Markov games with unknown random state-actions-dependent discount factors: Empirical estimation

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Abstract

The work deals with a class of discrete-time zero-sum Markov games under a discounted optimality criterion with random state-action-dependent discount factors of the form (Formula presented.), where xn,an,bn, and ξn+1 are the state, the actions of players, and a random disturbance at time n, respectively, taking values in Borel spaces. The one-stage payoff is assumed to be possibly unbounded. In addition, the process {ξn} is formed by observable, independent, and identically distributed random variables with common distribution θ, which is unknown to players. By using the empirical distribution to estimate θ, we introduce a procedure to approximate the value V of the game; such a procedure yields construction schemes of stationary optimal strategies and asymptotically optimal Markov strategies.

Original languageEnglish
JournalAsian Journal of Control
DOIs
StatePublished - 1 Jan 2019

Keywords

  • discounted optimality
  • empirical estimation
  • markov games
  • non-constant discount factors

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