Entropy-Regularized Stochastic Games
Abstract
In zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have perfect information about the stochastic transition model of the environment. However, implementing such strategies may make the players vulnerable to unforeseen changes in the environment. In this paper, we introduce entropy-regularized stochastic games where each player aims to maximize the causal entropy of its strategy in addition to its expected payoff. The regularization term balances each player's rationality with its belief about the level of misinformation about the transition model. We consider both entropy-regularized N-stage and entropy-regularized discounted stochastic games, and establish the existence of a value in both games. Moreover, we prove the sufficiency of Markovian and stationary mixed strategies to attain the value, respectively, in N-stage and discounted games. Finally, we present algorithms, which are based on convex optimization problems, to compute the optimal strategies. In a numerical example, we demonstrate the proposed method on a motion planning scenario and illustrate the effect of the regularization term on the expected payoff.
Additional Information
© 2019 IEEE. This work was supported in part by the grants AFRL # FA9550-19-1-0169 and DARPA # D19AP00004.Attached Files
Submitted - 1907.11543.pdf
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Additional details
- Eprint ID
- 105357
- Resolver ID
- CaltechAUTHORS:20200911-133139267
- Air Force Research Laboratory (AFRL)
- FA9550-19-1-0169
- Defense Advanced Research Projects Agency (DARPA)
- D19AP00004
- Created
-
2020-09-11Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Center for Autonomous Systems and Technologies (CAST)