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Policy Space Response Oracles (PSRO) is a reinforcement learning (RL) algo- rithm for two-player zero-sum games that has been empirically shown to find approximate Nash equilibria in large games. Although PSRO is guaranteed to converge to an approximate Nash equilibrium and can handle continuous actions, it may take an exponential number of iterations as the number of information states (infostates) grows. We propose Extensive-Form Double Oracle (XDO), an extensive-form double oracle algorithm for two-player zero-sum games that is guar- anteed to converge to an approximate Nash equilibrium linearly in the number of infostates. Unlike PSRO, which mixes best responses at the root of the game, XDO mixes best responses at every infostate. We also introduce Neural XDO (NXDO), where the best response is learned through deep RL. In tabular experiments on Leduc poker, we find that XDO achieves an approximate Nash equilibrium in a number of iterations an order of magnitude smaller than PSRO. Experiments on a modified Leduc poker game and Oshi-Zumo show that tabular XDO achieves a lower exploitability than CFR with the same amount of computation. We also find that NXDO outperforms PSRO and NFSP on a sequential multidimensional continuous-action game. NXDO is the first deep RL method that can find an approximate Nash equilibrium in high-dimensional continuous-action sequential games. Experiment code is available at https://github.com/indylab/nxdo.
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Team-PSRO for Learning Approximate TMECor in Large Team Games via Cooperative Reinforcement Learning
Recent algorithms have achieved superhuman performance at a number of twoplayer zero-sum games such as poker and go. However, many real-world situations are multi-player games. Zero-sum two-team games, such as bridge and football, involve two teams where each member of the team shares the same reward with every other member of that team, and each team has the negative of the reward of the other team. A popular solution concept in this setting, called TMECor, assumes that teams can jointly correlate their strategies before play, but are not able to communicate during play. This setting is harder than two-player zerosum games because each player on a team has different information and must use their public actions to signal to other members of the team. Prior works either have game-theoretic guarantees but only work in very small games, or are able to scale to large games but do not have game-theoretic guarantees. In this paper we introduce two algorithms: Team-PSRO, an extension of PSRO from twoplayer games to team games, and Team-PSRO Mix-and-Match which improves upon Team PSRO by better using population policies. In Team-PSRO, in every iteration both teams learn a joint best response to the opponent’s meta-strategy via reinforcement learning. As the reinforcement learning joint best response approaches the optimal best response, Team-PSRO is guaranteed to converge to a TMECor. In experiments on Kuhn poker and Liar’s Dice, we show that a tabular version of Team-PSRO converges to TMECor, and a version of Team PSRO using deep cooperative reinforcement learning beats self-play reinforcement learning in the large game of Google Research Football.
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- Award ID(s):
- 1901403
- PAR ID:
- 10550010
- Publisher / Repository:
- NeurIPS23
- Date Published:
- Format(s):
- Medium: X
- Location:
- New Orleans, LA
- Sponsoring Org:
- National Science Foundation
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