Posterior Inference in Latent Space for Scalable Constrained Black-box Optimization
This work addresses the scalability and mode collapse issues in generative model-based constrained optimization, which is crucial for scientific and engineering applications where feasible regions are hard to find.
The paper tackles high-dimensional constrained black-box optimization by proposing a framework that uses flow-based models and surrogate models to capture data distributions and predict constraints, then performs posterior inference in a smoother latent space to find feasible, high-value candidates. It demonstrates superior performance on synthetic and real-world tasks, with empirical results showing improved scalability and effectiveness in multi-modal scenarios.
Optimizing high-dimensional black-box functions under black-box constraints is a pervasive task in a wide range of scientific and engineering problems. These problems are typically harder than unconstrained problems due to hard-to-find feasible regions. While Bayesian optimization (BO) methods have been developed to solve such problems, they often struggle with the curse of dimensionality. Recently, generative model-based approaches have emerged as a promising alternative for constrained optimization. However, they suffer from poor scalability and are vulnerable to mode collapse, particularly when the target distribution is highly multi-modal. In this paper, we propose a new framework to overcome these challenges. Our method iterates through two stages. First, we train flow-based models to capture the data distribution and surrogate models that predict both function values and constraint violations with uncertainty quantification. Second, we cast the candidate selection problem as a posterior inference problem to effectively search for promising candidates that have high objective values while not violating the constraints. During posterior inference, we find that the posterior distribution is highly multi-modal and has a large plateau due to constraints, especially when constraint feedback is given as binary indicators of feasibility. To mitigate this issue, we amortize the sampling from the posterior distribution in the latent space of flow-based models, which is much smoother than that in the data space. We empirically demonstrate that our method achieves superior performance on various synthetic and real-world constrained black-box optimization tasks. Our code is publicly available \href{https://github.com/umkiyoung/CiBO}{here}.