Tracking the Best Strategy in an Extensive-Form Game
2026-08-10 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study a problem where a learner repeatedly plays a complex game and tries to do as well as possible against a fixed opponent. They focus on measuring how well the learner adapts when allowed to change strategies a limited number of times during the game. Their method achieves a good balance between switching strategies and overall performance, with a clear mathematical bound on regret (a measure of lost opportunity). The algorithm is also efficient and fast to run for each game round.
extensive-form gamebandit problemswitching regretmixed strategiesoblivious adversaryinformation setsregret boundalgorithm efficiency
Authors
Stephen Pasteris, Rahul Savani, Theodore Turocy
Abstract
We consider the extensive-form bandit problem where on each trial the learner plays an extensive-form game against an oblivious adversary. We focus on the notion of switching regret, which measures the expected performance of the learner against that of any switching sequence of mixed strategies in retrospect. Our algorithm takes a parameter $ρ>0$ and achieves a switching regret of $\tilde{\mathcal{O}}((1/ρ+ρK)\sqrt{H A T})$ where $K$ is the number of switches in the comparator sequence, $H$ is the maximum number of the learner's information sets that can be traversed during a play of the game and $A$ is the number of actions that the learner can possibly take. Our algorithm is extremely efficient, taking a per trial time of only $\mathcal{O}(H B)$ where $B$ is the maximum number of actions available to the learner at any of its information sets.