The Advantage Regret-Matching Actor-Critic

Regret minimization has played a key role in online learning, equilibrium computation in games, and reinforcement learning (RL). In this paper, we describe a general model-free RL method for no-regret learning based on repeated reconsideration of past behavior. We propose a model-free RL algorithm, the AdvantageRegret-Matching Actor-Critic (ARMAC): rather than saving past state-action data, ARMAC saves a buffer of past policies, replaying through them to reconstruct hindsight assessments of past behavior. These retrospective value estimates are used to predict conditional advantages which, combined with regret matching, produces a new policy. In particular, ARMAC learns from sampled trajectories in a centralized training setting, without requiring the application of importance sampling commonly used in Monte Carlo counterfactual regret (CFR) minimization; hence, it does not suffer from excessive variance in large environments. In the single-agent setting, ARMAC shows an interesting form of exploration by keeping past policies intact. In the multiagent setting, ARMAC in self-play approaches Nash equilibria on some partially-observable zero-sum benchmarks. We provide exploitability estimates in the significantly larger game of betting-abstracted no-limit Texas Hold'em.

Navigating the Landscape of Games

Games are traditionally recognized as one of the key testbeds underlying progress in artificial intelligence (AI), aptly referred to as the "Drosophila of AI". Traditionally, researchers have focused on using games to build strong AI agents that, e.g., achieve human-level performance. This progress, however, also requires a classification of how 'interesting' a game is for an artificial agent. Tackling this latter question not only facilitates an understanding of the characteristics of learnt AI agents in games, but also helps to determine what game an AI should address next as part of its training. Here, we show how network measures applied to so-called response graphs of large-scale games enable the creation of a useful landscape of games, quantifying the relationships between games of widely varying sizes, characteristics, and complexities. We illustrate our findings in various domains, ranging from well-studied canonical games to significantly more complex empirical games capturing the performance of trained AI agents pitted against one another. Our results culminate in a demonstration of how one can leverage this information to automatically generate new and interesting games, including mixtures of empirical games synthesized from real world games.

Real World Games Look Like Spinning Tops

This paper investigates the geometrical properties of real world games (e.g. Tic-Tac-Toe, Go, StarCraft II). We hypothesise that their geometrical structure resemble a spinning top, with the upright axis representing transitive strength, and the radial axis, which corresponds to the number of cycles that exist at a particular transitive strength, representing the non-transitive dimension. We prove the existence of this geometry for a wide class of real world games, exposing their temporal nature. Additionally, we show that this unique structure also has consequences for learning - it clarifies why populations of strategies are necessary for training of agents, and how population size relates to the structure of the game. Finally, we empirically validate these claims by using a selection of nine real world two-player zero-sum symmetric games, showing 1) the spinning top structure is revealed and can be easily re-constructed by using a new method of Nash clustering to measure the interaction between transitive and cyclical strategy behaviour, and 2) the effect that population size has on the convergence in these games.

The Automated Inspection of Opaque Liquid Vaccines

In the pharmaceutical industry the screening of opaque vaccines containing suspensions is currently a manual task carried out by trained human visual inspectors. We show that deep learning can be used to effectively automate this process. A moving contrast is required to distinguish anomalies from other particles, reflections and dust resting on a vial's surface. We train 3D-ConvNets to predict the likelihood of 20-frame video samples containing anomalies. Our unaugmented dataset consists of hand-labelled samples, recorded using vials provided by the HAL Allergy Group, a pharmaceutical company. We trained ten randomly initialized 3D-ConvNets to provide a benchmark, observing mean AUROC scores of 0.94 and 0.93 for positive samples (containing anomalies) and negative (anomaly-free) samples, respectively. Using Frame-Completion Generative Adversarial Networks we: (i) introduce an algorithm for computing saliency maps, which we use to verify that the 3D-ConvNets are indeed identifying anomalies; (ii) propose a novel self-training approach using the saliency maps to determine if multiple networks agree on the location of anomalies. Our self-training approach allows us to augment our data set by labelling 217,888 additional samples. 3D-ConvNets trained with our augmented dataset improve on the results we get when we train only on the unaugmented dataset.

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).

Multiagent Evaluation under Incomplete Information

This paper investigates the evaluation of learned multiagent strategies in the incomplete information setting, which plays a critical role in ranking and training of agents. Traditionally, researchers have relied on Elo ratings for this purpose, with recent works also using methods based on Nash equilibria. Unfortunately, Elo is unable to handle intransitive agent interactions, and other techniques are restricted to zero-sum, two-player settings or are limited by the fact that the Nash equilibrium is intractable to compute. Recently, a ranking method called {\alpha}-Rank, relying on a new graph-based game-theoretic solution concept, was shown to tractably apply to general games. However, evaluations based on Elo or {\alpha}-Rank typically assume noise-free game outcomes, despite the data often being collected from noisy simulations, making this assumption unrealistic in practice. This paper investigates multiagent evaluation in the incomplete information regime, involving general-sum many-player games with noisy outcomes. We derive sample complexity guarantees required to confidently rank agents in this setting. We propose adaptive algorithms for accurate ranking, provide correctness and sample complexity guarantees, then introduce a means of connecting uncertainties in noisy match outcomes to uncertainties in rankings. We evaluate the performance of these approaches in several domains, including Bernoulli games, a soccer meta-game, and Kuhn poker.

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.