Optimizing the Unknown: Black Box Bayesian Optimization with Energy-Based Model and Reinforcement Learning

Existing Bayesian Optimization (BO) methods typically balance exploration and exploitation to optimize costly objective functions. However, these methods often suffer from a significant one-step bias, which may lead to convergence towards local optima and poor performance in complex or high-dimensional tasks. Recently, Black-Box Optimization (BBO) has achieved success across various scientific and engineering domains, particularly when function evaluations are costly and gradients are unavailable. Motivated by this, we propose the Reinforced Energy-Based Model for Bayesian Optimization (REBMBO), which integrates Gaussian Processes (GP) for local guidance with an Energy-Based Model (EBM) to capture global structural information. Notably, we define each Bayesian Optimization iteration as a Markov Decision Process (MDP) and use Proximal Policy Optimization (PPO) for adaptive multi-step lookahead, dynamically adjusting the depth and direction of exploration to effectively overcome the limitations of traditional BO methods. We conduct extensive experiments on synthetic and real-world benchmarks, confirming the superior performance of REBMBO. Additional analyses across various GP configurations further highlight its adaptability and robustness. Our code is publicly available at: https: //github. com/ruiyaoMiao0809/Black-Box-Bayesian-Optimization-with-Energy-Based-Model-and-Reinforcement-Learning

Authors

• RUIYAO MIAO
• Junren Xiao
• Shiya Tsang
• Hui Xiong Hong Kong University of Science and Technology (Guangzhou)
• Ying Nian Wu University of California, Los Angeles

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