Learning to Beat ByteRL: Exploitability of Collectible Card Game Agents

While Poker, as a family of games, has been studied extensively in the last decades, collectible card games have seen relatively little attention. Only recently have we seen an agent that can compete with professional human players in Hearthstone, one of the most popular collectible card games. Although artificial agents must be able to work with imperfect information in both of these genres, collectible card games pose another set of distinct challenges. Unlike in many poker variants, agents must deal with state space so vast that even enumerating all states consistent with the agent's beliefs is intractable, rendering the current search methods unusable and requiring the agents to opt for other techniques. In this paper, we investigate the strength of such techniques for this class of games. Namely, we present preliminary analysis results of ByteRL, the state-of-the-art agent in Legends of Code and Magic and Hearthstone. Although ByteRL beat a top-10 Hearthstone player from China, we show that its play in Legends of Code and Magic is highly exploitable.

Learning not to Regret

Regret minimization is a key component of many algorithms for finding Nash equilibria in imperfect-information games. To scale to games that cannot fit in memory, we can use search with value functions. However, calling the value functions repeatedly in search can be expensive. Therefore, it is desirable to minimize regret in the search tree as fast as possible. We propose to accelerate the regret minimization by introducing a general ``learning not to regret'' framework, where we meta-learn the regret minimizer. The resulting algorithm is guaranteed to minimize regret in arbitrary settings and is (meta)-learned to converge fast on a selected distribution of games. Our experiments show that meta-learned algorithms converge substantially faster than prior regret minimization algorithms.

Player of Games

Games have a long history of serving as a benchmark for progress in artificial intelligence. Recently, approaches using search and learning have shown strong performance across a set of perfect information games, and approaches using game-theoretic reasoning and learning have shown strong performance for specific imperfect information poker variants. We introduce Player of Games, a general-purpose algorithm that unifies previous approaches, combining guided search, self-play learning, and game-theoretic reasoning. Player of Games is the first algorithm to achieve strong empirical performance in large perfect and imperfect information games -- an important step towards truly general algorithms for arbitrary environments. We prove that Player of Games is sound, converging to perfect play as available computation time and approximation capacity increases. Player of Games reaches strong performance in chess and Go, beats the strongest openly available agent in heads-up no-limit Texas hold'em poker (Slumbot), and defeats the state-of-the-art agent in Scotland Yard, an imperfect information game that illustrates the value of guided search, learning, and game-theoretic reasoning.

Search in Imperfect Information Games

From the very dawn of the field, search with value functions was a fundamental concept of computer games research. Turing's chess algorithm from 1950 was able to think two moves ahead, and Shannon's work on chess from $1950$ includes an extensive section on evaluation functions to be used within a search. Samuel's checkers program from 1959 already combines search and value functions that are learned through self-play and bootstrapping. TD-Gammon improves upon those ideas and uses neural networks to learn those complex value functions -- only to be again used within search. The combination of decision-time search and value functions has been present in the remarkable milestones where computers bested their human counterparts in long standing challenging games -- DeepBlue for Chess and AlphaGo for Go. Until recently, this powerful framework of search aided with (learned) value functions has been limited to perfect information games. As many interesting problems do not provide the agent perfect information of the environment, this was an unfortunate limitation. This thesis introduces the reader to sound search for imperfect information games.

Solving Common-Payoff Games with Approximate Policy Iteration

For artificially intelligent learning systems to have widespread applicability in real-world settings, it is important that they be able to operate decentrally. Unfortunately, decentralized control is difficult -- computing even an epsilon-optimal joint policy is a NEXP complete problem. Nevertheless, a recently rediscovered insight -- that a team of agents can coordinate via common knowledge -- has given rise to algorithms capable of finding optimal joint policies in small common-payoff games. The Bayesian action decoder (BAD) leverages this insight and deep reinforcement learning to scale to games as large as two-player Hanabi. However, the approximations it uses to do so prevent it from discovering optimal joint policies even in games small enough to brute force optimal solutions. This work proposes CAPI, a novel algorithm which, like BAD, combines common knowledge with deep reinforcement learning. However, unlike BAD, CAPI prioritizes the propensity to discover optimal joint policies over scalability. While this choice precludes CAPI from scaling to games as large as Hanabi, empirical results demonstrate that, on the games to which CAPI does scale, it is capable of discovering optimal joint policies even when other modern multi-agent reinforcement learning algorithms are unable to do so. Code is available at https://github.com/ssokota/capi .

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.

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.

Low-Variance and Zero-Variance Baselines for Extensive-Form Games

Extensive-form games (EFGs) are a common model of multi-agent interactions with imperfect information. State-of-the-art algorithms for solving these games typically perform full walks of the game tree that can prove prohibitively slow in large games. Alternatively, sampling-based methods such as Monte Carlo Counterfactual Regret Minimization walk one or more trajectories through the tree, touching only a fraction of the nodes on each iteration, at the expense of requiring more iterations to converge due to the variance of sampled values. In this paper, we extend recent work that uses baseline estimates to reduce this variance. We introduce a framework of baseline-corrected values in EFGs that generalizes the previous work. Within our framework, we propose new baseline functions that result in significantly reduced variance compared to existing techniques. We show that one particular choice of such a function --- predictive baseline --- is provably optimal under certain sampling schemes. This allows for efficient computation of zero-variance value estimates even along sampled trajectories.

Rethinking Formal Models of Partially Observable Multiagent Decision Making

Multiagent decision-making problems in partially observable environments are usually modeled as either extensive-form games (EFGs) within the game theory community or partially observable stochastic games (POSGs) within the reinforcement learning community. While most practical problems can be modeled in both formalisms, the communities using these models are mostly distinct with little sharing of ideas or advances. The last decade has seen dramatic progress in algorithms for EFGs, mainly driven by the challenge problem of poker. We have seen computational techniques achieving super-human performance, some variants of poker are essentially solved, and there are now sound local search algorithms which were previously thought impossible. While the advances have garnered attention, the fundamental advances are not yet understood outside the EFG community. This can be largely explained by the starkly different formalisms between the game theory and reinforcement learning communities and, further, by the unsuitability of the original EFG formalism to make the ideas simple and clear. This paper aims to address these hindrances, by advocating a new unifying formalism, a variant of POSGs, which we call Factored-Observation Games (FOGs). We prove that any timeable perfect-recall EFG can be efficiently modeled as a FOG as well as relating FOGs to other existing formalisms. Additionally, a FOG explicitly identifies the public and private components of observations, which is fundamental to the recent EFG breakthroughs. We conclude by presenting the two building-blocks of these breakthroughs --- counterfactual regret minimization and public state decomposition --- in the new formalism, illustrating our goal of a simpler path for sharing recent advances between game theory and reinforcement learning community.

Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games using Baselines

Learning strategies for imperfect information games from samples of interaction is a challenging problem. A common method for this setting, Monte Carlo Counterfactual Regret Minimization (MCCFR), can have slow long-term convergence rates due to high variance. In this paper, we introduce a variance reduction technique (VR-MCCFR) that applies to any sampling variant of MCCFR. Using this technique, per-iteration estimated values and updates are reformulated as a function of sampled values and state-action baselines, similar to their use in policy gradient reinforcement learning. The new formulation allows estimates to be bootstrapped from other estimates within the same episode, propagating the benefits of baselines along the sampled trajectory; the estimates remain unbiased even when bootstrapping from other estimates. Finally, we show that given a perfect baseline, the variance of the value estimates can be reduced to zero. Experimental evaluation shows that VR-MCCFR brings an order of magnitude speedup, while the empirical variance decreases by three orders of magnitude. The decreased variance allows for the first time CFR+ to be used with sampling, increasing the speedup to two orders of magnitude.