Discrete Bayesian Optimization via Machine Learning

Abstract

Bayesian Optimization (BO) is a family of powerful algorithms designed to solve complex optimization problems involving expensive black-box functions. These sequential algorithms iteratively update a surrogate model of the objective function (OF), effectively balancing exploration and exploitation to identify near-optimal solutions within a limited number of iterations. Originally designed for continuous, unconstrained domains, its efficiency has inspired adaptations for discrete, constrained optimization problems. On the other hand, Machine Learning (ML) models allow accurate predictions for black-box functions, although they typically require large amounts of data for training. Leveraging the strengths of BO and ML, research tackles the challenge of identifying optimal configurations in the context of cloud computing. This paradigm has become pervasive due to its ability to provide flexible and scalable resources. Identifying the optimal hardware-software configuration is essential for minimizing costs while meeting Quality of Service constraints. This task involves solving complex optimization problems over multidimensional discrete domains and black-box objective functions and constraints, within a limited number of iterations. To address this challenge, this work introduces d-MALIBOO, a BO-based algorithm that integrates ML techniques to enhance the efficiency of finding near-optimal solutions in discrete and bounded domains. While BO builds the surrogate model of the OF, ML models determine the feasible region of the black-box constraints and guide the BO algorithm toward promising regions of the discrete domain. Furthermore, we introduce an $\varepsilon$-greedy approach to favor exploration in domains with multiple local optima. Experimental results show that our algorithm outperforms OpenTuner, a popular framework for constrained optimization, by reducing the average regret by 29%, and SVM-CBO, a BO-based algorithm that integrates SVM models to determine the feasible region, by 82%.