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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Pipeline PSRO: A Scalable Approach for Finding Approximate Nash Equilibria in Large Games
challenging when the number of information states is large. Policy Space Response
Oracles (PSRO) is a deep reinforcement learning algorithm grounded in game
theory that is guaranteed to converge to an approximate Nash equilibrium. However, PSRO requires training a reinforcement learning policy at each iteration, making it too slow for large games. We show through counterexamples and experiments that DCH and Rectified PSRO, two existing approaches to scaling up PSRO, fail to converge even in small games. We introduce Pipeline PSRO (P2SRO), the first scalable PSRO-based method for finding approximate Nash equilibria in large zero-sum imperfect-information games. P2SRO is able to parallelize PSRO with convergence guarantees by maintaining a hierarchical pipeline of reinforcement learning workers, each training against the policies generated by lower levels in the hierarchy. We show that unlike existing methods, P2SRO converges to an approximate Nash equilibrium, and does so faster as the number of parallel workers increases, across a variety of imperfect information games. We also introduce an open-source environment for Barrage Stratego, a variant of Stratego with an approximate game tree complexity of 1050. P2SRO is able to achieve state-of-theart performance on Barrage Stratego and beats all existing bots. Experiment code is available at https://github.com/JBLanier/pipeline-psro.
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- Award ID(s):
- 1839429
- NSF-PAR ID:
- 10313269
- Date Published:
- Journal Name:
- Advances in neural information processing systems
- ISSN:
- 1049-5258
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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