Batch Multi-Fidelity Bayesian Optimization with Deep Auto-Regressive Networks

Abstract

Bayesian optimization (BO) is a powerful approach for optimizing black-box, expensive-to-evaluate functions. To enable a flexible trade-off between the cost and accuracy, many applications allow the function to be evaluated at different fidelities. In order to reduce the optimization cost while maximizing the benefit-cost ratio, in this paper, we propose Batch Multi-fidelity Bayesian Optimization with Deep Auto-Regressive Networks (BMBO-DARN). We use a set of Bayesian neural networks to construct a fully auto-regressive model, which is expressive enough to capture strong yet complex relationships across all the fidelities, so as to improve the surrogate learning and optimization performance. Furthermore, to enhance the quality and diversity of queries, we develop a simple yet efficient batch querying method, without any combinatorial search over the fidelities. We propose a batch acquisition function based on Max-value Entropy Search (MES) principle, which penalizes highly correlated queries and encourages diversity. We use posterior samples and moment matching to fulfill efficient computation of the acquisition function and conduct alternating optimization over every fidelity-input pair, which guarantees an improvement at each step. We demonstrate the advantage of our approach on four real-world hyperparameter optimization applications.

References in corpus (19)

• Adam: A Method for Stochastic Optimization
• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• Practical Bayesian Optimization of Machine Learning Algorithms
• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• Stochastic Gradient Hamiltonian Monte Carlo
• Scalable Bayesian Optimization Using Deep Neural Networks
• Particle hopping models and traffic flow theory
• Predictive Entropy Search for Efficient Global Optimization of Black-box Functions
• Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processes
• Dealing with Categorical and Integer-valued Variables in Bayesian Optimization with Gaussian Processes
• Batch Bayesian Optimization via Local Penalization
• Max-value Entropy Search for Efficient Bayesian Optimization
• Freeze-Thaw Bayesian Optimization
• Multi-fidelity Bayesian Optimisation with Continuous Approximations
• A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes
• Deep Gaussian Processes for Multi-fidelity Modeling
• Multi-fidelity Bayesian Optimization with Max-value Entropy Search and its parallelization
• Asynchronous Parallel Bayesian Optimisation via Thompson Sampling
• Practical Bayesian Optimization for Variable Cost Objectives