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.

References in corpus (7)

• Taming the Monster: A Fast and Simple Algorithm for Contextual Bandits
• Contextual Bandit Algorithms with Supervised Learning Guarantees
• The best of both worlds: stochastic and adversarial bandits
• Model Selection in Contextual Stochastic Bandit Problems
• The Pareto Regret Frontier for Bandits
• Regret Balancing for Bandit and RL Model Selection
• OSOM: A simultaneously optimal algorithm for multi-armed and linear contextual bandits

Cited by in corpus (2)

• Universal and data-adaptive algorithms for model selection in linear contextual bandits
• Pareto Optimal Model Selection in Linear Bandits