15,772 research outputs found
Operator approach to values of stochastic games with varying stage duration
We study the links between the values of stochastic games with varying stage
duration , the corresponding Shapley operators and and
the solution of . Considering general non
expansive maps we establish two kinds of results, under both the discounted or
the finite length framework, that apply to the class of "exact" stochastic
games. First, for a fixed length or discount factor, the value converges as the
stage duration go to 0. Second, the asymptotic behavior of the value as the
length goes to infinity, or as the discount factor goes to 0, does not depend
on the stage duration. In addition, these properties imply the existence of the
value of the finite length or discounted continuous time game (associated to a
continuous time jointly controlled Markov process), as the limit of the value
of any time discretization with vanishing mesh.Comment: 22 pages, International Journal of Game Theory, Springer Verlag, 201
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
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