Efficient Policy Space Response Oracles

Policy Space Response Oracle method (PSRO) provides a general solution to Nash equilibrium in two-player zero-sum games but suffers from two problems: (1) the computation inefficiency due to consistently evaluating current populations by simulations; and (2) the exploration inefficiency due to learning best responses against a fixed meta-strategy at each iteration. In this work, we propose Efficient PSRO (EPSRO) that largely improves the efficiency of the above two steps. Central to our development is the newly-introduced subroutine of minimax optimization on unrestricted-restricted (URR) games. By solving URR at each step, one can evaluate the current game and compute the best response in one forward pass with no need for game simulations. Theoretically, we prove that the solution procedures of EPSRO offer a monotonic improvement on exploitability. Moreover, a desirable property of EPSRO is that it is parallelizable, this allows for efficient exploration in the policy space that induces behavioral diversity. We test EPSRO on three classes of games and report a 50x speedup in wall-time, 10x data efficiency, and similar exploitability as existing PSRO methods on Kuhn and Leduc Poker games.