Non-Myopic Multi-Objective Bayesian Optimization
Syrine Belakaria, Alaleh Ahmadianshalchi, Barbara Engelhardt, Stefano Ermon, Janardhan Rao Doppa
TL;DR
The paper tackles finite-horizon sequential experimental design for multi-objective optimization with expensive black-box functions. It introduces a non-myopic MOBO framework by casting the multi-objective reward as hypervolume improvement $HVI$, enabling a Bellman-like lower bound to guide lookahead decisions under a budget $T$, and develops three acquisition functions: $NMMO$-Nested, $NMMO$-Joint, and $BINOM$, which integrate $EHVI$ and $BEHVI$ components to balance accuracy and computation. The approach is validated on six real-world MO problems, showing substantial improvements over state-of-the-art myopic baselines and providing scalable options for budget-constrained materials design and engineering optimization; code is released. This work demonstrates that incorporating lookahead via $HVI$-based rewards can significantly enhance Pareto front exploration under tight experimental budgets, with flexibility to accommodate alternative scalarizations beyond $HVI$.$HV$, $HVI$, $EHVI$, and $BEHVI$ are central to the formulation and are used to quantify and optimize future improvements in the Pareto front.
Abstract
We consider the problem of finite-horizon sequential experimental design to solve multi-objective optimization (MOO) of expensive black-box objective functions. This problem arises in many real-world applications, including materials design, where we have a small resource budget to make and evaluate candidate materials in the lab. We solve this problem using the framework of Bayesian optimization (BO) and propose the first set of non-myopic methods for MOO problems. Prior work on non-myopic BO for single-objective problems relies on the Bellman optimality principle to handle the lookahead reasoning process. However, this principle does not hold for most MOO problems because the reward function needs to satisfy some conditions: scalar variable, monotonicity, and additivity. We address this challenge by using hypervolume improvement (HVI) as our scalarization approach, which allows us to use a lower-bound on the Bellman equation to approximate the finite-horizon using a batch expected hypervolume improvement (EHVI) acquisition function (AF) for MOO. Our formulation naturally allows us to use other improvement-based scalarizations and compare their efficacy to HVI. We derive three non-myopic AFs for MOBO: 1) the Nested AF, which is based on the exact computation of the lower bound, 2) the Joint AF, which is a lower bound on the nested AF, and 3) the BINOM AF, which is a fast and approximate variant based on batch multi-objective acquisition functions. Our experiments on multiple diverse real-world MO problems demonstrate that our non-myopic AFs substantially improve performance over the existing myopic AFs for MOBO.