Probably Approximately Correct Nash Equilibrium Learning

We consider a multi-agent noncooperative game with agents' objective functions being affected by uncertainty. Following a data driven paradigm, we represent uncertainty by means of scenarios and seek a robust Nash equilibrium solution. We treat the Nash equilibrium computation problem within the realm of probably approximately correct (PAC) learning. Building upon recent developments in scenario-based optimization, we accompany the computed Nash equilibrium with a priori and a posteriori probabilistic robustness certificates, providing confidence that the computed equilibrium remains unaffected (in probabilistic terms) when a new uncertainty realization is encountered. For a wide class of games, we also show that the computation of the so called compression set - a key concept in scenario-based optimization - can be directly obtained as a byproduct of the proposed solution methodology. Finally, we illustrate how to overcome differentiability issues, arising due to the introduction of scenarios, and compute a Nash equilibrium solution in a decentralized manner. We demonstrate the efficacy of the proposed approach on an electric vehicle charging control problem.Comment: Preprint submitted to IEEE Transactions on Automatic Contro

Cognition-Based Networks: A New Perspective on Network Optimization Using Learning and Distributed Intelligence

IEEE Access Volume 3, 2015, Article number 7217798, Pages 1512-1530 Open Access Cognition-based networks: A new perspective on network optimization using learning and distributed intelligence (Article) Zorzi, M.a , Zanella, A.a, Testolin, A.b, De Filippo De Grazia, M.b, Zorzi, M.bc a Department of Information Engineering, University of Padua, Padua, Italy b Department of General Psychology, University of Padua, Padua, Italy c IRCCS San Camillo Foundation, Venice-Lido, Italy View additional affiliations View references (107) Abstract In response to the new challenges in the design and operation of communication networks, and taking inspiration from how living beings deal with complexity and scalability, in this paper we introduce an innovative system concept called COgnition-BAsed NETworkS (COBANETS). The proposed approach develops around the systematic application of advanced machine learning techniques and, in particular, unsupervised deep learning and probabilistic generative models for system-wide learning, modeling, optimization, and data representation. Moreover, in COBANETS, we propose to combine this learning architecture with the emerging network virtualization paradigms, which make it possible to actuate automatic optimization and reconfiguration strategies at the system level, thus fully unleashing the potential of the learning approach. Compared with the past and current research efforts in this area, the technical approach outlined in this paper is deeply interdisciplinary and more comprehensive, calling for the synergic combination of expertise of computer scientists, communications and networking engineers, and cognitive scientists, with the ultimate aim of breaking new ground through a profound rethinking of how the modern understanding of cognition can be used in the management and optimization of telecommunication network

Nonlinear Information Bottleneck

Information bottleneck (IB) is a technique for extracting information in one random variable $X$ that is relevant for predicting another random variable $Y$. IB works by encoding $X$ in a compressed "bottleneck" random variable $M$ from which $Y$ can be accurately decoded. However, finding the optimal bottleneck variable involves a difficult optimization problem, which until recently has been considered for only two limited cases: discrete $X$ and $Y$ with small state spaces, and continuous $X$ and $Y$ with a Gaussian joint distribution (in which case optimal encoding and decoding maps are linear). We propose a method for performing IB on arbitrarily-distributed discrete and/or continuous $X$ and $Y$, while allowing for nonlinear encoding and decoding maps. Our approach relies on a novel non-parametric upper bound for mutual information. We describe how to implement our method using neural networks. We then show that it achieves better performance than the recently-proposed "variational IB" method on several real-world datasets