Nonstochastic Bandits with Infinitely Many Experts

02/09/2021

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by   X. Flora Meng, et al.

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We study the problem of nonstochastic bandits with infinitely many experts: A learner aims to maximize the total reward by taking actions sequentially based on bandit feedback while benchmarking against a countably infinite set of experts. We propose a variant of Exp4.P that, for finitely many experts, enables inference of correct expert rankings while preserving the order of the regret upper bound. We then incorporate the variant into a meta-algorithm that works on infinitely many experts. We prove a high-probability upper bound of 𝒪̃( i^*K + √(KT)) on the regret, up to polylog factors, where i^* is the unknown position of the best expert, K is the number of actions, and T is the time horizon. We also provide an example of structured experts and discuss how to expedite learning in such case. Our meta-learning algorithm achieves the tightest regret upper bound for the setting considered when i^* = 𝒪̃( √(T/K)). If a prior distribution is assumed to exist for i^*, the probability of satisfying a tight regret bound increases with T, the rate of which can be fast.