Output Space Entropy Search Framework for Multi-Objective Bayesian Optimization

Abstract

We consider the problem of black-box multi-objective optimization (MOO) using expensive function evaluations (also referred to as experiments), where the goal is to approximate the true Pareto set of solutions by minimizing the total resource cost of experiments. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive computational simulations. The key challenge is to select the sequence of experiments to uncover high-quality solutions using minimal resources. In this paper, we propose a general framework for solving MOO problems based on the principle of output space entropy (OSE) search: select the experiment that maximizes the information gained per unit resource cost about the true Pareto front. We appropriately instantiate the principle of OSE search to derive efficient algorithms for the following four MOO problem settings: 1) The most basic single-fidelity setting, where experiments are expensive and accurate; 2) Handling black-box constraints which cannot be evaluated without performing experiments; 3) The discrete multi-fidelity setting, where experiments can vary in the amount of resources consumed and their evaluation accuracy; and 4) The continuous-fidelity setting, where continuous function approximations result in a huge space of experiments. Experiments on diverse synthetic and real-world benchmarks show that our OSE search based algorithms improve over state-of-the-art methods in terms of both computational-efficiency and accuracy of MOO solutions.

OpenBox: A Generalized Black-box Optimization Service

“…BBO with Multiple Objectives. Many multi-objective BBO algorithms have been proposed [4,5,25,29,37]. Couckuyt et.…”

“…We use the classic EI [36] for single-objective optimization task. For multi-objective problems, we select EHVI [11] when the number of objectives is less than 5; we use MESMO [4] algorithm for problems with a larger number of objectives, since EHVI's complexity increases exponentially as the number of objectives increases, which not only incurs a large computational overhead but also accumulates floating-point errors. We select the surrogate models in BO depending on the configuration space and the number of trials: If the input space has conditions, such as one parameter must be less than another parameter, or there are over 50 parameters in the input space, or the number of trials exceeds 500, we choose the Probabilistic Random Forest proposed in [27] instead of Gaussian Process (GP) as the surrogate to avoid incompatibility or high computational complexity of GP.…”

“…For single-objective optimization, Expected Improvement per second (EIPS) [43] can be used to find a good configuration as quickly as possible, and Expected Improvement with Local Penalization (LP-EI) [20] utilizes local penalizers to propose batches of configurations simultaneously. For multi-objective optimization, Max-value Entropy Search for Multi-objective Optimization (MESMO) [4] and Uncertainty-aware Search framework [5] for Multi-objective Optimization (USeMO) work efficiently when the number of objectives is large. Other implemented acquisition functions include Probability of Improvement (PI), and Upper Confidence Bound (UCB) [44].…”

Multi-objective Asynchronous Successive Halving

“…Pareto front entropy search (PFES) [52] is suitable when dealing with decoupled objectives. MESMO [2] builds on the max-value entropy-search criterion [58] and enjoys an asymptotic regret bound. Building on MESMO, two recent works have proposed MF-OSEMO [4] and iMOCA [3], two multi-fidelity based information-theoretic MBO techniques which internally use continuous fidelity Gaussian processes.…”

“…In Table 1, we report the results of this experiment, comparing MO algorithms versus the following algorithmic fairness methods: Zafar [60], Adversarial debiasing [63], Fair Empirical Risk Minimization (FERM and FERM pre-processed) [13], constrained BO approach (CBO) for fair models [44], and SMOTE [8]. 2 These results, show that the MO approach is very competitive compared to modeland constraint-specific methods (FERM, Zafar, Adversarial), and also without knowing a priori the threshold of our fairness constraint (as instead needed for CBO).…”