Games constitute a challenging domain of reinforcement learning (RL) for acquiring strategies because many of them include multiple players and many unobservable variables in a large state space. The difficulty of solving such realistic multiagent problems with partial observability arises mainly from the fact that the computational cost for the estimation and prediction in the whole state space, including unobservable variables, is too heavy. To overcome this intractability and enable an agent to learn in an unknown environment, an effective approximation method is required with explicit learning of the environmental model. We present a model-based RL scheme for large-scale multiagent problems with partial observability and apply it to a card game, hearts. This game is a well-defined example of an imperfect information game and can be approximately formulated as a partially observable Markov decision process (POMDP) for a single learning agent. To reduce the computational cost, we use a sampling technique in which the heavy integration required for the estimation and prediction can be approximated by a plausible number of samples. Computer simulation results show that our method is effective in solving such a difficult, partially observable multiagent problem.

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