Safe Linear Thompson Sampling With Side Information

The design and performance analysis of bandit algorithms in the presence stage-wise safety or reliability constraints has recently garnered significant interest. In this work, we consider linear stochastic problem under additional unknown that need to be satisfied at each round. For problem, present analyze a new safe algorithm based on Thompson Sampling (TS). Our shows that, with high probability, chooses actions are round achieve cumulative regret order O (d 3/2 log xmlns:xlink="http://www.w3.org/1999/xlink">1/2 d ·T T). Remarkably, matches bound provided by [1], [2] for standard TS absence constraints. Also, our highlights how inherently randomized nature selection rule suffices properly expand set access particular, compare behavior alternative algorithms, which typically require distinct rounds randomization dedicated learning