DISCOVERING DIVERSE MULTI-AGENT STRATEGIC BEHAVIOR VIA REWARD RANDOMIZATION

Abstract

We propose a simple, general and effective technique, Reward Randomization for discovering diverse strategic policies in complex multi-agent games. Combining reward randomization and policy gradient, we derive a new algorithm, Reward-Randomized Policy Gradient (RPG). RPG is able to discover multiple distinctive human-interpretable strategies in challenging temporal trust dilemmas, including grid-world games and a real-world game Agar.io, where multiple equilibria exist but standard multi-agent policy gradient algorithms always converge to a fixed one with a sub-optimal payoff for every player even using state-of-the-art exploration techniques. Furthermore, with the set of diverse strategies from RPG, we can (1) achieve higher payoffs by fine-tuning the best policy from the set; and (2) obtain an adaptive agent by using this set of strategies as its training opponents. The source code and example videos can be found in our website: https://sites.google.

1. INTRODUCTION

Games have been a long-standing benchmark for artificial intelligence, which prompts persistent technical advances towards our ultimate goal of building intelligent agents like humans, from Shannon's initial interest in Chess (Shannon, 1950) and IBM DeepBlue (Campbell et al., 2002) , to the most recent deep reinforcement learning breakthroughs in Go (Silver et al., 2017 ), Dota II (OpenAI et al., 2019) and Starcraft (Vinyals et al., 2019) . Hence, analyzing and understanding the challenges in various games also become critical for developing new learning algorithms for even harder challenges. Most recent successes in games are based on decentralized multi-agent learning (Brown, 1951; Singh et al., 2000; Lowe et al., 2017; Silver et al., 2018) , where agents compete against each other and optimize their own rewards to gradually improve their strategies. In this framework, Nash Equilibrium (NE) (Nash, 1951) , where no player could benefit from altering its strategy unilaterally, provides a general solution concept and serves as a goal for policy learning and has attracted increasingly significant interests from AI researchers (Heinrich & Silver, 2016; Lanctot et al., 2017; Foerster et al., 2018; Kamra et al., 2019; Han & Hu, 2019; Bai & Jin, 2020; Perolat et al., 2020) : many existing works studied how to design practical multi-agent reinforcement learning (MARL) algorithms that can provably converge to an NE in Markov games, particularly in the zero-sum setting. Despite the empirical success of these algorithms, a fundamental question remains largely unstudied in the field: even if an MARL algorithm converges to an NE, which equilibrium will it converge to? The existence of multiple NEs is extremely common in many multi-agent games. Discovering as many NE strategies as possible is particularly important in practice not only because different NEs can produce drastically different payoffs but also because when facing unknown players who are trained to play an NE strategy, we can gain advantage by identifying which NE strategy the opponent is playing and choosing the most appropriate response. Unfortunately, in many games where multiple distinct NEs exist, the popular decentralized policy gradient algorithm (PG), which has led to great successes in numerous games including Dota II and Stacraft, always converge to a particular NE with non-optimal payoffs and fail to explore more diverse modes in the strategy space. Consider an extremely simple example, a 2-by-2 matrix game Stag-Hunt (Rousseau, 1984; Skyrms, 2004) , where two pure strategy NEs exist: a "risky" cooperative equilibrium with the highest payoff

