An adaptive approach to Bayesian Optimization with switching costs

TL;DR

This work addresses sequential Bayesian optimization under switching costs that penalize changing costly design variables. It extends batch-constrained BO to a sequential, resource-aware setting and proposes four algorithms, including a parameter-free cost-aware EI method (EIPU) and two strategies—pReuseBO and periodic switching—along with adaptations of PSBO and PSBO Nested. Empirical results on seven scalable test functions across dimensions $d \in \{2,3,4\}$ show that the cost-aware EIPU algorithm achieves comparable or superior performance to tuned baselines and increasingly benefits as the switching cost grows, while pReuseBO and PSBO variants reveal the importance of balancing exploration and setup changes. The findings demonstrate robustness to landscape features and switching-cost trade-offs, offering practical guidance for optimization in resource-constrained environments where adaptability to resource variability matters.

Abstract

We investigate modifications to Bayesian Optimization for a resource-constrained setting of sequential experimental design where changes to certain design variables of the search space incur a switching cost. This models the scenario where there is a trade-off between evaluating more while maintaining the same setup, or switching and restricting the number of possible evaluations due to the incurred cost. We adapt two process-constrained batch algorithms to this sequential problem formulation, and propose two new methods: one cost-aware and one cost-ignorant. We validate and compare the algorithms using a set of 7 scalable test functions in different dimensionalities and switching-cost settings for 30 total configurations. Our proposed cost-aware hyperparameter-free algorithm yields comparable results to tuned process-constrained algorithms in all settings we considered, suggesting some degree of robustness to varying landscape features and cost trade-offs. This method starts to outperform the other algorithms with increasing switching-cost. Our work broadens out from other recent Bayesian Optimization studies in resource-constrained settings that consider a batch setting only. While the contributions of this work are relevant to the general class of resource-constrained problems, they are particularly relevant to problems where adaptability to varying resource availability is of high importance

Figures (4)

• Figure 1: Example of a $d=2$ problem with $d_\text{costly} = 1$. The x-axis and y-axis represent the cheap and costly dimensions, respectively. The dotted line is the set of evaluations that use the current setup. The squares are the candidate points and the dot is the last evaluation.
• Figure 2: Maximization problem on synthetic function with axes $x_0$ and $x_1$ respresenting the expensive and cheap dimensions in the search space respectively. The grey dots represent the initial starting points, which are randomly selected. The red and blue lines then denote two evaluation strategies. The red line represents a strategy where the algorithm changes the setup at each evaluation, while the strategy represented by the blue line uses the same setup for evaluations 2, 3, 5, and 8. The second evaluation policy performs 9 evaluations, while the first policy performs only 6 due to its more expensive nature. Reusing the same setup allows for more total evaluations at the expense of fewer evaluations performed across the costly dimension $x_0$.
• Figure 3: Periodic switching of $k$. The costly decision variables are changed only every $k$ evaluations.
• Figure 4: Left: The mean GAP performance (and 95% CI) of the method pReuseBO plotted against 21 values of $p$, where $GAP=1$ means that the optimal solution was found, for 20 independent runs and averaged over the 7 test functions with 4 dimensions and 1 costly dimension. The approximately equivalent $k$ for Periodic Switching is shown on the x-axis. The dotted line shows the effect of $p$ averaged over all the switching costs to highlight its steady increase in performance followed by its sharp decline. Right: The median of the highest performing $p$ hyperparameters for each problem and costly dimensionality setting plotted against switch cost. $p$ is much more sensitive to tune with respect to different values of switch cost in the problems with high dimensionality and low costly dimensionality.