Parallelizing Counterfactual Regret Minimization

2026-05-13

AI Summary

This work addresses the limited scalability of existing counterfactual regret minimization (CFR) algorithms in large-scale imperfect-information games, which stems from the absence of efficient parallelization methods. The paper introduces, for the first time, a general-purpose parallelization framework applicable to the entire family of CFR algorithms—including CFR+ and discounted CFR—by reformulating their computations as sequences of linear algebra operations. This reformulation enables seamless integration with established high-performance parallel computing techniques. Implemented on GPUs, the proposed framework overcomes the sequential bottlenecks inherent in traditional CPU-based approaches, achieving up to four orders of magnitude speedup over the CPU implementation in Google DeepMind’s OpenSpiel and substantially accelerating the solution of large-scale games.

Abstract

Parallelization has played an instrumental role in the field of artificial intelligence (AI), drastically reducing the time taken to train and evaluate large AI models. In contrast to its impact in the broader field of AI, applying parallelization to computational game solving is relatively unexplored, despite its great potential. In this paper, we parallelize the family of counterfactual regret minimization (CFR) algorithms, which were central to important breakthroughs for solving large imperfect-information games. We present a generalized parallelization framework, reframing CFR as a series of linear algebra operations. Then, existing techniques for parallelizing linear algebra operations can be applied to accelerate CFR. We also describe how our technique can be applied to other tabular members of the CFR family of algorithms, including the state-of-the-art, such as CFR+, discounted CFR, and predictive variants of CFR. Experimentally, we show that our CFR implementation on a GPU is up to four orders of magnitude faster than Google DeepMind OpenSpiel's CFR implementations on a CPU.

Problem

• parallelization
• counterfactual regret minimization
• imperfect-information games
• computational game solving
• CFR algorithms

Innovation

• parallelization
• counterfactual regret minimization
• linear algebra
• imperfect-information games
• GPU acceleration