Satisficing in multi-armed bandit problems

TL;DR

This paper introduces satisficing objectives for multi-armed bandit problems, establishing their equivalence to standard maximizing problems, and develops modified UCL algorithms that efficiently achieve satisfactory reward levels.

Contribution

It proposes new satisficing objectives for bandit problems, proves their equivalence to existing models, and develops algorithms that efficiently meet performance thresholds.

Findings

Satisficing objectives are equivalent to standard bandit problems under certain conditions.

Modified UCL algorithms effectively achieve satisficing performance.

Different satisficing objectives lead to qualitatively different exploration behaviors.

Abstract

Satisficing is a relaxation of maximizing and allows for less risky decision making in the face of uncertainty. We propose two sets of satisficing objectives for the multi-armed bandit problem, where the objective is to achieve reward-based decision-making performance above a given threshold. We show that these new problems are equivalent to various standard multi-armed bandit problems with maximizing objectives and use the equivalence to find bounds on performance. The different objectives can result in qualitatively different behavior; for example, agents explore their options continually in one case and only a finite number of times in another. For the case of Gaussian rewards we show an additional equivalence between the two sets of satisficing objectives that allows algorithms developed for one set to be applied to the other. We then develop variants of the Upper Credible Limit (UCL) algorithm that solve the problems with satisficing objectives and show that these modified UCL algorithms achieve efficient satisficing performance.