No-Regret Learning in Extensive-Form Games with Imperfect Recall
This work addresses a limitation in game theory and AI for researchers and practitioners, enabling more efficient learning in complex games with imperfect recall, though it is incremental as it extends existing CFR theory.
The paper tackles the problem of applying Counterfactual Regret Minimization (CFR) to extensive-form games with imperfect recall, where CFR's guarantees previously did not hold, and presents the first regret bound for a general class of such games, showing that CFR can achieve a small increase in regret for significant memory reduction in domains like die-roll poker, phantom tic-tac-toe, and Bluff.
Counterfactual Regret Minimization (CFR) is an efficient no-regret learning algorithm for decision problems modeled as extensive games. CFR's regret bounds depend on the requirement of perfect recall: players always remember information that was revealed to them and the order in which it was revealed. In games without perfect recall, however, CFR's guarantees do not apply. In this paper, we present the first regret bound for CFR when applied to a general class of games with imperfect recall. In addition, we show that CFR applied to any abstraction belonging to our general class results in a regret bound not just for the abstract game, but for the full game as well. We verify our theory and show how imperfect recall can be used to trade a small increase in regret for a significant reduction in memory in three domains: die-roll poker, phantom tic-tac-toe, and Bluff.