Markov games model interactions among multiple players in a stochastic, dynamic environment. Each player in a Markov game maximizes its expected total discounted reward, which depends upon the policies of the other players. We formulate a class of Markov games, termed affine Markov games, where an affine reward function couples the players’ actions. We introduce a novel solution concept, the soft-Bellman equilibrium, where each player is boundedly rational and chooses a soft-Bellman policy rather than a purely rational policy as in the well-known Nash equilibrium concept. We provide conditions for the existence and uniqueness of the soft-Bellman equilibrium and propose a nonlinear least-squares algorithm to compute such an equilibrium in the forward problem. We then solve the inverse game problem of inferring the players’ reward parameters from observed state-action trajectories via a projected-gradient algorithm. Experiments in a predator-prey OpenAI Gym environment show that the reward parameters inferred by the proposed algorithm outper- form those inferred by a baseline algorithm: they reduce the Kullback-Leibler divergence between the equilibrium policies and observed policies by at least two orders of magnitude.
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Anticipating Oblivious Opponents in Stochastic Games
We present an approach for systematically anticipating the actions and policies employed by oblivious environments in concurrent stochastic games, while maximizing a reward function. Our main contribution lies in the synthesis of a finite information state machine (ISM) whose alphabet ranges over the actions of the environment. Each state of the ISM is mapped to a belief state about the policy used by the environment. We introduce a notion of consistency that guarantees that the belief states tracked by the ISM stays within a fixed distance of the precise belief state obtained by knowledge of the full history. We provide methods for checking consistency of an automaton and a synthesis approach which, upon successful termination, yields an ISM. We construct a Markov Decision Process (MDP) that serves as the starting point for computing optimal policies for maximizing a reward function defined over plays. We present an experimental evaluation over benchmark examples including human activity data for tasks such as cataract surgery and furniture assembly, wherein our approach successfully anticipates the policies and actions of the environment in order to maximize the reward.
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- Award ID(s):
- 2146563
- PAR ID:
- 10575682
- Editor(s):
- Amato, Nancy; Driggs-Campbell, Katie; Ekenna, Chinwe; Morales, Marco; O'Kane, Jason
- Publisher / Repository:
- Springer Proceedings in Advanced Robotics (SPAR)
- Date Published:
- Format(s):
- Medium: X
- Location:
- Chicago, USA
- Sponsoring Org:
- National Science Foundation
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