qPOTS: Efficient batch multiobjective Bayesian optimization via Pareto optimal Thompson sampling

Ashwin Renganathan

Abstract:

Classical evolutionary approaches for multiobjective optimization are quite effective but
incur a lot of queries to the objectives; this can
be prohibitive when objectives are expensive
oracles. A sample-efficient approach to solving multiobjective optimization is via Gaussian process (GP) surrogates and Bayesian
optimization (BO). Multiobjective Bayesian
optimization (MOBO) involves the construction of an acquisition function which is optimized to acquire new observation candidates.
This “inner” optimization can be hard due
to various reasons: acquisition functions being nonconvex, nondifferentiable and/or unavailable in analytical form; the success of
MOBO heavily relies on this inner optimization. We do away with this hard acquisition
function optimization step and propose a simple, but effective, Thompson sampling based
approach (qPOTS) where new candidate(s) are
chosen from the Pareto frontier of random GP
posterior sample paths obtained by solving
a much cheaper multiobjective optimization
problem. To further improve computational
tractability in higher dimensions we propose
an automated active set of candidates selection combined with a Nystr ̈om approximation.
Our approach applies to arbitrary GP prior
assumptions and demonstrates strong empirical performance over the state of the art,
both in terms of accuracy and computational
efficiency, on synthetic as well as real-world
experiments.