E-PAL: An Active Learning Approach to the Multi-Objective Optimization Problem

Abstract

In many fields one encounters the challenge of identifying out of a pool of possible designs those that simultaneously optimize multiple objectives. In many applications an exhaustive search for the Pareto-optimal set is infeasible. To address this challenge, we propose the $\epsilon$-Pareto Active Learning ($\epsilon$-PAL) algorithm which adaptively samples the design space to predict a set of Pareto-optimal solutions that cover the true Pareto front of the design space with some granularity regulated by a parameter $\epsilon$. Key features of $\epsilon$-PAL include (1) modeling the objectives as draws from a Gaussian process distribution to capture structure and accommodate noisy evaluation; (2) a method to carefully choose the next design to evaluate to maximize progress; and (3) the ability to control prediction accuracy and sampling cost. We provide theoretical bounds on $\epsilon$-PAL's sampling cost required to achieve a desired accuracy. Further, we perform an experimental evaluation on three real-world data sets that demonstrate $\epsilon$-PAL's effectiveness; in comparison to the state-of-the-art active learning algorithm PAL, $\epsilon$-PAL reduces the amount of computations and the number of samples from the design space required to meet the user's desired level of accuracy. In addition, we show that $\epsilon$-PAL improves significantly over a state-of-the-art multi- objective optimization method, saving in most cases 30\% to 70\% evaluations to achieve the same accuracy.