Racing Multi-Objective Selection Probabilities

TL;DR

This paper introduces a racing method for efficiently estimating selection probabilities in noisy multi-objective optimization, reducing computational costs by dynamically allocating sampling budgets during selection.

Contribution

It proposes a Hoeffding race-based approach to directly estimate selection probabilities, improving efficiency over static sampling methods in noisy optimization scenarios.

Findings

Outperforms static budget approaches in noisy NSGA-II experiments

Reduces computational cost while maintaining selection accuracy

Effective in approximating Pareto sets under uncertainty

Abstract

In the context of Noisy Multi-Objective Optimization, dealing with uncertainties requires the decision maker to define some preferences about how to handle them, through some statistics (e.g., mean, median) to be used to evaluate the qualities of the solutions, and define the corresponding Pareto set. Approximating these statistics requires repeated samplings of the population, drastically increasing the overall computational cost. To tackle this issue, this paper proposes to directly estimate the probability of each individual to be selected, using some Hoeffding races to dynamically assign the estimation budget during the selection step. The proposed racing approach is validated against static budget approaches with NSGA-II on noisy versions of the ZDT benchmark functions.