Pareto-Optimal Anytime Algorithms via Bayesian Racing

TL;DR

This paper introduces a novel Bayesian racing framework for comparing optimization algorithms over time, forming Pareto sets without needing bounds or normalization, thus enabling more robust and flexible algorithm selection.

Contribution

It proposes a Pareto optimization approach for anytime algorithms using Bayesian inference and ranking models, avoiding normalization and enabling adaptive, early elimination of dominated algorithms.

Findings

The method accurately identifies Pareto-optimal algorithms across diverse instances.

It requires no prior bounds or normalization for objective values.

The approach supports flexible, risk-aware algorithm selection.

Abstract

Selecting an optimization algorithm requires comparing candidates across problem instances, but the computational budget for deployment is often unknown at benchmarking time. Current methods either collapse anytime performance into a scalar, require manual interpretation of plots, or produce conclusions that change when algorithms are added or removed. Moreover, methods based on raw objective values require normalization, which needs bounds or optima that are often unavailable and breaks coherent aggregation across instances. We propose a framework that formulates anytime algorithm comparison as Pareto optimization over time: an algorithm is non-dominated if no competitor beats it at every timepoint. By using rankings rather than objective values, our approach requires no bounds, no normalization, and aggregates coherently across arbitrary instance distributions without requiring known optima. We introduce PolarBear (Pareto-optimal anytime algorithms via Bayesian racing), a procedure that identifies the anytime Pareto set through adaptive sampling with calibrated uncertainty. Bayesian inference over a temporal Plackett-Luce ranking model provides posterior beliefs about pairwise dominance, enabling early elimination of confidently dominated algorithms. The output Pareto set together with the posterior supports downstream algorithm selection under arbitrary time preferences and risk profiles without additional experiments.