Bayesian optimization (BO) is a successful methodology to optimize black-box functions that are expensive to evaluate. While traditional methods optimize each black-box function in isolation, there has been recent interest in speeding up BO by transferring knowledge across multiple related black-box functions. In this work, we introduce a method to automatically design the BO search space by relying on evaluations of previous black-box functions. We depart from the common practice of defining a set of arbitrary search ranges a priori by considering search space geometries that are learnt from historical data. This simple, yet effective strategy can be used to endow many existing BO methods with transfer learning properties. Despite its simplicity, we show that our approach considerably boosts BO by reducing the size of the search space, thus accelerating the optimization of a variety of black-box optimization problems. In particular, the proposed approach combined with random search results in a parameter-free, easy-to-implement, robust hyperparameter optimization strategy. We hope it will constitute a natural baseline for further research attempting to warm-start BO.

My concern about generalization still remains, and I hope the authors can devote maybe a sentence or two to it in the final draft - even something to the effect of "it is a concern; experimental evidence suggests it is not a great concern."] Summary: For any given ML algorithm, e.g., random forests, the paper proposes a transfer-learning approach for selection of hyperparameters (limited to those parameters that can be ordered) wherein a bounding space is constructed from previous evaluations of that algorithm on other datasets. Two types of bounding spaces are described. The box space is the tightest bounding box covering the best known hyperparameter settings for previous datasets. The ellipsoid is found as the smallest-volume ellipsoid covering the best known settings (via convex optimization).

Bayesian optimization (BO) is a successful methodology to optimize black-box functions that are expensive to evaluate. While traditional methods optimize each black-box function in isolation, there has been recent interest in speeding up BO by transferring knowledge across multiple related black-box functions. In this work, we introduce a method to automatically design the BO search space by relying on evaluations of previous black-box functions. We depart from the common practice of defining a set of arbitrary search ranges a priori by considering search space geometries that are learnt from historical data. This simple, yet effective strategy can be used to endow many existing BO methods with transfer learning properties.

The reviewers appreciated the simplicity of the approach and the rigorous evaluation. They recommended discussing the generalizability of the approach in one or two sentences in the final version of the paper.

Bayesian optimization (BO) is a successful methodology to optimize black-box functions that are expensive to evaluate. While traditional methods optimize each black-box function in isolation, there has been recent interest in speeding up BO by transferring knowledge across multiple related black-box functions. In this work, we introduce a method to automatically design the BO search space by relying on evaluations of previous black-box functions. We depart from the common practice of defining a set of arbitrary search ranges a priori by considering search space geometries that are learnt from historical data. This simple, yet effective strategy can be used to endow many existing BO methods with transfer learning properties.

Bayesian optimization (BO) is a successful methodology to optimize black-box functions that are expensive to evaluate. While traditional methods optimize each black-box function in isolation, there has been recent interest in speeding up BO by transferring knowledge across multiple related black-box functions. In this work, we introduce a method to automatically design the BO search space by relying on evaluations of previous black-box functions. We depart from the common practice of defining a set of arbitrary search ranges a priori by considering search space geometries that are learnt from historical data. This simple, yet effective strategy can be used to endow many existing BO methods with transfer learning properties.