Black box optimization requires specifying a search space to explore for solutions, e.g. a d-dimensional compact space, and this choice is critical for getting the best results at a reasonable budget. Unfortunately, determining a high quality search space can be challenging in many applications. For example, when tuning hyperparameters for machine learning pipelines on a new problem given a limited budget, one must strike a balance between excluding potentially promising regions and keeping the search space small enough to be tractable. The goal of this work is to motivate—through example applications in tuning deep neural networks—the problem of predicting the quality of search spaces conditioned on budgets, as well as to provide a simple scoring method based on a utility function applied to a probabilistic response surface model, similar to Bayesian optimization. We show that the method we present can compute meaningful budget-conditional scores in a variety of situations. We also provide experimental evidence that accurate scores can be useful in constructing and pruning search spaces. Ultimately, we believe scoring search spaces should become standard practice in the experimental workflow for deep learning.

Many contemporary machine learning models require extensive tuning of hyperparameters to perform well. A variety of methods, such as Bayesian optimization, have been developed to automate and expedite this process. However, tuning remains extremely costly as it typically requires repeatedly fully training models. To address this issue, Bayesian optimization methods have been extended to use cheap, partially trained models to extrapolate to expensive complete models. While this approach enlarges the set of explored hyperparameters, including many low-fidelity observations adds to the intrinsic randomness of the procedure and makes extrapolation challenging. We propose to accelerate hyperparameter tuning for neural networks in a robust way by taking into account the relative amount of information contributed by each training example. To do so, we integrate importance sampling with Bayesian optimization, which significantly increases the quality of the black-box function evaluations and their runtime. To overcome the additional overhead cost of using importance sampling, we cast hyperparameter search as a multi-task Bayesian optimization problem over both hyperparameters and importance sampling design, which achieves the best of both worlds. Through learning a trade-off between training complexity and quality, our method improves upon validation error, in the average and worst-case. We show that this results in more reliable performance of our method in less wall-clock time across a variety of and datasets complex neural architectures.

There exist many problems in science and engineering that involve optimization of an unknown or partially unknown objective function. Recently, Bayesian Optimization (BO) has emerged as a powerful tool for solving optimization problems whose objective functions are only available as a black box and are expensive to evaluate. Many practical problems, however, involve optimization of an unknown objective function subject to unknown constraints. This is an important yet challenging problem for which, unlike optimizing an unknown function, existing methods face several limitations. In this paper, we present a novel constrained Bayesian optimization framework to optimize an unknown objective function subject to unknown constraints. We introduce an equivalent optimization by augmenting the objective function with constraints, introducing auxiliary variables for each constraint, and forcing the new variables to be equal to the main variable. Building on the Alternating Direction Method of Multipliers (ADMM) algorithm, we propose ADMM-Bayesian Optimization (ADMMBO) to solve the problem in an iterative fashion. Our framework leads to multiple unconstrained subproblems with unknown objective functions, which we then solve via BO. Our method resolves several challenges of state-of-the-art techniques: it can start from infeasible points, is insensitive to initialization, can efficiently handle `decoupled problems' and has a concrete stopping criterion. Extensive experiments on a number of challenging BO benchmark problems show that our proposed approach outperforms the state-of-the-art methods in terms of the speed of obtaining a feasible solution and convergence to the global optimum as well as minimizing the number of total evaluations of unknown objective and constraints functions.