Near Optimal Pure Exploration in Logistic Bandits

TL;DR

This paper introduces the first near-optimal track-and-stop algorithm for pure exploration in logistic bandits, addressing a significant gap in the field by providing an efficient solution that approaches the theoretical lower bound.

Contribution

The paper develops Log-TS, the first algorithm for pure exploration in logistic bandits, achieving asymptotic optimality up to a logarithmic factor.

Findings

Log-TS asymptotically matches the instance-specific lower bound.

Efficient algorithm for pure exploration in generalized linear model bandits.

Addresses a gap in optimal algorithms for complex bandit settings.

Abstract

Bandit algorithms have garnered significant attention due to their practical applications in real-world scenarios. However, beyond simple settings such as multi-arm or linear bandits, optimal algorithms remain scarce. Notably, no optimal solution exists for pure exploration problems in the context of generalized linear model (GLM) bandits. In this paper, we narrow this gap and develop the first track-and-stop algorithm for general pure exploration problems under the logistic bandit called logistic track-and-stop (Log-TS). Log-TS is an efficient algorithm that asymptotically matches an approximation for the instance-specific lower bound of the expected sample complexity up to a logarithmic factor.