Marcela Zuluaga, Andreas Krause, Guillaume Sergent and Markus PŁschel (Proc. International Conference on Machine Learning (ICML), pp. 462-470, 2013)
Active Learning for Multi-Objective Optimization
Preprint (4.7 MB)
Bibtex

In many fields one encounters the challenge of identifying, out of a pool of possible designs, those that simultaneously optimize multiple objectives. This means that usually there is not one optimal design but an entire set of Pareto-optimal ones with optimal trade-offs in the objectives. In many applications, evaluating one design is expensive; thus, an exhaustive search for the Pareto-optimal set is unfeasible. To address this challenge, we propose the Pareto Active Learning (PAL) algorithm which intelligently samples the design space to predict the Pareto-optimal set. Key features of PAL include (1) modeling the objectives as samples from a Gaussian process distribution to capture structure and accomodate 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 PALís sampling cost required to achieve a desired accuracy. Further, we show an experimental evaluation on three real-world data sets. The results show PALís effectiveness; in particular it improves significantly over a state-of-the-art multi-objective optimization method, saving in many cases about 33% evaluations to achieve the same accuracy.

Keywords:
Search/Learning for optimization

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