In Information, Learning, Optimization and Quantum (ILOQ), our main goal is to develop advanced mathematical tools to understand the systems upon which the digital age is built. We take interest in many fundamental problems that arise in those systems such as: data compression, data communication, artificial intelligence, online learning, reinforcement learning, optimization, optimal control, equilibria in games, distributed learning, quantum storage and communication, to name but a few. We propose mathematical models for those problems, design algorithms to solve them, and investigate their fundamental limits. Our work spans a large spectrum of disciplines across applied mathematics: probability and statistics, information theory (classical and quantum), optimization theory, learning theory and game theory. While most of our contributions are of methodological nature, we also take interest in their industrial applications.
We investigate information theoretic problems such as data compression, error correction coding, distributed hypothesis testing, minimax bounds for statistical problems and so on. Applications include the design of future communication networks, the design of data storage systems, the design of sensor networks, to name but a few.Also, we use information theoretic tools in other topics of interest presented here, particularly in learning theory and quantum systems.
We focus on several topics in learning theory: estimation problems, multi-armed bandits, online learning, reinforcement learning, distributed learning and learning in games. For all those problems, we propose algorithms to minimize regret and/or estimation error, and investigate fundamental limits that quantify the best performance achievable by the best algorithms. We also investigate the trade-offs between computational complexity and statistical performance. Those problems are naturally applied to communication networks, recommender systems, transportation networks, industrial systems, and so on.
We take interest in problems in optimization, optimal control and game theory: existence of solutions, the development of efficient numerical methods in order to approximate those solutions and the computational complexity required to do so. Those problems are often inspired by applications mentioned in the other topics of interest: communication networks, artificial intelligence, distributed systems and so on. Also, optimization and optimal control have a strong synergy with our other topics of interest such as learning theory and information theory.
We are interested in quantum systems, in particular in quantum information theory, quantum algorithms as well as quantum error correction codes.
Those problems find applications in the design of future quantum computers, and more generally the design of any microscopic system exhibiting quantum behaviour such as optical systems.
Associate Professor – CentraleSupélec
Télécoms et réseaux – ILOQ
richard.combes@l2s.centralesupelec.fr
Bât. Breguet .
