Learning relevant contextual variables within Bayesian optimization

Julien Martinelli, Ayush Bharti, Armi Tiihonen, S. T. John, Louis Filstroff, Sabina J. Sloman, Patrick Rinke, Samuel Kaski

Keywords: Bayesian Optimization, Variable selection, Contextual BO

TL;DR: We extend Contextual Bayesian Optimization to the case where 1) the set of relevant contextual variables is unknown and 2) contextual variables can be integrated to the set of optimized variables at a cost, leading to a cost vs exploration tradeoff

Abstract:

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 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.

List Of Authors: Martinelli, Julien and Bharti, Ayush and Tiihonen, Armi and John, ST and Filstroff, Louis and Sloman, Sabina J and Rinke, Patrick and Kaski, Samuel

Submission Number: 238