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Equivalence Analysis between Counterfactual Regret Minimization and Online Mirror Descent
Weiming Liu · Huacong Jiang · Bin Li · Houqiang Li

Tue Jul 19 08:35 AM -- 08:40 AM (PDT) @ Room 309
in Theory: Online Learning/Bandits »

Follow-the-Regularized-Leader (FTRL) and Online Mirror Descent (OMD) are regret minimization algorithms for Online Convex Optimization (OCO), they are mathematically elegant but less practical in solving Extensive-Form Games (EFGs). Counterfactual Regret Minimization (CFR) is a technique for approximating Nash equilibria in EFGs. CFR and its variants have a fast convergence rate in practice, but their theoretical results are not satisfactory. In recent years, researchers have been trying to link CFRs with OCO algorithms, which may provide new theoretical results and inspire new algorithms. However, existing analysis is restricted to local decision points. In this paper, we show that CFRs with Regret Matching and Regret Matching+ are equivalent to special cases of FTRL and OMD, respectively. According to these equivalences, a new FTRL and a new OMD algorithm, which can be considered as extensions of vanilla CFR and CFR+, are derived. The experimental results show that the two variants converge faster than conventional FTRL and OMD, even faster than vanilla CFR and CFR+ in some EFGs.

Keywords: T: Game Theory · T: Online Learning and Bandits

Author Information

Weiming Liu (University of Science and Technology of China)
Huacong Jiang (University of Science and Technology of China)
Bin Li (University of Science and Technology of China)
Houqiang Li (University of Science and Technology of China)

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