Counterfactual regret minimization (CFR) is a family of algorithms for effectively solving imperfect-information games. To enhance CFR's applicability in large games, researchers use neural networks to approximate its behavior. However, existing methods are mainly based on vanilla CFR and struggle to effectively integrate more advanced CFR variants. In this work, we propose an efficient model-free neural CFR algorithm, overcoming the limitations of existing methods in approximating advanced CFR variants. At each iteration, it collects variance-reduced sampled advantages based on a value network, fits cumulative advantages by bootstrapping, and applies discounting and clipping operations to simulate the update mechanisms of advanced CFR variants. Experimental results show that, compared with model-free neural algorithms, it exhibits faster convergence in typical imperfect-information games and demonstrates stronger adversarial performance in a large poker game.

Counterfactual regret minimization (CFR) is a family of iterative algorithms showing promising results in solving imperfect-information games. Recent novel CFR variants (e.g., CFR+, DCFR) have significantly improved the convergence rate of the vanilla CFR. The key to these CFR variants’ performance is weighting each iteration non-uniformly, i.e., discounting earlier iterations. However, these algorithms use a fixed, manually-specified scheme to weight each iteration, which enormously limits their potential. In this work, we propose Dynamic Discounted CFR (DDCFR), the first equilibrium-finding framework that discounts prior iterations using a dynamic, automatically-learned scheme. We formalize CFR’s iteration process as a carefully designed Markov decision process and transform the discounting scheme learning problem into a policy optimization problem within it. The learned discounting scheme dynamically weights each iteration on the fly using information available at runtime. Experimental results across multiple games demonstrate that DDCFR’s dynamic discounting scheme has a strong generalization ability and leads to faster convergence with improved performance. The code is available at https://github.com/rpSebastian/DDCFR.

Owing to the unremitting efforts from a few institutes, researchers have recently made significant progress in designing superhuman artificial intelligence (AI) in no-limit Texas hold'em (NLTH), the primary testbed for large-scale imperfect-information game research. However, it remains challenging for new researchers to study this problem since there are no standard benchmarks for comparing with existing methods, which hinders further developments in this research area. This work presents OpenHoldem, an integrated benchmark for large-scale imperfect-information game research using NLTH. OpenHoldem makes three main contributions to this research direction: 1) a standardized evaluation protocol for thoroughly evaluating different NLTH AIs; 2) four publicly available strong baselines for NLTH AI; and 3) an online testing platform with easy-to-use APIs for public NLTH AI evaluation. We will publicly release OpenHoldem and hope it facilitates further studies on the unsolved theoretical and computational issues in this area and cultivates crucial research problems like opponent modeling and human-computer interactive learning.

Counterfactual regret minimization (CFR) is the most commonly used algorithm to approximately solving two-player zero-sum imperfect-information games (IIGs). In recent years, a series of novel CFR variants such as CFR+, Linear CFR, DCFR have been proposed and have significantly improved the convergence rate of the vanilla CFR. However, most of these new variants are hand-designed by researchers through trial and error based on different motivations, which generally requires a tremendous amount of efforts and insights. This work proposes to meta-learn novel CFR algorithms through evolution to ease the burden of manual algorithm design. We first design a search language that is rich enough to represent many existing hand-designed CFR variants. We then exploit a scalable regularized evolution algorithm with a bag of acceleration techniques to efficiently search over the combinatorial space of algorithms defined by this language. The learned novel CFR algorithm can generalize to new IIGs not seen during training and performs on par with or better than existing state-of-the-art CFR variants. The code is available at https://github.com/rpSebastian/AutoCFR.

Opponent modeling is essential to exploit sub-optimal opponents in strategic interactions. Most previous works focus on building explicit models to predict the opponents' styles or strategies, which require a large amount of data to train the model and lack adaptability to unknown opponents. In this work, we propose a novel Learning to Exploit (L2E) framework for implicit opponent modeling. L2E acquires the ability to exploit opponents through a few interactions with different opponents during training of a neural network and can quickly adapt to new opponents with unknown styles during testing. To automatically produce challenging and diverse opponents for training, we further present a novel opponent strategy generation algorithm. We evaluate L2E on two poker games and one grid soccer game, which are the commonly used benchmarks for opponent modeling. Comprehensive experimental results indicate that L2E rapidly adapts to diverse styles of unknown opponents.