Policy Space Response Oracles (PSRO) is a reinforcement learning (RL) algorithm for two-player zero-sum games that has been empirically shown to find approximate Nash equilibria in large games.

This paper introduces deep synoptic Monte Carlo planning (DSMCP) for large imperfect information games.

Policy Space Response Oracles (PSRO) is a reinforcement learning (RL) algorithm 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 guaranteed 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.

's population policies chooses action In a given iteration, consider the restricted game for a single GMP game. If player 2 is not allowed an action unavailable to player 1, player 2's BR will be a new action In pk,m q-clone GMP with n classes, XDO adds at most 2 n actions for each player . In total, 2n actions may be added for each player.Proposition 6. Like in that work, we represent actions that are in the restricted game by bold arrows. Extensive-form pure strategies specify an action at every infostate.

Our agent does not use any information abstraction, whether lossy or lossless. The agent computes a unique policy for each infostate.

Regret minimization is a general approach to online optimization which plays a crucial role in many algorithms for approximating Nash equilibria in two-player zero-sum games. The literature mainly focuses on solving individual games in isolation. However, in practice, players often encounter a distribution of similar but distinct games. For example, when trading correlated assets on the stock market, or when refining the strategy in subgames of a much larger game. Recently, offline meta-learning was used to accelerate one-sided equilibrium finding on such distributions. We build upon this, extending the framework to the more challenging self-play setting, which is the basis for most state-of-the-art equilibrium approximation algorithms for domains at scale. When selecting the strategy, our method uniquely integrates information across all decision states, promoting global communication as opposed to the traditional local regret decomposition. Empirical evaluation on normal-form games and river poker subgames shows our meta-learned algorithms considerably outperform other state-of-the-art regret minimization algorithms.