Reinforcement learning, energy systems and deep neural nets

ABSTRACT. Reinforcement leaning is a highly-successful subfield of artificial intelligence where an agent is ought to interact with its environment to maximize a sum of rewards. In this talk, Damien Ernst will argue that this learning paradigm can be very powerful to solve many decision-making problems in the energy sector, as for example investment problems, the design of bidding strategies for playing with the intraday electricity market or problems related to the control of microgrids. He will also describe some very recent progresses in the field on deep reinforcement learning that could be used to foster the performances of reinforcement learning agents when confronted with environments that can exhibit sudden changes in their dynamics, as it is often the case with energy systems.

PhD Prize Lecture: Geometric and Dual Approaches to Cumulative Scheduling

ABSTRACT. Citation from the prize committee: ``The work of Nicolas Bonifas falls in the scope of constraint-based scheduling. In this framework, the most frequently encountered resource constraint is the cumulative, which enables the modeling of parallel processes. In his thesis, Nicolas studies the cumulative constraint with the help of tools rarely used in constraint programming (polyhedral analysis, linear programming duality, projective geometry duality) and propose two contributions for the domain. Cumulative strengthening is a means of generating tighter redundant cumulative constraints, analogous to the generation of cuts in integer linear programming. This is one of the first examples of a redundant global constraint. Energy Reasoning is an extremely powerful propagation for cumulative constraint, with hitherto a high complexity of O(n^{^3}). Nicolas Bonifas proposes an algorithm that computes this propagation with a O(n^{^2} log n) complexity, which is a significant improvement of this algorithm known for more than 25 years.''

Phd Prize Lecture: Stochastic approximation and least-squares regression, with applications to machine learning

ABSTRACT. Citation from the prize committee: ``Many problems in machine learning are naturally cast as the minimization of a smooth function defined on a Euclidean space. While small problems are efficiently solved by classical optimization algorithms, large-scale problems are typically solved with first-order techniques based on gradient descent. Nicolas Flammarion considers, in his thesis, the particular case of the quadratic loss. He addresses its minimization when gradients are only accessible through a stochastic oracle and proposes optimal algorithms in different cases. His work offers many perspectives of applications of the quadratic loss in machine learning. Clustering and estimation with shape constraints are the two first applications already considered.''

ABSTRACT. Algebraic Vision is an emerging viewpoint of problems in computer vision that aims to examine polynomial models in vision through the lens of algebra. A key problem in computer vision is the estimation of the three-dimensional shape of a world scene from images and the parameters (position, orientation, etc.) of the cameras that captured them. This problem, studied under the name structure-from-motion or multi-view geometry, has its origins in photogrammetry and perspective drawings. The modeling language for these problems is projective geometry, which naturally leads to polynomial models with rich and beautiful structure that beg for algebraic tools. In this talk I will show some of the surprising structure, properties, and algorithmic successes that have emerged from this algebraic viewpoint.

Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations

ABSTRACT. We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability distributions centered at the uniform distribution on the training samples, and we seek decisions that perform best in view of the worst-case distribution within this Wasserstein ball. The state-of-the-art methods for solving the resulting distributionally robust optimization problems rely on global optimization techniques, which quickly become computationally excruciating. In this paper we demonstrate that, under mild assumptions,
the distributionally robust optimization problems over Wasserstein balls can in fact be reformulated as finite convex programs - in many interesting cases even as tractable linear programs. Leveraging recent measure concentration results, we also show that their solutions enjoy powerful finite-sample performance guarantees. Our theoretical results are exemplified in mean-risk portfolio optimization, uncertainty quantification and machine learning.

Optimization Models and Algorithms for Network Reconfiguration

ABSTRACT. In future cognitive networks, thanks to Software Defined Networking (SDN),
network reconfiguration and traffic migration will be triggered by
intelligent software tools. This requires efficient algorithms, but also clear objectives in order to know wen trigger and how to conduct network reconfiguration. In this talk, we will discuss seamless network reconfiguration, as well as various minimum disruption objectives, when a seamless reconfiguration cannot be conducted, i.e., minimize (i) the number of disruptions, (ii) the maximum number of concurrent disruptions, (iii) the overall duration of the disruptions, and (iv) the maximum disruption duration. We survey these four different minimum disruption objectives for the RWA (Routing and Wavelength Assignment) and RSA (Routing and Spectrum Assignment) lightpath migration in optical networks. For each of them,
the defragmentation problem can be reduced to a graph theory problem
(Minimum Feedback Vertex, Vertex Separation, Graph Bandwidth, Minimum
Sum Cut) or formulated as an Integer Linear Program. We investigate the
most efficient available exact algorithms. For seamless reconfiguration, we will discuss a nested decomposition scheme. Extensive numerical experiments are conducted on different traffic and network instances, in order to compare the level of disruption entailed by the different objectives.