A Unified Optimism-Agnostic Framework for Linear Bandits over Spherical Action Sets

Linear bandits model sequential decision-making problems with noisy rewards that are linear in the decision variable, where an agent must simultaneously learn about an unknown parameter that governs the mean rewards, while maximizing (expected) rewards over time. Two prominent algorithmic families--upper confidence bound (UCB) and Thompson sampling (TS)--achieve a balance of exploration (to estimate said parameter) and exploitation (utilization of knowledge about it) across time. The quality of estimation of that parameter depends on the eigenvalues of a design matrix. In this paper, we begin by showing that if the inference quality obtained from exploration, encoded in the minimum eigenv...

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