Learning to Play No-Press Diplomacy with Best Response Policy Iteration

Recent advances in deep reinforcement learning (RL) have led to considerable progress in many 2-player zero-sum games, such as Go, Poker and Starcraft. The purely adversarial nature of such games allows for conceptually simple and principled application of RL methods. However real-world settings are many-agent, and agent interactions are complex mixtures of common-interest and competitive aspects. We consider Diplomacy, a 7-player board game designed to accentuate dilemmas resulting from many-agent interactions. It also features a large combinatorial action space and simultaneous moves, which are challenging for RL algorithms. We propose a simple yet effective approximate best response operator, designed to handle large combinatorial action spaces and simultaneous moves. We also introduce a family of policy iteration methods that approximate fictitious play. With these methods, we successfully apply RL to Diplomacy: we show that our agents convincingly outperform the previous state-of-the-art, and game theoretic equilibrium analysis shows that the new process yields consistent improvements.

Approximate exploitability: Learning a best response in large games

A common metric in games of imperfect information is exploitability, i.e. the performance of a policy against the worst-case opponent. This metric has many nice properties, but is intractable to compute in large games as it requires a full search of the game tree to calculate a best response to the given policy. We introduce a new metric, approximate exploitability, that calculates an analogous metric to exploitability using an approximate best response. This method scales to large games with tractable belief spaces. We focus only on the two-player, zero-sum case. Additionally, we provide empirical results for a specific instance of the method, demonstrating that it can effectively exploit agents in large games. We demonstrate that our method converges to exploitability in the tabular setting and the function approximation setting for small games, and demonstrate that it can consistently find exploits for weak policies in large games, showing results on Chess, Go, Heads-up No Limit Texas Hold'em, and other games.

From Poincaré Recurrence to Convergence in Imperfect Information Games: Finding Equilibrium via Regularization

In this paper we investigate the Follow the Regularized Leader dynamics in sequential imperfect information games (IIG). We generalize existing results of Poincar\'e recurrence from normal-form games to zero-sum two-player imperfect information games and other sequential game settings. We then investigate how adapting the reward (by adding a regularization term) of the game can give strong convergence guarantees in monotone games. We continue by showing how this reward adaptation technique can be leveraged to build algorithms that converge exactly to the Nash equilibrium. Finally, we show how these insights can be directly used to build state-of-the-art model-free algorithms for zero-sum two-player Imperfect Information Games (IIG).

OpenSpiel: A Framework for Reinforcement Learning in Games

OpenSpiel is a collection of environments and algorithms for research in general reinforcement learning and search/planning in games. OpenSpiel supports n-player (single- and multi- agent) zero-sum, cooperative and general-sum, one-shot and sequential, strictly turn-taking and simultaneous-move, perfect and imperfect information games, as well as traditional multiagent environments such as (partially- and fully- observable) grid worlds and social dilemmas. OpenSpiel also includes tools to analyze learning dynamics and other common evaluation metrics. This document serves both as an overview of the code base and an introduction to the terminology, core concepts, and algorithms across the fields of reinforcement learning, computational game theory, and search.

A Generalized Training Approach for Multiagent Learning

This paper investigates a population-based training regime based on game-theoretic principles called Policy-Spaced Response Oracles (PSRO). PSRO is general in the sense that it (1) encompasses well-known algorithms such as fictitious play and double oracle as special cases, and (2) in principle applies to general-sum, many-player games. Despite this, prior studies of PSRO have been focused on two-player zero-sum games, a regime wherein Nash equilibria are tractably computable. In moving from two-player zero-sum games to more general settings, computation of Nash equilibria quickly becomes infeasible. Here, we extend the theoretical underpinnings of PSRO by considering an alternative solution concept, {\alpha}-Rank, which is unique (thus faces no equilibrium selection issues, unlike Nash) and tractable to compute in general-sum, many-player settings. We establish convergence guarantees in several games classes, and identify links between Nash equilibria and {\alpha}-Rank. We demonstrate the competitive performance of {\alpha}-Rank-based PSRO against an exact Nash solver-based PSRO in 2-player Kuhn and Leduc Poker. We then go beyond the reach of prior PSRO applications by considering 3- to 5-player poker games, yielding instances where {\alpha}-Rank achieves faster convergence than approximate Nash solvers, thus establishing it as a favorable general games solver. We also carry out an initial empirical validation in MuJoCo soccer, illustrating the feasibility of the proposed approach in another complex domain.

Neural Replicator Dynamics

In multiagent learning, agents interact in inherently nonstationary environments due to their concurrent policy updates. It is, therefore, paramount to develop and analyze algorithms that learn effectively despite these nonstationarities. A number of works have successfully conducted this analysis under the lens of evolutionary game theory (EGT), wherein a population of individuals interact and evolve based on biologically-inspired operators. These studies have mainly focused on establishing connections to value-iteration based approaches in stateless or tabular games. We extend this line of inquiry to formally establish links between EGT and policy gradient (PG) methods, which have been extensively applied in single and multiagent learning. We pinpoint weaknesses of the commonly-used softmax PG algorithm in adversarial and nonstationary settings and contrast PG's behavior to that predicted by replicator dynamics (RD), a central model in EGT. We consequently provide theoretical results that establish links between EGT and PG methods, then derive Neural Replicator Dynamics (NeuRD), a parameterized version of RD that constitutes a novel method with several advantages. First, as NeuRD reduces to the well-studied no-regret Hedge algorithm in the tabular setting, it inherits no-regret guarantees that enable convergence to equilibria in games. Second, NeuRD is shown to be more adaptive to nonstationarity, in comparison to PG, when learning in canonical games and imperfect information benchmarks including Poker. Thirdly, modifying any PG-based algorithm to use the NeuRD update rule is straightforward and incurs no added computational costs. Finally, while single-agent learning is not the main focus of the paper, we verify empirically that NeuRD is competitive in these settings with a recent baseline algorithm.

Computing Approximate Equilibria in Sequential Adversarial Games by Exploitability Descent

In this paper, we present exploitability descent, a new algorithm to compute approximate equilibria in two-player zero-sum extensive-form games with imperfect information, by direct policy optimization against worst-case opponents. We prove that when following this optimization, the exploitability of a player's strategy converges asymptotically to zero, and hence when both players employ this optimization, the joint policies converge to a Nash equilibrium. Unlike fictitious play (XFP) and counterfactual regret minimization (CFR), our convergence result pertains to the policies being optimized rather than the average policies. Our experiments demonstrate convergence rates comparable to XFP and CFR in four benchmark games in the tabular case. Using function approximation, we find that our algorithm outperforms the tabular version in two of the games, which, to the best of our knowledge, is the first such result in imperfect information games among this class of algorithms.

Autocurricula and the Emergence of Innovation from Social Interaction: A Manifesto for Multi-Agent Intelligence Research

Evolution has produced a multi-scale mosaic of interacting adaptive units. Innovations arise when perturbations push parts of the system away from stable equilibria into new regimes where previously well-adapted solutions no longer work. Here we explore the hypothesis that multi-agent systems sometimes display intrinsic dynamics arising from competition and cooperation that provide a naturally emergent curriculum, which we term an autocurriculum. The solution of one social task often begets new social tasks, continually generating novel challenges, and thereby promoting innovation. Under certain conditions these challenges may become increasingly complex over time, demanding that agents accumulate ever more innovations.

The Hanabi Challenge: A New Frontier for AI Research

From the early days of computing, games have been important testbeds for studying how well machines can do sophisticated decision making. In recent years, machine learning has made dramatic advances with artificial agents reaching superhuman performance in challenge domains like Go, Atari, and some variants of poker. As with their predecessors of chess, checkers, and backgammon, these game domains have driven research by providing sophisticated yet well-defined challenges for artificial intelligence practitioners. We continue this tradition by proposing the game of Hanabi as a new challenge domain with novel problems that arise from its combination of purely cooperative gameplay and imperfect information in a two to five player setting. In particular, we argue that Hanabi elevates reasoning about the beliefs and intentions of other agents to the foreground. We believe developing novel techniques capable of imbuing artificial agents with such theory of mind will not only be crucial for their success in Hanabi, but also in broader collaborative efforts, and especially those with human partners. To facilitate future research, we introduce the open-source Hanabi Learning Environment, propose an experimental framework for the research community to evaluate algorithmic advances, and assess the performance of current state-of-the-art techniques.

Actor-Critic Policy Optimization in Partially Observable Multiagent Environments

Optimization of parameterized policies for reinforcement learning (RL) is an important and challenging problem in artificial intelligence. Among the most common approaches are algorithms based on gradient ascent of a score function representing discounted return. In this paper, we examine the role of these policy gradient and actor-critic algorithms in partially-observable multiagent environments. We show several candidate policy update rules and relate them to a foundation of regret minimization and multiagent learning techniques for the one-shot and tabular cases, leading to previously unknown convergence guarantees. We apply our method to model-free multiagent reinforcement learning in adversarial sequential decision problems (zero-sum imperfect information games), using RL-style function approximation. We evaluate on commonly used benchmark Poker domains, showing performance against fixed policies and empirical convergence to approximate Nash equilibria in self-play with rates similar to or better than a baseline model-free algorithm for zero sum games, without any domain-specific state space reductions.