Pareto Set Identification With Posterior Sampling

TL;DR

This paper introduces PSIPS, a posterior sampling-based algorithm for Pareto set identification in multi-objective problems, achieving asymptotic optimality and efficient performance without high computational costs.

Contribution

It proposes a novel PSIPS algorithm that handles correlated objectives in Pareto set identification efficiently, improving over existing oracle-based methods.

Findings

PSIPS is asymptotically optimal from both frequentist and Bayesian perspectives.

The algorithm performs well empirically on real-world and synthetic data.

It effectively manages structure and correlation without high computational costs.

Abstract

The problem of identifying the best answer among a collection of items having real-valued distribution is well-understood. Despite its practical relevance for many applications, fewer works have studied its extension when multiple and potentially conflicting metrics are available to assess an item's quality. Pareto set identification (PSI) aims to identify the set of answers whose means are not uniformly worse than another. This paper studies PSI in the transductive linear setting with potentially correlated objectives. Building on posterior sampling in both the stopping and the sampling rules, we propose the PSIPS algorithm that deals simultaneously with structure and correlation without paying the computational cost of existing oracle-based algorithms. Both from a frequentist and Bayesian perspective, PSIPS is asymptotically optimal. We demonstrate its good empirical performance in real-world and synthetic instances.