Sparsity-Agnostic Linear Bandits with Adaptive Adversaries

• URL: http://arxiv.org/abs/2406.01192v1
• Date: Mon, 3 Jun 2024 10:54:58 GMT
• Title: Sparsity-Agnostic Linear Bandits with Adaptive Adversaries
• Authors: Tianyuan Jin, Kyoungseok Jang, Nicolò Cesa-Bianchi,
• Abstract summary: We study linear bandits where, in each round, the learner receives a set of actions (i.e., feature vectors) from which it chooses an element and obtains a reward. The expected reward is a fixed but unknown linear function of the chosen action. We study sparse regret bounds, that depend on the number $S$ of non-zero coefficients in the linear reward function.
• Score: 19.84322270472381
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study stochastic linear bandits where, in each round, the learner receives a set of actions (i.e., feature vectors), from which it chooses an element and obtains a stochastic reward. The expected reward is a fixed but unknown linear function of the chosen action. We study sparse regret bounds, that depend on the number $S$ of non-zero coefficients in the linear reward function. Previous works focused on the case where $S$ is known, or the action sets satisfy additional assumptions. In this work, we obtain the first sparse regret bounds that hold when $S$ is unknown and the action sets are adversarially generated. Our techniques combine online to confidence set conversions with a novel randomized model selection approach over a hierarchy of nested confidence sets. When $S$ is known, our analysis recovers state-of-the-art bounds for adversarial action sets. We also show that a variant of our approach, using Exp3 to dynamically select the confidence sets, can be used to improve the empirical performance of stochastic linear bandits while enjoying a regret bound with optimal dependence on the time horizon.

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