Bayesian optimization for modular black-box systems with switching costs

Most existing black-box optimization methods assume that all variables in the system being optimized have equal cost and can change freely at each iteration. However, in many real-world systems, inputs are passed through a sequence of different operations or modules, making variables in earlier stages of processing more costly to update. Such structure induces a dynamic cost from switching variables in the early parts of a data processing pipeline. In this work, we propose a new algorithm for switch-cost-aware optimization called Lazy Modular Bayesian Optimization (LaMBO). This method efficiently identifies the global optimum while minimizing cost through a passive change of variables in early modules. The method is theoretically grounded which achieves a vanishing regret regularized with switching cost. We apply LaMBO to multiple synthetic functions and a three-stage image segmentation pipeline used in a neuroimaging task, where we obtain promising improvements over existing cost-aware Bayesian optimization algorithms. Our results demonstrate that LaMBO is an effective strategy for black-box optimization capable of minimizing switching costs.