10,486 research outputs found
Game-theoretical control with continuous action sets
Motivated by the recent applications of game-theoretical learning techniques
to the design of distributed control systems, we study a class of control
problems that can be formulated as potential games with continuous action sets,
and we propose an actor-critic reinforcement learning algorithm that provably
converges to equilibrium in this class of problems. The method employed is to
analyse the learning process under study through a mean-field dynamical system
that evolves in an infinite-dimensional function space (the space of
probability distributions over the players' continuous controls). To do so, we
extend the theory of finite-dimensional two-timescale stochastic approximation
to an infinite-dimensional, Banach space setting, and we prove that the
continuous dynamics of the process converge to equilibrium in the case of
potential games. These results combine to give a provably-convergent learning
algorithm in which players do not need to keep track of the controls selected
by the other agents.Comment: 19 page
Learning Equilibria with Partial Information in Decentralized Wireless Networks
In this article, a survey of several important equilibrium concepts for
decentralized networks is presented. The term decentralized is used here to
refer to scenarios where decisions (e.g., choosing a power allocation policy)
are taken autonomously by devices interacting with each other (e.g., through
mutual interference). The iterative long-term interaction is characterized by
stable points of the wireless network called equilibria. The interest in these
equilibria stems from the relevance of network stability and the fact that they
can be achieved by letting radio devices to repeatedly interact over time. To
achieve these equilibria, several learning techniques, namely, the best
response dynamics, fictitious play, smoothed fictitious play, reinforcement
learning algorithms, and regret matching, are discussed in terms of information
requirements and convergence properties. Most of the notions introduced here,
for both equilibria and learning schemes, are illustrated by a simple case
study, namely, an interference channel with two transmitter-receiver pairs.Comment: 16 pages, 5 figures, 1 table. To appear in IEEE Communication
Magazine, special Issue on Game Theor
Two More Classes of Games with the Fictitious Play Property
Fictitious play is the oldest and most studied learning process for games. Since the already classical result for zero-sum games, convergence of beliefs to the set of Nash equilibria has been established for some important classes of games, including weighted potential games, supermodular games with diminishing returns, and 3x3 supermodular games. Extending these results, we establish convergence for ordinal potential games and quasi-supermodular games with diminishing returns. As a by-product we obtain convergence for 3xm and 4x4 quasi-supermodular games.Fictitious Play, Learning Process, Ordinal Potential Games, Quasi-Supermodular Games
Reinforcement learning with restrictions on the action set
Consider a 2-player normal-form game repeated over time. We introduce an
adaptive learning procedure, where the players only observe their own realized
payoff at each stage. We assume that agents do not know their own payoff
function, and have no information on the other player. Furthermore, we assume
that they have restrictions on their own action set such that, at each stage,
their choice is limited to a subset of their action set. We prove that the
empirical distributions of play converge to the set of Nash equilibria for
zero-sum and potential games, and games where one player has two actions.Comment: 28 page
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