Thompson Sampling for Robust Transfer in Multi-Task Bandits

TL;DR

This paper introduces a Thompson Sampling-based algorithm for multi-task bandit problems, demonstrating its near-optimal theoretical performance and superior empirical results over UCB-based methods and non-transfer baselines.

Contribution

It extends Thompson Sampling to multi-task bandits with a novel analysis, showing near-optimal guarantees and improved empirical performance.

Findings

Thompson Sampling achieves near-optimal performance in multi-task bandits.

The proposed algorithm outperforms UCB-based and non-transfer baselines.

A new concentration inequality for multi-task data aggregation is developed.

Abstract

We study the problem of online multi-task learning where the tasks are performed within similar but not necessarily identical multi-armed bandit environments. In particular, we study how a learner can improve its overall performance across multiple related tasks through robust transfer of knowledge. While an upper confidence bound (UCB)-based algorithm has recently been shown to achieve nearly-optimal performance guarantees in a setting where all tasks are solved concurrently, it remains unclear whether Thompson sampling (TS) algorithms, which have superior empirical performance in general, share similar theoretical properties. In this work, we present a TS-type algorithm for a more general online multi-task learning protocol, which extends the concurrent setting. We provide its frequentist analysis and prove that it is also nearly-optimal using a novel concentration inequality for multi-task data aggregation at random stopping times. Finally, we evaluate the algorithm on synthetic data and show that the TS-type algorithm enjoys superior empirical performance in comparison with the UCB-based algorithm and a baseline algorithm that performs TS for each individual task without transfer.