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

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 is an element of-ParetoActive Learning (is an element of-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 is an element of. Key features of is an element of-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 is an element of-PAL ' s sampling cost required to achieve a desired accuracy. Further, we perform an experimental evaluation on three real-world data sets that demonstrate is an element of-PAL ' s e ff ectiveness; in comparison to the state-of-the-art active learning algorithm PAL, is an element of-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 is an element of-PAL improves signi fi cantly over a state-of-the-art multi-objective optimization method, saving in most cases 30% to 70% evaluations to achieve the same accuracy.