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Output Space Entropy Search Framework for Multi-Objective Bayesian Optimization

Journal of Artificial Intelligence Research

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.


Information-Theoretic Multi-Objective Bayesian Optimization with Continuous Approximations

arXiv.org Artificial Intelligence

Many real-world applications involve black-box optimization of multiple objectives using continuous function approximations that trade-off accuracy and resource cost of evaluation. For example, in rocket launching research, we need to find designs that trade-off return-time and angular distance using continuous-fidelity simulators (e.g., varying tolerance parameter to trade-off simulation time and accuracy) for design evaluations. The goal is to approximate the optimal Pareto set by minimizing the cost for evaluations. In this paper, we propose a novel approach referred to as information-Theoretic Multi-Objective Bayesian Optimization with Continuous Approximations (iMOCA)} to solve this problem. The key idea is to select the sequence of input and function approximations for multiple objectives which maximize the information gain per unit cost for the optimal Pareto front. Our experiments on diverse synthetic and real-world benchmarks show that iMOCA significantly improves over existing single-fidelity methods.


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

arXiv.org Artificial Intelligence

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 approximate 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.


Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints

arXiv.org Artificial Intelligence

We consider the problem of constrained multi-objective blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto set of solutions satisfying a set of constraints while minimizing the number of function evaluations. For example, in aviation power system design applications, we need to find the designs that trade-off total energy and the mass while satisfying specific thresholds for motor temperature and voltage of cells. This optimization requires performing expensive computational simulations to evaluate designs. In this paper, we propose a new approach referred as {\em Max-value Entropy Search for Multi-objective Optimization with Constraints (MESMOC)} to solve this problem. MESMOC employs an output-space entropy based acquisition function to efficiently select the sequence of inputs for evaluation to uncover high-quality pareto-set solutions while satisfying constraints. We apply MESMOC to two real-world engineering design applications to demonstrate its effectiveness over state-of-the-art algorithms.


Uncertainty aware Search Framework for Multi-Objective Bayesian Optimization with Constraints

arXiv.org Machine Learning

We consider the problem of constrained multi-objective (MO) blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto set of solutions satisfying a set of constraints while minimizing the number of function evaluations. We propose a novel framework named Uncertainty-aware Search framework for Multi-Objective Optimization with Constraints (USeMOC) to efficiently select the sequence of inputs for evaluation to solve this problem. The selection method of USeMOC consists of solving a cheap constrained MO optimization problem via surrogate models of the true functions to identify the most promising candidates and picking the best candidate based on a measure of uncertainty. We applied this framework to optimize the design of a multi-output switched-capacitor voltage regulator via expensive simulations. Our experimental results show that USeMOC is able to achieve more than 90 % reduction in the number of simulations needed to uncover optimized circuits.