[@abe1999associative] and [@foster2020beyond] — this is kind of surprising, as the idea behind the derivation of our algorithm is very different from the ideas behind [@abe1999associative] and [@foster2020beyond]. This suggests that such simple probabilistic selection strategies might be more intriguing and more essential for bandits than people previously think, and we believe that they worth further attention from the bandit community. We hope that our work, together with [@abe1999associative] and [@foster2020beyond], can provide diverse perspectives on how to understand such strategies.

As a final remark, we emphasize that compared with each line of research that we mention above, our approach has new contributions beyond them which seem necessary for our arguments to hold. We will elaborate on such new contributions in §\[sec:alg\] and §\[sec:analysis\].

Organization and Notations
--------------------------

The rest of the paper is organized as follows. We begin our study focusing on the case of finite function classes in §\[sec:alg\] and §\[sec:analysis\]. In §\[sec:alg\], we introduce our algorithm and state its properties as well as theoretical guarantees. In §\[sec:analysis\], we present our statistical analysis and explain the idea behind our algorithm. In §\[sec:extension\], we extend our results to the case of infinite function classes. We conclude our paper in 