Maximize expected multiobjective outcomes under uncertainty using hypervolume
Expected Hypervolume Maximization for Multiobjective Optimization under Uncertainties
Machine Learning
Summary
Optimizing multiple goals at once can be hard when there’s uncertainty in the results. Instead of just averaging each goal separately, the authors propose a new way to look at the problem by focusing on improving the overall combination of objectives together, called the hypervolume. They use smart mathematical techniques to handle tricky cases and suggest building simpler models to make the process easier when direct calculations are difficult. Their ideas also include ways to choose data points more efficiently to improve the model, tested on simple example problems.
What this means in practice
- •For machine learning engineers: Optimize models with multiple uncertain performance metrics using expected hypervolume to better balance trade-offs and handle noise.
- •For engineering design teams: Use the proposed method to efficiently find design options that perform well on several criteria under uncertain conditions.
Authors
Victor Trappler
Abstract
The problem of multiobjective optimization under uncertainties is often approached by taking the expectation of each objective. In this work, we propose instead to formulate this as a Bayesian decision problem and to rely on the expected value of the hypervolume, which is to be maximized with respect to a finite set of input points. We show that this can be performed using methods based on gradients in a stochastic optimization framework, provided that care is taken with respect to dominated points. Moreover, in the absence of readily available differentiable code, we propose to use Gaussian Processes as differentiable surrogate models, in order to perform the optimization. An additional contribution in this work are some active learning strategies, through acquisition functions which helps construct a surrogate model well-designed for the multiobjective optimization problem at stake. These strategies are compared on simple analytical problems to assess their performances.