Multi-Fidelity Multi-Objective Bayesian Optimization: An Output Space Entropy Search Approach

Abstract

We study the novel problem of blackbox optimization of multiple objectives via multi-fidelity function evaluations that vary in the amount of resources consumed and their accuracy. The overall goal is to appromixate the true Pareto set of solutions by minimizing the resources consumed for function evaluations. For example, in power system design optimization, we need to find designs that trade-off cost, size, efficiency, and thermal tolerance using multi-fidelity simulators for design evaluations. In this paper, we propose a novel approach referred as Multi-Fidelity Output Space Entropy Search for Multi-objective Optimization (MF-OSEMO) to solve this problem. The key idea is to select the sequence of candidate input and fidelity-vector pairs that maximize the information gained about the true Pareto front per unit resource cost. Our experiments on several synthetic and real-world benchmark problems show that MF-OSEMO, with both approximations, significantly improves over the state-of-the-art single-fidelity algorithms for multi-objective optimization.

Output Space Entropy Search Framework for Multi-Objective Bayesian Optimization

“…These are strong assumptions and may not hold in general multi-fidelity settings including the problems from our experimental evaluation. Our proposed MF-OSEMO (Belakaria et al, 2020a) and iMOCA algorithms (generalized versions of MESMO (Belakaria et al, 2019) solve MOO problem in discrete and continuous-fidelity settings respectively using the principle of output space entropy search and leverage some technical ideas from the prior work on single-objective optimization. We are not aware of any prior work on generic discrete/continuous-fidelity algorithms for MOO problems in the BO literature.…”

“…We mainly present the results for iMOCA with MESMO and MF-OSEMO as baselines for the following reasons: First, iMOCA is the generalisation of both MESMO and MF-OSEMO to the most general setting (continuous-fidelity); and second, the performance, robustness, and effectiveness of MESMO and MF-OSEMO have been shown in (Belakaria et al, 2019) and (Belakaria et al, 2020a) respectively.…”

“…Acknowledgements. Some of the material in this paper was first published at NeurIPS-2019 (Belakaria et al, 2019) and AAAI-2020 (Belakaria et al, 2020a). The authors gratefully acknowledge the support from National Science Foundation (NSF) grants IIS-1845922, OAC-1910213, and SII-2030159.…”

“…Output space entropy search has many advantages over algorithms based on input space entropy search (Belakaria, Deshwal, & Doppa, 2019): a) it allows much tighter approximation; b) it is cheaper to compute; and c) it naturally lends itself to robust optimization with respect to the number of samples Output Space Entropy Search Framework for Multi-Objective Bayesian Optimization used for acquisition function computation. We appropriately instantiate the OSE principle to derive efficient algorithms for solving four qualitatively different MOO problems: the most basic single-fidelity setting (Belakaria et al, 2019), MOO with black-box constraints, discrete multi-fidelity setting (Belakaria, Deshwal, & Doppa, 2020a), and continuous-fidelity setting. Comprehensive experiments on diverse synthetic and real-world benchmarks show that our OSE search based algorithms are computationally-efficient and perform better than the state-of-the-art algorithms.…”

“…• Development of an approach referred to as MF-OSEMO to solve MOO problems in the discrete multi-fidelity setting, where experiments can vary in the amount of resources consumed and their evaluation accuracy (Belakaria et al, 2020a).…”