2020/08/10 by Nadav Merlis, Shie Mannor, Merlis, Nadav +1 · 3 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Optimization and Search Problems #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.2008.03959
Accepted to AAAI2021
openalex publication_date 2020/08/10 · arxiv created 2021/09/12 · arxiv updated 2021/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the Multi-Armed Bandit (MAB) problem, where an agent sequentially chooses actions and observes rewards for the actions it took. While the majority of algorithms try to minimize the regret, i.e., the cumulative difference between the reward of the best action and the agent's action, this criterion might lead to undesirable results. For example, in large problems, or when the interaction with the environment is brief, finding an optimal arm is infeasible, and regret-minimizing algorithms tend to over-explore. To overcome this issue, algorithms for such settings should instead focus on playing near-optimal arms. To this end, we suggest a new, more lenient, regret criterion that ignores suboptimality gaps smaller than some ε. We then present a variant of the Thompson Sampling (TS) algorithm, called ε-TS, and prove its asymptotic optimality in terms of the lenient regret. Importantly, we show that when the mean of the optimal arm is high enough, the lenient regret of ε-TS is bounded by a constant. Finally, we show that ε-TS can be applied to improve the performance when the agent knows a lower bound of the suboptimality gaps.