under linear dynamics and quadratic control costs and open-loop information structures with linear dynamics, convex cost functions, and convex constraints. We show that these games can be rewritten as simple transformations of dynamic games in which each player chooses a controller in a fictitious game, facing an adversary who is penalized for deviating from the other players' policies. This formulation naturally induces a novel notion of dynamic equilibrium, which we term a strategically robust dynamic equilibrium. In the closed-loop case, we establish the existence and uniqueness of such equilibria, showing that the equilibrium policies are Markovian, linear, and can be efficiently computed via coupled backward Riccati equations. Furthermore we show how strategically robust equilibria can be seen as a natural interpolation between closed-loop feedback Nash equilibria and H-infinity control. In the open-loop case, we establish the existence of such equilibria and provide a rigorous analysis of the games' monotonicity. Through numerical simulations, including a network game and a capacity accumulation game, we illustrate the benefits of strategic robustness for designing resilient decentralized control schemes. Our experiments also expose a ``free-lunch'' phenomenon: achieving robustness does not inherently degrade nominal performance, and can paradoxically yield improvements in individual utilities and overall social welfare.

ABSTRACT. Game-theoretic models have been used to predict the behavior of interacting agents and inform decision-making in multi-agent control systems. Applications ranging from autonomous vehicles to energy networks rely on equilibrium predictions to anticipate the actions of others and synthesize control policies. However, these predictions depend on assumptions about agents’ objectives and incentives, which are often uncertain or imperfectly known in practice. This talk examines the robustness of game-theoretic predictions under objective misspecification. We first introduce the game-to-real gap, a framework for quantifying the discrepancy between predicted and realized performance when agents reason using heterogeneous game models. We show that even small modeling errors can lead to large performance losses and identify structural properties that govern this sensitivity. We then consider dynamic settings in which agents employ model predictive game controllers. When agents possess different conjectures of one another’s objectives, prediction misalignments propagate through the closed-loop system. We present recent results characterizing the sensitivity of equilibrium predictions to objective perturbations and provide sufficient conditions guaranteeing stability despite heterogeneous game models. These results provide new insight into when game-theoretic models can be trusted as predictive tools for multi-agent control and how their limitations can be systematically analyzed.

ABSTRACT. A “Tragedy of the Commons" refers to scenarios in which individuals acting according to their own self-interest leads to over-consumption and consequently the collapse of a shared common resource. They arise in numerous consequential real-world problems (ranging from climate change, traffic congestion, and epidemics) that pit selfish individual desires against collective benefits. A long-standing challenge is to understand the factors that enable cooperative behaviors to emerge, and ultimately for tragedies to be averted. Two primary approaches involve 1) devising incentive policies that discourage consumption behavior and 2) understanding how individuals learn and make decisions, warranting the use of game-theoretic tools. In this talk, I will discuss recent results and opportunities for which evolutionary game-theoretic models can be extended, focusing on the the impact of alternate and heterogeneous agent learning behaviors that go beyond the well-studied replicator equation. In particular, we study agents endowed with varying levels of rationality and find that, counterintuitively, agents with high rationality cannot coordinate on collective benefits. We discuss these results in the context of a class of evolutionary game models known as “feedback-evolving games”, which has emerged as an effective framework to address these challenges.

ABSTRACT. Recent advances in generative AI have raised important questions regarding both the efficiency of post-training algorithms for large language models and the theoretical foundations of diffusion-based generative models. In this talk, I will present two recent lines of work addressing these challenges.

In the first part, I will discuss the efficiency of Group Relative Policy Optimization (GRPO), a reinforcement learning algorithm that has played an important role in the post-training of modern reasoning language models. I will present recent theoretical insights into the sample efficiency and optimization behavior of GRPO, highlighting the role of normalization and relative advantage estimation in improving learning performance.

In the second part, I will focus on the generalization behavior of diffusion models. While existing theory suggests that sampling with the empirical score function should lead to exact memorization of the training data, practical diffusion models are capable of generating diverse and novel samples. I will present a theoretical framework that explains this apparent discrepancy. In particular, I will show that the empirical score function can be expressed as a softmax-weighted combination of Gaussian component scores and that, in the low-noise regime, the corresponding weights become highly concentrated, causing the sampling dynamics to be dominated by individual training examples. I will then explain how neural network training implicitly smooths the score function, mitigating this memorization effect and enabling sampling trajectories to follow local data geometry instead of isolated training points. Building on this understanding, I will discuss explicit score-smoothing techniques, including Noise Unconditioning and Temperature Smoothing, which further enhance generalization while maintaining generation quality.

Together, these works illustrate how optimization theory can help explain and improve the performance of modern generative AI systems, spanning both reinforcement learning for large language models and diffusion-based generative modeling.

ABSTRACT. Cooperative multi-agent reinforcement learning (MARL) involves complex agent interactions and requires effective exploration strategies. A prominent class of MARL algorithms, decentralized softmax policy gradient (DecSPG), addresses this through energy-based policy updates. In practice, however, such energy-based policies are intractable to maintain and are commonly projected onto the Gaussian policy class. In this work, we show that the limited expressiveness of Gaussian policies severely hinders exploration in DecSPG, and this limitation worsens as the number of agents grows. To address this issue, we propose decentralized diffusion policy learning (DDPL), which parameterizes each agent's policy with a denoising diffusion probabilistic model, an expressive generative model that captures multi-modal action distributions for enhanced exploration. DDPL enables efficient online training of diffusion policies via importance sampling score matching (ISSM), a novel training method with theoretical guarantee. We evaluate DDPL on representative continuous-action MARL benchmarks, including multi-agent particle environment, multi-agent MuJoCo, IsaacLab, and JAX-reimplemented StarCraft multi-agent challenge, and observe consistently improved performance.

ABSTRACT. Off-dynamics offline reinforcement learning seeks to learn a target-domain policy from a large source dataset and a limited target dataset under mismatched transition dynamics. Existing approaches such as reward augmentation and data filtering are constrained to the source dataset and cannot synthesize new target behavior to improve coverage beyond the collected source trajectories. While recent model-based methods attempt to address this by learning target-aware dynamics, the generated experience is constructed only at the transition level, which leads to accumulated errors over long horizons. These limitations necessitate a shift toward trajectory-level generation for off-dynamics offline RL. We propose CEDGE, a Cross-domain Energy-guided Diffusion GEneration framework. CEDGE trains a trajectory diffusion model on source-domain trajectories and adapts the generated samples to the target domain through energy guidance. This guidance is derived by minimizing the distribution mismatch between the source and desired target-domain trajectories and is decomposed into return, domain, and behavior energy components. The resulting energy-guided trajectories are useful both for direct planning and as synthetic data for policy learning. Since target adaptation is achieved via energy guidance rather than retraining the diffusion model, CEDGE can be efficiently adapted to new target dynamics compared to previous methods. Experiments on the ODRL benchmark demonstrate that trajectory-level energy-guided generation improves diffusion planning under dynamics shifts and produces synthetic data that improves downstream target policy learning.

ABSTRACT. We study the problem of posterior sampling in the context of score based generative models in a setting where we have a trained score network for a prior p(x), a measurement model p(y|x), and are tasked with sampling from the posterior p(x|y). Prior work has shown this to be intractable in KL (in the worst case) under well-accepted computational hardness assumptions. Despite this, popular algorithms for tasks such as image super-resolution, stylization, and reconstruction enjoy empirical success. Rather than establishing distributional assumptions or restricted settings under which exact posterior sampling is tractable, we view this as a more general "tilting" problem of biasing a distribution towards a measurement. Under minimal assumptions, we show that one can tractably sample from a distribution that is simultaneously close to the posterior of a noised prior in KL divergence and the true posterior in Fisher divergence. Intuitively, this combination ensures that the resulting sample is consistent with both the measurement and the prior. To the best of our knowledge these are the first formal results for (approximate) posterior sampling in polynomial time.

ABSTRACT. We propose a fast, optimization-free method for learning the transition operators of high-dimensional Markov processes. The central idea is to perform a Galerkin projection of the transition operator to a suitable set of low-order bases that capture the correlations between the dimensions. Such a discretized operator can be obtained from moments corresponding to our choice of basis without curse of dimensionality. Furthermore, by exploiting its low-rank structure and the spatial decay of correlations, we can obtain a compressed representation with computational complexity of order O(dN), where d is the dimensionality and N is the sample size. We further theoretically analyze the approximation error of the proposed compressed representation. We numerically demonstrate that the learned operator allows efficient prediction of future events and solving high-dimensional boundary value problems. This gives rise to a simple linear algebraic method for high-dimensional rare-events simulations.

ABSTRACT. While continuous diffusion models have achieved remarkable success, discrete diffusion offers a unified framework for jointly modeling text and images. Beyond unification, discrete diffusion provides faster inference, finer control, and principled training-free guidance, making it well-suited for posterior sampling. Existing approaches to posterior sampling using discrete diffusion face severe challenges: derivative-free guidance yields sparse signals, continuous relaxations limit applicability, and split Gibbs samplers suffer from the curse of dimensionality. To overcome these limitations, we introduce Anchored Posterior Sampling (APS), built on two key innovations: quantized expectation for gradient-like guidance in discrete embedding space, and anchored remasking for adaptive decoding. APS achieves state-of-the-art performance among discrete diffusion samplers on both linear and nonlinear inverse problems across the standard image benchmarks. We demonstrate the generality of APS through training-free stylization and text-guided editing. We further apply APS to a large-scale diffusion language model, showing consistent improvement in question answering.

To be presented at ICML 2026.

ABSTRACT. While reproducing kernel Hilbert space (RKHS) methods traditionally rely on global kernel regressors, regularity of most kernels suggests an alternative: a smoothness-based approach that exploits local approximations. We show that these perspectives are deeply connected through the spectral properties of isotropic kernels.

In particular, we characterize the Fourier spectra of the Matérn, square-exponential, rational-quadratic, γ-exponential, piecewise-polynomial, and Dirichlet kernels, and show that the decay rate determines asymptotic regret from both viewpoints. For global algorithms, spectral decay yields upper bounds on the maximum information gain, governing worst-case regret, while for local methods, the same decay rates establish Hölder space embeddings and Besov space norm-equivalences, enabling local continuity analysis. These connections show that kernel-based and locally adaptive algorithms can be analyzed within a unified framework. This allows us to derive explicit regret bounds for each kernel family, obtaining novel results in several cases and providing improved analysis for others. Furthermore, we analyze LP-GP-UCB, an algorithm that combines both local and global approaches, augmenting global Gaussian process surrogates with local polynomial estimators. While the hybrid approach does not uniformly dominate specialized methods, it achieves order-optimality across multiple kernel families.

ABSTRACT. Understanding the theoretical limits of learning mechanisms and determining their fundamental capabilities remains a key challenge in machine learning. This paper presents optimal performance bounds for linear models by exploiting the combinatorial geometry of datasets. For a given dataset consisting of points in a $d$-dimensional Euclidean space, our approach uses local computations on small subsets of points---each comprising $(d+2)$ points---to predict the global performance of classifiers. We derive optimal training error bounds for linear classifiers by analyzing linear separability within these local subsets. For Support Vector Machines (SVMs), we establish margin bounds that align with their performance on similarly sized subsets. Theoretical analysis and empirical evaluation demonstrate that these bounds can be efficiently computed with a limited sampling of local subsets of data, enabling practical application of the method. By uncovering the geometric structure of the underlying data, this research provides insights into the predictive capabilities of machine learning models.

ABSTRACT. We consider the problem of constructing a $K$-class classifier from the conjunction of $O(\log(K))$ binary classifiers -- this is a natural paradigm to construct a sophisticated classifier in a distributed manner with each agent performing a relatively straightforward task. For a stylized model where classes are i.i.d. Gaussian points in $\R^d$ and the binary classifiers are hyperplanes we derive sharp performance bounds in a variety of settings.

ABSTRACT. Deep neural networks have demonstrated remarkable success in a gamut of applications. In practice however, they are susceptible to perturbed input samples, including adversarial manipulations or noisy sensing mechanisms. Adversarial training enhances model resilience by judiciously perturbing the input data. While effective for numerous cases, they fall short of dealing with unseen norms or sophisticated adaptive attacks. Broader challenges remain, including the computational burden of input manipulation and the need for full model retraining. To alleviate these burdens, this paper incorporates a fundamentally different approach. We adopt error correcting coding (ECC) to represent and decode the output labels, thereby enhancing generalization and robustness. Each class label is encoded using a prudent Bose–Chaudhuri–Hocquenghem (BCH) binary codeword, and prediction is performed for each bit independently, followed by a decoding process in the code space based on Hamming distance or probability scores. We exploit well-established ECC codes to simplify the encoding procedure while enabling reliable correction of up to a prescribed number of errors. Our approach is computationally efficient, requires minimal architectural modifications to state-of-the-art models, and complements adversarial training. Experiment results corroborate the effectiveness of the proposed framework on several benchmark datasets under various adversarial attacks.

ABSTRACT. Cross‐validation (CV) is the de facto standard for estimating a model’s generalization performance, but in smaller datasets it exhibits an underappreciated quirk: across folds, training and test errors are strongly negatively correlated, while training and holdout errors show a moderate anti-correlation and test versus holdout errors are essentially uncorrelated. Herein, we document these phenomena empirically on both real and synthetic datasets under AdaBoost and introduce a simple generative model that explains them. By viewing each CV split as hypergeometric sampling from a finite population and incorporating an overfitting parameter $\delta$ that shifts expected errors on train, test, and holdout sets, we derive closed‐form expressions for the covariances among observed error rates. Our analysis shows that sampling‐induced anti-correlation dominates in small datasets, while overfitting contributes an additional negative term, thus accounting for the observed error dynamics. We discuss the limitations of our approach and suggest directions for more refined models and extensions to regression settings.

ABSTRACT. Information lattice learning (ILL) learns interpretable rules of a signal by alternately projecting the signal onto a partition lattice that encodes a hierarchy of abstractions and lifting selected rules back to the signal domain. When the signal is a probability mass function, we show the probabilistic rules learned by ILL admit a natural probabilistic graphical model (PGM) interpretation and develop this interpretation in detail. A partition in ILL induces a deterministic quotient variable, and a rule is the marginal law of that quotient variable. A rule set is therefore a collection of marginal constraints over interpretable abstractions. General lifting is the feasible family of all joint distributions satisfying those constraints, while special lifting chooses a maximum-ignorance reconstruction, implemented in ILL by an L2 uniformity principle closely related to maximum entropy. Under a Shannon-entropy lifting, the same constraints yield a log-linear factor graph whose factors are indexed by learned abstractions. The information lattice itself, however, is not a Bayesian network: its edges encode refinement and coarsening of abstractions, not conditional dependence. Thus ILL is best viewed as structure learning for interpretable constraint-based factor graphs over quotient variables. This view clarifies how ILL relates to graphical models and maximum entropy models, while suggesting new directions for inference, identifiability, and hybrid symbolic-probabilistic learning.

ABSTRACT. Synthetic data augmentation is widely used to mitigate class imbalance, yet empirical findings on its benefits are mixed and its theoretical effects on score-based classification remain poorly understood. This paper develops a framework for characterizing when synthetic minority augmentation can improve threshold-integrated and threshold-optimized metrics, including AUROC, AUPRC, best-threshold balanced accuracy, and best-threshold \(\F_1\) score. We separate the effect of augmentation into two components: a change in effective class weighting and a discrepancy between the synthetic and true minority distributions. Under well-specified score models, the raw estimator already targets the likelihood-ratio ordering, which is population-optimal for the metrics considered. Consequently, augmentation cannot provide a fundamental population-level improvement beyond possible finite-sample variance reduction, and may introduce additional bias through synthetic distributional error. We further establish minimax lower bounds showing that the raw estimator already achieves the optimal metric-regret rate in the well-specified regime. Under misspecification, however, augmentation can play a qualitatively different role: by changing the effective class balance, it can alter the restricted-class projection and correct ranking errors induced by the raw imbalanced objective. We provide explicit improvement bounds quantifying the roles of approximation error, finite-sample estimation error, and synthetic distributional error. Simulation studies corroborate the theory, demonstrating limited gains under well specification and nontrivial but nonmonotone improvements under misspecification.

ABSTRACT. We study how regularization shapes equilibrium behavior in large population games, where many agents repeatedly revise their strategies based on observed payoffs, and examine how the resulting dynamics can be influenced through incentive design.

We analyze a learning rule in which agents balance maximizing their payoff against staying close to a reference behavior — a form of regularized best response known as KLD-RL dynamics. A key insight is that, in the high-noise limit, the equilibrium of the population is uniquely determined by the reference behavior. This means a designer can steer the population toward a desired equilibrium, by choosing the reference behavior appropriately.

We propose and analyze a simple adaptive mechanism in which the reference behavior is periodically updated to reflect the current state of the population. We show that under this scheme, the population reliably converges to a Nash equilibrium, and characterize how the approximation error depends on population size and the strength of regularization. The results hold even when agents face delays in observing payoffs — a realistic constraint in large-scale systems.

ABSTRACT. Coordinating decisions over networks is a fundamental primitive in socio-technical systems. While traditional logit dynamics in such systems assumes homogeneous agents characterized by a common rationality parameter, the vast majority of systems comprised of humans as well as machines (robots, large language models, IoT devices, or combinations thereof) are not homogeneous and respond to utilities according to different rationalities. Such settings are generally not covered by the existing literature, primarily due to the absence of a Gibbs-like stationary distribution in closed form. In this paper we propose a correction term for the heterogeneous logit learning dynamics, where an updating agent corrects the traditional learning dynamics by adding a term that accounts for the discrepancies with its neighbors. This new learning dynamics induces a Gibbs-like stationary distribution based on a weighted potential function for the network coordination game. We further show how to leverage this property to design a network that maximizes the probability of coordinated states as a function of the rationality of the agents in the system.

ABSTRACT. Large populations of learning agents arise in transportation, resource allocation, networked systems, and artificial intelligence. Population games provide a useful framework for studying how these agents revise their strategies in response to changing payoffs.

This talk reviews counterclockwise dissipativity as a system theoretic tool for proving convergence in such populations. Most learning rules move the population toward strategies with higher payoffs. When this behavior is combined with a counterclockwise payoff mechanism, the population can be shown to approach the Nash equilibrium set.

The main focus is Lyapunov stability. Existing counterclockwise results establish convergence without directly constructing a Lyapunov function. I will explain how suitable storage functions can be used to build one. This approach clarifies why Lyapunov analysis is possible and provides stronger guarantees for stability, robustness, and equilibrium selection.

The discussion will also show how these ideas can support incentive design. A coordinator may shape payoffs to stabilize a desired equilibrium while preserving useful features of the original system and avoiding unnecessarily large interventions.

ABSTRACT. We study decentralized equilibrium selection in stochastic games under severe information and communication constraints. In such settings, convergence to equilibrium alone is insufficient, as stochastic games typically admit many equilibria with markedly different welfare properties. We address decentralized optimal equilibrium selection, where agents coordinate on equilibria that optimize a designer-specified social welfare objective while allowing heterogeneous tolerance to deviations from strict best responses. Agents observe only the global state trajectory and their realized rewards, and exchange a single randomized bit of feedback per agent per round. This semantic content/discontent signaling mechanism implicitly aligns decentralized learning dynamics with the global welfare objective. We develop explore-and-commit and online variants applicable to general stochastic games, accommodating heterogeneous model-based or model-free methods for solving the induced Markov decision processes, and establish explicit finite-time regret guarantees, showing logarithmic expected regret under mild conditions.

ABSTRACT. We study the long-term behavior of fictitious play dynamics in repeated extensive-form games of imperfect information. Under this framework, each player maintains the belief that moves at all other information sets are chosen independently according to fixed randomized strategies. Accordingly, players select moves at their own information sets to maximize their expected payoff, assuming that play elsewhere tracks the empirical frequencies of past choices. We extend the well-known Monderer–Shapley result, the convergence of empirical frequencies to the set of Nash equilibria, to a class of extensive-form games with identical interests. We then strengthen this result by incorporating inertia and fading memory, proving that the realized play paths ultimately settle on a final path of moves that are optimal at each information set across all such games.

ABSTRACT. In this talk, we discuss the problem of transmitting an analog source over an additive white Gaussian noise (AWGN) channel using only a few channel uses. This few-shot communication setting introduces a natural challenge: the transmitter may not have accurate knowledge of the channel quality, or equivalently, the signal-to-noise ratio (SNR). The main question is whether one can design a communication scheme that performs close to optimally with very few channel uses, uniformly over all SNRs.

To address this question, we develop an infinite constellation for representing the analog source, based on a novel progressive expansion technique. The construction protects the most significant components of the source representation from the effect of noise on less significant components. As a result, the proposed scheme achieves a near-optimal SNR-distortion tradeoff universally across all SNR regimes.

ABSTRACT. We study the fundamental limits of covert communication over state-dependent Gaussian channels in the presence of a concurrent legitimate link. We consider a scenario where the legitimate receiver serves as a warden, tasked with detecting the presence of a covert signal while simultaneously decoding its primary message from the legitimate transmitter. Our study centers on the impact of asymmetric non-causal channel state knowledge at the legitimate and covert transmitters. We assume neither the legitimate not the covert receiver have channel state knowledge apart from its statistics. We show that despite the legitimate transmitter having a noisier state observation, the covert transmitter cannot escape the traditional square root operational regime (i.e. asymptotically zero covert rate) when the legitimate link operates at its capacity. We also show that the covert transmitter possessing knowledge of a component of the channel state that remains unknown to the legitimate transmitter, called "split state" setting, is a sufficient condition for achieving positive covert communication rate. For the split state scenario, we provide achievable covert rates under the assumption that the legitimate transmitter uses a variation of Costas’s dirty paper coding.

ABSTRACT. We consider a wireless communications system where a transmitter with a single antenna communicates with multiple receivers by multiplexing data for all the receivers into the same symbol(s). In such systems, each receiver can infer data intended for other receivers by simply observing its received symbol, resulting in compromised confidentiality. We consider the addition of amplify-and-forward relays into such a network, where we assume that the power amplifiers at the relays are non-linear. The resulting system has a neural-network-like structure where the power-amplifier non-linearities act like activation functions in neural networks, enabling the entire network to perform non-linear computation. By applying deep-learning techniques with appropriate loss functions, we demonstrate that physical-layer confidentiality can be increased in such networks by reducing the mutual information between the signal at each receiver and the data intended for other receivers. In addition, we show that such a reduction in data leakage to unintended receivers is not possible to achieve with non-linear relays alone, without a significant reduction in data communication rates. This work thus illustrates how amplifier non-linearity can be exploited in wireless relay networks to enhance confidentiality in new ways.

ABSTRACT. The problem of finding the optimal compression rate for a given random variable has been traditionally studied under two main constraints: distortion and perception. The distortion constraint enforces the fidelity of our reconstruction with respect to the observed realization of the random variable, while the perception constraint ensures that the reconstruction is close to a sample from the distribution of our interested random variable. In this work, we explore the possibility of reconstruction, such that the reconstructed sample is still within a desired fidelity level with our original realization of the random variable, but at the same time, it resembles a sample from a different \emph{target} distribution. We term this criteria as the \emph{deception} constraint and find the fundamental tradeoffs of rate-distortion and deception.

ABSTRACT. Deployment optimization of base stations (BSs) is critical for improving cellular network performance metrics such as coverage and capacity, directly impacting user experience, scalability, and infrastructure cost-effectiveness. Traditional approaches that optimize precise BS locations often provide limited insight into network evolution, while stochastic geometry offers a more interpretable density-based framework but rarely incorporates real-world user location data. We propose a data-driven stochastic geometry-based approach that models BS deployment as an inhomogeneous Poisson point process whose intensity function is optimized for a target network performance metric. The resulting infinite-dimensional problem is discretized over the deployment area and solved empirically using sampled user locations. We characterize the excess error induced by these approximations and introduce an efficient stochastic mirror ascent algorithm for the resulting optimization problem. Unlike traditional methods, the proposed approach yields an intensity function that reveals optimal BS density across regions, providing actionable insights adaptable to real user patterns, practical constraints, multi-tier networks, and incremental deployment scenarios.

ABSTRACT. Engineered systems naturally experience nonlinear disturbances that have the potential to disrupt desired behavior. For example, a fault in a power system may lead to blackout conditions. Whether the system recovers from a particular finite-time disturbance to a desired operating point depends on system parameter values. Partition the system parameters into controllable parameters, such as setpoints and controller settings, and uncontrollable parameters, such as background load and its dynamics. The latter are typically uncertain and time-varying, so to quantify proximity to vulnerability we define the safety margin to be the smallest change in uncontrollable parameter values such that the system will no longer be able to recover from the given disturbance. Numerical algorithms are introduced to compute safety margins by exploiting the large sensitivity of the system trajectory near the region of attraction boundary to small perturbations. These methods are then adapted to develop algorithms for varying controllable parameter values so as to increase the safety margin, and thereby reduce vulnerability. Unlike most methods for reducing vulnerability of parameterized nonlinear systems, such as those involving robust region of attraction estimation, these algorithms are computationally efficient for high dimensional state and parameter spaces, compute safety margins non-conservatively, and are not limited to specialized settings such as polynomial or rational systems. Local convergence guarantees for the methods are provided for a large class of nonlinear systems. The algorithms are applied for vulnerability assessment and preventive action on a modified IEEE 39-bus benchmark power system.

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.

Burer (2009) showed that any mixed-integer quadratic program (like unit commitment) 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.

In recent work, we used the CPP reformulation and its copositive dual to design pricing mechanisms for unit commitment. We refer to this as copositive duality pricing (CDP). In this paper, we examine the relationship between CDP and convex hull pricing (CHP), which is regarded as the gold standard for pricing unit commitment. We show that several variations of CHP are all special cases of CDP. This leads to novel economic interpretations and semidefinite approximations of CHP.

ABSTRACT. This paper presents a global optimization routine for solving the combined AC Optimal Power Flow (AC-OPF) and Security Constrained Unit Commitment (SCUC) problems. The proposed methods are wrapped into a GPU-accelerated numerical solver and exploit iteratively tightened convex relaxations, via sequential moment lifting, in conjunction with new, “low-rank” (i.e., highly scalable) Semidefinite Programming (SDP) methods. The framework targets hard operational constraints (e.g., nonlinear AC physics) and massive operational search spaces (e.g., line switching and binary generator commitment), enabling highly efficient, secure, and reliable power grid operations and energy market clearing.

ABSTRACT. Expediting AC contingency analysis is important for the secure operation and reliable planning of electric power systems. Machine learning (ML) models trained to predict AC power-flow (AC-PF) solutions across diverse loading conditions and outage scenarios offer a promising means of reducing the associated computational burden. However, training a separate ML model for each contingency can require substantial offline data generation and training effort. To address this challenge, this paper proposes a fixed-point framework that incorporates a single ML model trained exclusively on the base-case topology to predict post-contingency AC-PF solutions. The proposed framework is compatible with any base-case ML predictor. Under an approximate model, the convergence analysis yields two key findings. First, the base-case ML model must be trained on a slightly enlarged set of AC-PF specifications to ensure the iterative scheme operates properly. Second, except for a small set of near-critical lines characterized by near-unity self-power transfer distribution factors, the proposed method is guaranteed to converge within a few iterations. Numerical results on benchmark power systems corroborate the analysis and demonstrate the method's self-mapping and contraction properties.

ABSTRACT. This paper studies graph matching under the correlated Erdos–Renyi (ER) graph pair model. This model first samples an ER base graph, whose edges are then independently subsampled twice with probability s to produce two correlated ER graphs. We propose a graph matching algorithm that has almost quadratic time complexity and achieves almost exact recovery with high probability (under certain assumptions on s and lambda (the average degree)). The proposed algorithm is based on local tree correlation tests. It uses a rank-based algorithm to match the vertex pairs instead of threshold-based rules in the literature. This avoids the need of computing an explicit threshold, which is computationally difficult to obtain. To prove the almost exact recovery result, we establish a new analysis of tree correlation tests in the diverging-degree regime, where both the mean degree and the tree depth grow with n, the number of nodes in the ER graphs. Based on this new result, we establish the existence of a threshold for a threshold-based graph matching algorithm via local tree correlation tests. Finally, we couple the performance of the rank-based algorithm with the threshold-based algorithm to show almost exact recovery.

ABSTRACT. We consider the problem of load balancing in a system with one dispatcher and $N$ parallel servers. The dispatcher must select one server to dispatch new jobs at every time-step and each server buffers incoming jobs in a queue. However, the dispatcher does not know the servers' backlogs and must make dispatching decisions based on previous observations. The dispatcher's objective is to dispatch jobs to the shortest queue. This problem can be formulated as a restless multi-arm bandit (RMAB) problem where each arm's state is its corresponding belief vector. Our goal is to verify Whittle indexability for this problem and derive a low complexity Whittle index policy. Previous Whittle indexability results cannot be directly applied due to the multi-dimensional nature of the belief vector. To overcome this issue, we define the RMAB state as the tuple of the most recent backlog observation and the time since this observation. We consider two model variations, a standard finite queue model and a blocking queue model. We show that the single-arm decoupled problems of both these models have threshold optimal solutions under some assumptions. For the standard finite queue model, we prove indexability and derive the Whittle index policy in closed form. For the blocking queue model, we derive a sufficient condition for indexability under threshold optimality and use it to show indexability for some special cases.

ABSTRACT. Rank statistics are exactly calibrated under exchangeability, but this calibration can fail for data observed along a dependent trajectory. We study temporal ranks for stationary Markov observations Y_t = f(X_t), where the current value is ranked against a finite window of its past. Although stationarity preserves the marginal law of Y_t, Markov dependence breaks exchangeability, so the temporal rank need not follow the uniform rank law. We quantify this effect by bounding the Kolmogorov distance between the temporal-rank distribution and the discrete uniform distribution. The analysis relates the rank statistic to an empirical distribution function evaluated at the dependent endpoint Y_t, yielding finite-sample bounds under beta-mixing assumptions. These bounds show how rank miscalibration depends on window length, blocking scale, and mixing rate. We also study thinned temporal ranks, proving analogous bounds in which the dependence term is reduced by the thinning lag. As a consequence, we obtain false-alarm guarantees for rank-based online detectors under Markovian in-control dynamics. Numerical illustrations with stationary Gaussian autoregressive chains show that strong dependence can visibly distort temporal ranks, while longer windows and lag-spaced comparisons improve calibration.

ABSTRACT. In sparse signal recovery, uncertainty in the sensing matrix can significantly affect the estimator, even when the measurement noise is small. An approach to alleviate this issue is robust regression, which minimizes the worst-case residual over bounded perturbations of the data matrix. In this work, we use the Convex Gaussian Min–max Theorem (CGMT) to study an operator-norm robust LASSO for sparse linear regression with adversarial uncertainty in the measurement operator. The analysis yields a precise characterization of the asymptotic error of such robust estimators. Furthermore, the CGMT stationarity equations reveal a finite-dimensional fixed point for the robust es- timator. While standard first-order methods can solve the robust objective, this fixed point naturally yields a nonseparable AMP- style algorithm for computing the robust estimator. Numerical experiments demonstrate that our scalar prediction captures the error trend under isotropic attacks, and that the derived iteration matches the optimal objective values of standard solvers like FISTA and PDHG in substantially fewer iterations.

ABSTRACT. Recovering structured signals from a limited number of linear measurements plays a central role in signal processing and communication applications. Convex relaxations are often used to solve such signal recovery problems. In this work, we propose a novel framework for designing such convex relaxations and demonstrate improved recovery thresholds. The proposed framework is derived using the implicit bias property of mirror descent by designing the gradient mapping of the convex conjugate potential. Leveraging our framework, we develop new convex relaxations for simultaneously sparse and quantized signals that have improved recovery thresholds compared to the minimum of the $\ell_1$ and $\ell_{\infty}$ norms.

ABSTRACT. The minimax framework is one of the most famous methods for comparing estimator performance and finding optimal estimators. In this paper, we study the signal-to-noise ratio (SNR) aware minimax problem for a sparse Gaussian sequence model in the adaptive setting, where the estimator is designed without prior knowledge of the signal's sparsity level and strength. Previously, this problem has been studied in the so-called oracle case, in which one assumes knowledge of these quantities across low-, moderate-, and high-SNR regimes. The first contribution of this paper is to design an adaptive estimator in the low-SNR regime and prove that it attains the same minimax risk as the oracle estimator. The second contribution is to design an adaptive dictionary-based estimator selector for the moderate and high-SNR regimes. Simulations demonstrate the efficacy of the adaptive estimators and show that the dictionary-based estimator selector tracks the expected SNR-dependent transition.

ABSTRACT. Quantum state tomography estimates an unknown density operator from measurement data. Dense reconstruction however, can be impractical for many-qubit systems because the Hilbert-space dimension grows exponentially. This contribution develops a rank-adaptive matrix-free approach to low-rank quantum state tomography based on rank-one atomic coordinates. The density operator is represented as a convex combination of pure-state atoms, which preserves positivity and unit trace while avoiding dense density, measurement, and gradient matrices. The resultant algorithm combines atom updates, simplex-constrained coefficient reweighting, and periodic spectral refactorization using only predicted probability vectors, atom vectors, and descriptor-level measurement actions. These computations decompose across measurement outcomes, and admit a master--worker implementation with the measurements partitioned across workers. A rank penalty adapts the representation size during optimization. Provable feasibility, prediction consistency, monotone descent of the penalized objective, and an exact spectral proximal characterization of the refactorization step are established. Simulations with Pauli measurements show favorable accuracy--runtime--memory tradeoffs relative to competing alternatives.

ABSTRACT. Annealed Markov chains are widely used to generate biased ensembles on finite state spaces, but low temperature can make the resulting law sensitive to small modeling changes. We study finite-state annealed dynamics under perturbations of the energy function, transition kernel, and cooling schedule. First, we record Gibbs perturbation estimates showing that a uniform energy error of size delta changes partition functions, likelihood ratios, total variation distance, KL divergence, and bounded observables at the scale beta delta. We then combine these estimates with a nonhomogeneous Markov-kernel perturbation argument to bound the final-law distance between two annealed chains in terms of per-step kernel errors and Dobrushin contraction coefficients. For Metropolis kernels with a common proposal, this gives explicit finite-time bounds under energy and schedule perturbations. Finally, we translate final-law perturbation into changes in event probabilities, score tails, and p-values. Exact computations on a two-basin finite landscape illustrate the resulting tradeoff, as annealing improves concentration on low-energy states but increases sensitivity to perturbations.

ABSTRACT. Decentralized machine learning often outsources computational tasks, such as gradient evaluations, to untrusted workers. Existing robust aggregation methods typically rely on an honest majority and may fail when adversaries control most workers. We study this adversary-dominated setting through an incentive-oriented mechanism in which workers’ reports are accepted and rewarded only when they are mutually consistent within a prescribed threshold.

This mechanism forces adversaries to trade off increasing estimation error against the risk of rejection and loss of reward. In iterative optimization, this creates a long-horizon challenge: permissive thresholds speed up progress but allow more corruption, while strict thresholds improve accuracy but cause more rejections. We propose VISTA, an adaptive algorithm that tunes the acceptance threshold based on observed history. Through numerical evaluations and convergence analysis, we show that incentive-aware adaptation enables adversary-dominated decentralized learning to retain the asymptotic convergence behavior of standard SGD without requiring an honest majority.

ABSTRACT. We consider the problem of strategic information sharing in a Markov games, in which a Sender informed about the state of the Markov Decision Process may choose to influence the state belief of an uninformed Receiver through Bayesian Persuasion. While this ideas has been explored in the literature, existing works treat communication as an abstract commitment, independent of the Sender's physical actions. Here, we consider the problem of a privately informed Sender who can both commit to a signaling strategy ex-ante, and also take (physical) actions in the MDP environment ex-post, creating information leakage. We formulate this as a bi-level optimization problem, and explore the conflict between physical efficiency and strategic signaling. (Based on joint work with Atefeh Mollabagher.)

ABSTRACT. We consider decentralized optimization where multiple agents minimize the average of their (strongly) convex, smooth losses over a communication graph. Convergence of the existing decentralized methods generally hinges on an apriori, proper selection of the stepsize. Choosing this value is notoriously delicate: (i) it demands global knowledge from all the agents of the graph's connectivity and every local smoothness/strong-convexity constants--information they rarely have; (ii) even with perfect information, the worst-case tuning forces an overly small stepsize, slowing convergence in practice; and (iii) large-scale trial-and-error tuning is prohibitive. This work introduces a decentralized algorithm that is fully adaptive in the choice of the agents' stepsizes, without any global information and using only neighbor-to-neighbor communications--agents need not even know whether the problem is strongly convex or merely convex. The algorithm retains strong guarantees: it converges at linear rate when the losses are strongly convex and at sublinear rate otherwise, matching the best-known rates of parameter-dependent methods. Extensions to composite optimization are also obtained.

ABSTRACT. Optimizers that exploit the matrix structure of gradients are central to modern LLM pre-training, with two distinct frontiers: explicit Kronecker-factored preconditioning---most recently KL-Shampoo, which estimates the preconditioner via KL divergence minimization---and orthogonalization of the gradient momentum, exemplified by Muon and analyzed as steepest descent under the spectral norm. The two routes are typically developed in isolation. We make a structural observation about KL-Shampoo's Kronecker preconditioners: their eigenvalue spectra exhibit a spike-and-flat shape---a few dominant eigenvalues followed by an approximately uniform tail---across layers and training stages, holding exactly under a rank-$\rho$ signal-plus-noise gradient model. We exploit this structure by restricting one of KL-Shampoo's Kronecker factors to a parametric family aligned with the spike-and-flat shape: full spectral structure on a tracked $r$-dimensional subspace, single shared eigenvalue across the remaining $n-r$ directions. On these directions, we apply orthogonalization. An identity shows that this orthogonalization recovers the algebraic form of full KL-Shampoo's preconditioner. On four pre-training scales (GPT-2 124M / 350M, LLaMA 134M / 450M), Pro-KLShampoo consistently outperforms KL-Shampoo at every subspace rank we test in validation loss, peak per-GPU memory, and wallclock time to reach each loss level.

ABSTRACT. Behavioral systems theory models dynamical systems as sets of trajectories, without committing to a particular representation. Although classical in systems theory and recently brought back into focus by data-driven control, this viewpoint remains largely unexplored as a foundation for dynamic optimization. I will argue that its representation-free nature enables scalable and modular optimization formulations, especially when model-based and data-driven system representations must coexist. The talk will develop this perspective through case studies spanning distributed optimal control and inverse problems in signal processing.

ABSTRACT. Important systems in engineering and physics are described in terms of operators mapping input functions to output functions. Operator learning seeks to approximate these mappings based on observed input—output data, which can be expensive to collect. Our work seeks to identify classes of operators whose structure can be exploited to obtain accurate approximations from small amounts of training data. In this talk we focus on a class of linear Hilbert-Schmidt integral operators whose kernels may be non-symmetric, but have an asymptotic smoothness (AS) property modeling the behavior of elliptic Greens functions by allowing a singularity on the diagonal with increasing smoothness away from it. We provide a learning algorithm querying the operator’s action nonadaptively on n randomized input functions to produce an approximation whose error in Hilbert-Schmidt norm is O(e^(-c n^(1/(d+1))) with high probability. To do this, we show that operators with AS kernels are well-approximated by hierarchically rank-structured matrices with known row-subspaces. We then extend the fixed-sparsity matrix approximation algorithm of (Amsel et al., SIMAX, 2026) to obtain near-optimal approximations in the known structure using input—output pairs. Our results shed light on the types of underlying structures that enable data-efficient operator learning, and begins to close the gap between theory and physical problems where data-efficient operator learning is observed to occur.

ABSTRACT. Direct data-driven control methods such as data-enabled predictive control (DeePC) represent a system's behavior implicitly through raw trajectory data, sidestepping parametric identification. Two questions sit at the heart of making such methods dependable: how should we characterize the reliability of these nonparametric models and use it toward robust, safe control, and how should we leverage online data to adapt to real-time operating conditions? In this talk, I take a subspace-geometric view that speaks to both, quantifying the reliability of data-driven predictors through distances between subspaces, and enabling online adaptation to unknown and time-varying systems. I will discuss what this perspective offers for direct data-driven control and the open questions it raises.

ABSTRACT. Autoencoders are commonly used to learn low-dimensional dynamical models from trajectory data lying on low-dimensional submanifolds. In this talk, I will discuss fundamental limitations and capabilities of this approach, together with related tradeoffs and cautionary tales. This material is based on joint work with Josh McCarter and Eduardo Sontag.

ABSTRACT. We discuss a framework for addressing questions of controllability of bilinear systems on infinite-dimensional Hilbert spaces using techniques from the theory of von Neumann algebras. In the setup, we assume that the drift and control terms arising in a controlled system are affiliated with a von Neumann algebra of finite type acting on a Hilbert space. Based on this assumption, we build operator-theoretic formulations of various control problems such as existence of time-optimal controls and approximate controllability, where the relevant drift and control operators may be unbounded. We also discuss connections between classical variants of this approach and the Koopman operator formalism.

ABSTRACT. Despite the popularity of Koopman modeling for nonlinear systems, in the presence of input variables, the evident nonexistence of a fully linear time-invariant model (even in infinite dimensions) renders the "Koopman-based control" essentially an open problem to date. Focusing on discrete-time systems in this paper (which eschews from using operator semigroups with unbounded infinitesimal generators), it is proven in this paper that the nonlinear dynamics, if satisfying an appropriate smoothness condition, can be expressed exactly as an bilinear dynamics, when both the state variables and input variables are lifted into a reproducing kernel Hilbert space (RKHS). To account for the existence of an equilibrium point at the origin, the RKHS is defined by a linear-radial product kernel, and hence the functions belonging to this RKHS are spanned by the multiplications of component functions and Sobolev functions. The stabilization problem, namely the determination of a feedback law that causes a Lyapunov function (expressed as a kernel sum-of-squares form) to decrease, is then posed as an infinite-dimensional optimization problem over state-dependent conditional probability measures over the input space.