Multi-Environment Meta-Learning in Stochastic Linear Bandits

TL;DR

This paper explores meta-learning in multi-environment stochastic linear bandits, proposing a regularized OFUL algorithm that effectively adapts to tasks from a mixture of environments, improving regret bounds over traditional methods.

Contribution

It introduces a novel regularized OFUL algorithm for meta-learning in mixture environment bandits, handling environment misclassification and outperforming existing approaches.

Findings

Achieves low regret on new tasks without environment knowledge.

Effectively manages environment misclassification impacts.

Outperforms learning each task separately or without environment recognition.

Abstract

In this work we investigate meta-learning (or learning-to-learn) approaches in multi-task linear stochastic bandit problems that can originate from multiple environments. Inspired by the work of [1] on meta-learning in a sequence of linear bandit problems whose parameters are sampled from a single distribution (i.e., a single environment), here we consider the feasibility of meta-learning when task parameters are drawn from a mixture distribution instead. For this problem, we propose a regularized version of the OFUL algorithm that, when trained on tasks with labeled environments, achieves low regret on a new task without requiring knowledge of the environment from which the new task originates. Specifically, our regret bound for the new algorithm captures the effect of environment misclassification and highlights the benefits over learning each task separately or meta-learning without recognition of the distinct mixture components.