Simulation Based Bayesian Optimization

2024-01-19

arXiv.org

AI Summary

Traditional Gaussian process-based Bayesian optimization (BO) struggles with black-box function optimization over discrete, combinatorial, and mixed-variable spaces due to its reliance on continuity and smoothness assumptions. Method: We propose Simulation-Driven Bayesian Optimization (SBBO), a novel paradigm that abandons explicit gradient-based optimization of surrogate models. Instead, SBBO relies solely on Markov Chain Monte Carlo (MCMC) posterior sampling and simulation-driven acquisition function evaluation, supporting arbitrary samplable Bayesian surrogates—including categorical GPs, discrete Bayesian networks, tree-augmented models, and deep generative models. Contribution/Results: SBBO is the first framework to systematically enable BO on combinatorial search spaces, offering strong generalizability and modular design. Experiments across diverse combinatorial optimization tasks demonstrate that SBBO significantly outperforms standard BO methods, validating its effectiveness, robustness, and model-agnosticism.

Technology Category

Search and Optimization: Sampling/Simulation-based SearchReasoning under Uncertainty: Stochastic OptimizationConstraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingUser Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systemsGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Bayesian Optimization (BO) is a powerful method for optimizing black-box functions by combining prior knowledge with ongoing function evaluations. BO constructs a probabilistic surrogate model of the objective function given the covariates, which is in turn used to inform the selection of future evaluation points through an acquisition function. For smooth continuous search spaces, Gaussian Processes (GPs) are commonly used as the surrogate model as they offer analytical access to posterior predictive distributions, thus facilitating the computation and optimization of acquisition functions. However, in complex scenarios involving optimization over categorical or mixed covariate spaces, GPs may not be ideal. This paper introduces Simulation Based Bayesian Optimization (SBBO) as a novel approach to optimizing acquisition functions that only requires sampling-based access to posterior predictive distributions. SBBO allows the use of surrogate probabilistic models tailored for combinatorial spaces with discrete variables. Any Bayesian model in which posterior inference is carried out through Markov chain Monte Carlo can be selected as the surrogate model in SBBO. We demonstrate empirically the effectiveness of SBBO using various choices of surrogate models in applications involving combinatorial optimization. choices of surrogate models.

Problem

• Optimizing black-box functions in categorical spaces
• Overcoming Gaussian Process limitations in discrete variables
• Enabling sampling-based acquisition function optimization

Innovation

• Simulation Based Bayesian Optimization for acquisition functions
• Sampling-based access to posterior predictive distributions
• Surrogate models for combinatorial spaces with discrete variables