J. Zico Kolter

Samuel Sokota, Ryan D'Orazio, Chun Kai Ling et al.

In their seminal work, Nayyar et al. (2013) showed that imperfect information can be abstracted away from common-payoff games by having players publicly announce their policies as they play. This insight underpins sound solvers and decision-time planning algorithms for common-payoff games. Unfortunately, a naive application of the same insight to two-player zero-sum games fails because Nash equilibria of the game with public policy announcements may not correspond to Nash equilibria of the original game. As a consequence, existing sound decision-time planning algorithms require complicated additional mechanisms that have unappealing properties. The main contribution of this work is showing that certain regularized equilibria do not possess the aforementioned non-correspondence problem -- thus, computing them can be treated as perfect-information problems. Because these regularized equilibria can be made arbitrarily close to Nash equilibria, our result opens the door to a new perspective to solving two-player zero-sum games and yields a simplified framework for decision-time planning in two-player zero-sum games, void of the unappealing properties that plague existing decision-time planning approaches.

Samuel Sokota, Ryan D'Orazio, J. Zico Kolter et al.

This work studies an algorithm, which we call magnetic mirror descent, that is inspired by mirror descent and the non-Euclidean proximal gradient algorithm. Our contribution is demonstrating the virtues of magnetic mirror descent as both an equilibrium solver and as an approach to reinforcement learning in two-player zero-sum games. These virtues include: 1) Being the first quantal response equilibria solver to achieve linear convergence for extensive-form games with first order feedback; 2) Being the first standard reinforcement learning algorithm to achieve empirically competitive results with CFR in tabular settings; 3) Achieving favorable performance in 3x3 Dark Hex and Phantom Tic-Tac-Toe as a self-play deep reinforcement learning algorithm.

Max Rudolph, Nathan Lichtle, Sobhan Mohammadpour et al.

In the past decade, motivated by the putative failure of naive self-play deep reinforcement learning (DRL) in adversarial imperfect-information games, researchers have developed numerous DRL algorithms based on fictitious play (FP), double oracle (DO), and counterfactual regret minimization (CFR). In light of recent results of the magnetic mirror descent algorithm, we hypothesize that simpler generic policy gradient methods like PPO are competitive with or superior to these FP-, DO-, and CFR-based DRL approaches. To facilitate the resolution of this hypothesis, we implement and release the first broadly accessible exact exploitability computations for four large games. Using these games, we conduct the largest-ever exploitability comparison of DRL algorithms for imperfect-information games. Over 5600 training runs, we find that FP-, DO-, and CFR-based approaches fail to outperform generic policy gradient methods. Code is available at https://github.com/nathanlct/IIG-RL-Benchmark and https://github.com/gabrfarina/exp-a-spiel .