# Satisficing in Time-Sensitive Bandit Learning

## TL;DR

This paper introduces satisficing Thompson sampling, an algorithm designed for time-sensitive bandit problems, which focuses on near-optimal actions requiring less information, showing significant advantages over traditional methods like Thompson sampling.

## Contribution

The paper proposes satisficing Thompson sampling, providing theoretical bounds and demonstrating its effectiveness in linear and infinite-armed bandits, addressing time sensitivity in learning.

## Key findings

- Satisficing Thompson sampling reduces expected discounted regret.
- The approach outperforms traditional Thompson sampling in certain bandit settings.
- The method links satisficing with rate distortion theory for action selection.

## Abstract

Much of the recent literature on bandit learning focuses on algorithms that aim to converge on an optimal action. One shortcoming is that this orientation does not account for time sensitivity, which can play a crucial role when learning an optimal action requires much more information than near-optimal ones. Indeed, popular approaches such as upper-confidence-bound methods and Thompson sampling can fare poorly in such situations. We consider instead learning a satisficing action, which is near-optimal while requiring less information, and propose satisficing Thompson sampling, an algorithm that serves this purpose. We establish a general bound on expected discounted regret and study the application of satisficing Thompson sampling to linear and infinite-armed bandits, demonstrating arbitrarily large benefits over Thompson sampling. We also discuss the relation between the notion of satisficing and the theory of rate distortion, which offers guidance on the selection of satisficing actions.