Learning Relevant Contextual Variables Within Bayesian Optimization
This addresses a cost-sensitive optimization problem for machine learning practitioners using Bayesian optimization, but it is incremental as it builds on existing contextual BO methods.
The paper tackles the problem of contextual Bayesian optimization when contextual variables have unknown relevance and some can be optimized at a cost, proposing a method that adaptively selects contextual variables based on relevance-cost trade-offs. The result is a consistent improvement over alternatives in synthetic and real-world experiments.
Contextual Bayesian Optimization (CBO) efficiently optimizes black-box functions with respect to design variables, while simultaneously integrating contextual information regarding the environment, such as experimental conditions. However, the relevance of contextual variables is not necessarily known beforehand. Moreover, contextual variables can sometimes be optimized themselves at an additional cost, a setting overlooked by current CBO algorithms. Cost-sensitive CBO would simply include optimizable contextual variables as part of the design variables based on their cost. Instead, we adaptively select a subset of contextual variables to include in the optimization, based on the trade-off between their relevance and the additional cost incurred by optimizing them compared to leaving them to be determined by the environment. We learn the relevance of contextual variables by sensitivity analysis of the posterior surrogate model while minimizing the cost of optimization by leveraging recent developments on early stopping for BO. We empirically evaluate our proposed Sensitivity-Analysis-Driven Contextual BO (SADCBO) method against alternatives on both synthetic and real-world experiments, together with extensive ablation studies, and demonstrate a consistent improvement across examples.