Meta-Learning for Simple Regret Minimization

TL;DR

This paper introduces novel meta-learning algorithms for simple regret minimization in bandit problems, providing theoretical guarantees and empirical evaluations for Bayesian and frequentist approaches.

Contribution

It presents the first Bayesian and frequentist meta-learning algorithms for simple regret minimization in bandits, with theoretical regret bounds and practical instantiations.

Findings

Bayesian meta-learning achieves regret of O(m / \u221a n)

Frequentist meta-learning achieves regret of O( m n + m /  n)

Algorithms perform well across various bandit environments.

Abstract

We develop a meta-learning framework for simple regret minimization in bandits. In this framework, a learning agent interacts with a sequence of bandit tasks, which are sampled i.i.d.\ from an unknown prior distribution, and learns its meta-parameters to perform better on future tasks. We propose the first Bayesian and frequentist meta-learning algorithms for this setting. The Bayesian algorithm has access to a prior distribution over the meta-parameters and its meta simple regret over $m$ bandit tasks with horizon $n$ is mere $\tilde{O}(m / \sqrt{n})$. On the other hand, the meta simple regret of the frequentist algorithm is $\tilde{O}(\sqrt{m} n + m/ \sqrt{n})$. While its regret is worse, the frequentist algorithm is more general because it does not need a prior distribution over the meta-parameters. It can also be analyzed in more settings. We instantiate our algorithms for several classes of bandit problems. Our algorithms are general and we complement our theory by evaluating them empirically in several environments.