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We propose a simple model selection approach for algorithms in stochasticbandit and reinforcement learning problems. As opposed to prior work that(implicitly) assumes knowledge of the optimal regret, we only require that eachbase algorithm comes with a candidate regret bound that may or may not holdduring all rounds. In each round, our approach plays a base algorithm to keepthe candidate regret bounds of all remaining base algorithms balanced, andeliminates algorithms that violate their candidate bound. We prove that thetotal regret of this approach is bounded by the best valid candidate regretbound times a multiplicative factor. This factor is reasonably small in severalapplications, including linear bandits and MDPs with nested function classes,linear bandits with unknown misspecification, and LinUCB applied to linearbandits with different confidence parameters. We further show that, under asuitable gap-assumption, this factor only scales with the number of basealgorithms and not their complexity when the number of rounds is large enough.Finally, unlike recent efforts in model selection for linear stochasticbandits, our approach is versatile enough to also cover cases where the contextinformation is generated by an adversarial environment, rather than astochastic one.

Regret Bound Balancing and Elimination for Model Selection in Bandits and RL