Best Arm Identification with Minimal Regret

• URL: http://arxiv.org/abs/2409.18909v1
• Date: Fri, 27 Sep 2024 16:46:02 GMT
• Title: Best Arm Identification with Minimal Regret
• Authors: Junwen Yang, Vincent Y. F. Tan, Tianyuan Jin,
• Abstract summary: Best arm identification problem elegantly amalgamates regret minimization and BAI. Agent's goal is to identify the best arm with a prescribed confidence level. Double KL-UCB algorithm achieves optimality as the confidence level tends to zero.
• Score: 55.831935724659175
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Motivated by real-world applications that necessitate responsible experimentation, we introduce the problem of best arm identification (BAI) with minimal regret. This innovative variant of the multi-armed bandit problem elegantly amalgamates two of its most ubiquitous objectives: regret minimization and BAI. More precisely, the agent's goal is to identify the best arm with a prescribed confidence level $\delta$, while minimizing the cumulative regret up to the stopping time. Focusing on single-parameter exponential families of distributions, we leverage information-theoretic techniques to establish an instance-dependent lower bound on the expected cumulative regret. Moreover, we present an intriguing impossibility result that underscores the tension between cumulative regret and sample complexity in fixed-confidence BAI. Complementarily, we design and analyze the Double KL-UCB algorithm, which achieves asymptotic optimality as the confidence level tends to zero. Notably, this algorithm employs two distinct confidence bounds to guide arm selection in a randomized manner. Our findings elucidate a fresh perspective on the inherent connections between regret minimization and BAI.

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