We consider the problem of multi-objective (MO) blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto-set of solutions by minimizing the number of function evaluations. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive simulations. We propose a novel approach referred to as Max-value Entropy Search for Multi-objective Optimization (MESMO) to solve this problem. MESMO employs an output-space entropy based acquisition function to efficiently select the sequence of inputs for evaluation for quickly uncovering high-quality solutions. We also provide theoretical analysis to characterize the efficacy of MESMO. Our experiments on several synthetic and real-world benchmark problems show that MESMO consistently outperforms state-of-the-art algorithms.

We consider the problem of multi-objective (MO) blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto-set of solutions by minimizing the number of function evaluations. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive simulations. We propose a novel approach referred to as Max-value Entropy Search for Multi-objective Optimization (MESMO) to solve this problem. MESMO employs an output-space entropy based acquisition function to efficiently select the sequence of inputs for evaluation for quickly uncovering high-quality solutions. We also provide theoretical analysis to characterize the efficacy of MESMO.

We present MESMOC, a Bayesian optimization method that can be used to solve constrained multi-objective problems when the objectives and the constraints are expensive to evaluate. MESMOC works by minimizing the entropy of the solution of the optimization problem in function space, i.e., the Pareto frontier, to guide the search for the optimum. The execution cost of MESMOC is linear in the number of objectives and constraints. Furthermore, it is often significantly smaller than the cost of alternative methods based on minimizing the entropy of the Pareto set. The reason for this is that it is easier to approximate the required computations in MESMOC. Moreover, MESMOC's acquisition function is expressed as the sum of one acquisition per each black-box (objective or constraint). Thus, it can be used in a decoupled evaluation setting in which one chooses not only the next input location to evaluate, but also which black-box to evaluate there. We compare MESMOC with related methods in synthetic and real optimization problems. These experiments show that MESMOC is competitive with other information-based methods for constrained multi-objective Bayesian optimization, but its execution time is smaller.

We consider the problem of multi-objective (MO) blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto-set of solutions by minimizing the number of function evaluations. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive simulations. We propose a novel approach referred to as Max-value Entropy Search for Multi-objective Optimization (MESMO) to solve this problem. MESMO employs an output-space entropy based acquisition function to efficiently select the sequence of inputs for evaluation for quickly uncovering high-quality solutions. We also provide theoretical analysis to characterize the efficacy of MESMO.

Bayesian optimization (BO) is a model-based approach to sequentially optimize expensive black-box functions, such as the validation error of a deep neural network with respect to its hyperparameters. In many real-world scenarios, the optimization is further subject to a priori unknown constraints. For example, training a deep network configuration may fail with an out-of-memory error when the model is too large. In this work, we focus on a general formulation of Gaussian process-based BO with continuous or binary constraints. We propose constrained Max-value Entropy Search (cMES), a novel information theoretic-based acquisition function implementing this formulation. We also revisit the validity of the factorized approximation adopted for rapid computation of the MES acquisition function, showing empirically that this leads to inaccurate results. On an extensive set of real-world constrained hyperparameter optimization problems we show that cMES compares favourably to prior work, while being simpler to implement and faster than other constrained extensions of Entropy Search.

Entropy Search (ES) and Predictive Entropy Search (PES) are popular and empirically successful Bayesian Optimization techniques. Both rely on a compelling information-theoretic motivation, and maximize the information gained about the $\arg\max$ of the unknown function; yet, both are plagued by the expensive computation for estimating entropies. We propose a new criterion, Max-value Entropy Search (MES), that instead uses the information about the maximum function value. We show relations of MES to other Bayesian optimization methods, and establish a regret bound. We observe that MES maintains or improves the good empirical performance of ES/PES, while tremendously lightening the computational burden. In particular, MES is much more robust to the number of samples used for computing the entropy, and hence more efficient for higher dimensional problems.