Bandit Pareto Set Identification in a Multi-Output Linear Model

TL;DR

This paper addresses the problem of identifying the Pareto set in a structured multi-output linear bandit model, proposing optimal algorithms with strong theoretical guarantees and validating them through extensive experiments.

Contribution

It introduces the first optimal design-based algorithms for Pareto Set Identification in multi-output linear bandits, with nearly optimal guarantees in various settings.

Findings

Algorithms achieve near-optimal performance in fixed-budget and fixed-confidence scenarios.

The difficulty of the PSI task mainly depends on the sub-optimality gaps of only h arms.

Experimental results validate the effectiveness of the proposed methods on synthetic and real datasets.

Abstract

We study the Pareto Set Identification (PSI) problem in a structured multi-output linear bandit model. In this setting, each arm is associated a feature vector belonging to $\mathbb{R}^h$, and its mean vector in $\mathbb{R}^d$ linearly depends on this feature vector through a common unknown matrix $\Theta \in \mathbb{R}^{h \times d}$. The goal is to identify the set of non-dominated arms by adaptively collecting samples from the arms. We introduce and analyze the first optimal design-based algorithms for PSI, providing nearly optimal guarantees in both the fixed-budget and the fixed-confidence settings. Notably, we show that the difficulty of these tasks mainly depends on the sub-optimality gaps of $h$ arms only. Our theoretical results are supported by an extensive benchmark on synthetic and real-world datasets.