The Role of Contextual Information in Best Arm Identification
This work addresses the problem of faster and more efficient decision-making in bandit algorithms for researchers and practitioners, though it is incremental as it builds on existing methods.
The paper tackles the best-arm identification problem in stochastic bandits by incorporating contextual information to improve efficiency, showing that a context-aware strategy asymptotically matches lower bounds and reduces sample complexity compared to prior work.
We study the best-arm identification problem with fixed confidence when contextual (covariate) information is available in stochastic bandits. Although we can use contextual information in each round, we are interested in the marginalized mean reward over the contextual distribution. Our goal is to identify the best arm with a minimal number of samplings under a given value of the error rate. We show the instance-specific sample complexity lower bounds for the problem. Then, we propose a context-aware version of the "Track-and-Stop" strategy, wherein the proportion of the arm draws tracks the set of optimal allocations and prove that the expected number of arm draws matches the lower bound asymptotically. We demonstrate that contextual information can be used to improve the efficiency of the identification of the best marginalized mean reward compared with the results of Garivier & Kaufmann (2016). We experimentally confirm that context information contributes to faster best-arm identification.