Online Sign Identification: Minimization of the Number of Errors in Thresholding Bandits

TL;DR

This paper introduces a family of algorithms for the fixed budget thresholding bandit problem, demonstrating that adaptive methods outperform non-adaptive ones in minimizing errors, with theoretical guarantees and empirical evidence.

Contribution

It presents a new family of algorithms inspired by Frank-Wolfe, providing performance analysis and showing adaptive methods outperform non-adaptive oracles in this setting.

Findings

Adaptive algorithms outperform non-adaptive oracles empirically.

New explicit algorithms achieve losses close to non-adaptive oracle performance.

Surprising adaptive advantage explained through a toy problem.

Abstract

In the fixed budget thresholding bandit problem, an algorithm sequentially allocates a budgeted number of samples to different distributions. It then predicts whether the mean of each distribution is larger or lower than a given threshold. We introduce a large family of algorithms (containing most existing relevant ones), inspired by the Frank-Wolfe algorithm, and provide a thorough yet generic analysis of their performance. This allowed us to construct new explicit algorithms, for a broad class of problems, whose losses are within a small constant factor of the non-adaptive oracle ones. Quite interestingly, we observed that adaptive methods empirically greatly out-perform non-adaptive oracles, an uncommon behavior in standard online learning settings, such as regret minimization. We explain this surprising phenomenon on an insightful toy problem.