Upper Confidence Bounds for Combining Stochastic Bandits

Abstract

We provide a simple method to combine stochastic bandit algorithms. Our approach is based on a "meta-UCB" procedure that treats each of N individual bandit algorithms as arms in a higher-level N -armed bandit problem that we solve with a variant of the classic UCB algorithm. Our final regret depends only on the regret of the base algorithm with the best regret in hindsight. This approach provides an easy and intuitive alternative strategy to the CORRAL algorithm for adversarial bandits, without requiring the stability conditions imposed by CORRAL on the base algorithms. Our results match lower bounds in several settings, and we provide empirical validation of our algorithm on misspecified linear bandit and model selection problems.

Universal and data-adaptive algorithms for model selection in linear contextual bandits

“…One of the first such approaches is the Corral algorithm of Agarwal et al [3], which uses online mirror descent with the log-barrier regularizer as the meta-algorithm. Subsequent work focuses on adapting Corral to the stochastic setting [31,28] and developing UCB-style meta-algorithms [11,4]. These approaches are quite general and can often be used with abstract non-linear function classes.…”