The Parallel Knowledge Gradient Method for Batch Bayesian Optimization (1606.04414v4)

Abstract: In many applications of black-box optimization, one can evaluate multiple points simultaneously, e.g. when evaluating the performances of several different neural network architectures in a parallel computing environment. In this paper, we develop a novel batch Bayesian optimization algorithm --- the parallel knowledge gradient method. By construction, this method provides the one-step Bayes-optimal batch of points to sample. We provide an efficient strategy for computing this Bayes-optimal batch of points, and we demonstrate that the parallel knowledge gradient method finds global optima significantly faster than previous batch Bayesian optimization algorithms on both synthetic test functions and when tuning hyperparameters of practical machine learning algorithms, especially when function evaluations are noisy.

• The paper introduces a novel parallel KG method that selects evaluation batches to accelerate global optimization in noisy settings.
• It employs a Gaussian process framework with an acquisition function based on infinitesimal perturbation analysis for efficient gradient evaluation.
• Numerical results demonstrate improved performance over standard methods on synthetic functions and practical hyperparameter tuning tasks.

Overview of the Parallel Knowledge Gradient Method for Batch Bayesian Optimization

The paper "The Parallel Knowledge Gradient Method for Batch Bayesian Optimization" by Jian Wu and Peter I. Frazier presents a novel approach to optimizing expensive-to-evaluate black-box functions using batch Bayesian optimization (BO). The authors introduce the parallel knowledge gradient (KG) method, which is designed to efficiently identify global optima with fewer evaluations than existing batch BO algorithms, particularly in scenarios where function evaluations are noisy.

Key Contributions and Methodology

This work makes significant contributions to the field of Bayesian optimization by addressing the need for efficient parallel evaluation strategies. Unlike traditional BO strategies which are often sequential, the parallel knowledge gradient method allows for simultaneous evaluation of multiple points in each iteration, increasing computational efficiency when resources permit parallel computations.

1. Bayesian Optimization Framework: The algorithm operates by placing a Gaussian process prior on the objective function, updating this distribution with each newly observed data point. Decisions on subsequent points for evaluation are made based on an acquisition function, which in this work is the knowledge gradient extended to a batch setting.
2. Novel Acquisition Function: The parallel KG method incorporates a decision-theoretic analysis to choose the next batch of points optimally in terms of expected outcome, considering all candidate points collectively rather than extending from single-evaluation acquisition functions like expected improvement (EI) or upper confidence bound (UCB).
3. Efficient Computation: Recognizing computational challenges inherent in optimizing the parallel KG acquisition function, the authors develop a technique based on infinitesimal perturbation analysis (IPA) for efficient gradient evaluation, enabling practical optimization over potentially high-dimensional spaces.

Numerical Results and Benchmarking

The paper extensively evaluates the proposed method against other state-of-the-art batch BO algorithms on both synthetic test functions and real-world machine learning tasks, such as hyperparameter tuning for logistic regression and convolutional neural networks.

• Performance on Synthetic Functions: The parallel KG method consistently outperforms or matches the performance of competing methods in locating near-optimal solutions, particularly in scenarios with noisy function evaluations.
• Real-world Applications: When applied to hyperparameter tuning tasks, the proposed algorithm demonstrates significant improvements in finding efficient configurations, proving its utility in practical machine learning pipelines.

Implications and Future Directions

The development of the parallel KG method presents practical and theoretical implications:

• Practical Implications: This method is particularly advantageous in high-performance computing environments where parallel resources can be utilized to reduce overall optimization time. It provides a more robust framework for dealing with noise in function evaluations, which is often encountered in real-world applications.
• Theoretical Insights: The decision-theoretic basis and the flexibility in handling noisy measurements enrich the theoretical landscape of Bayesian optimization, providing foundations for further exploration in multi-fidelity and distributed optimization settings.

For future work, the parallel KG method could be extended to handle more complex model structures or integrated with other global optimization strategies to further enhance its efficiency and applicability. Additionally, adapting this method to asynchronous settings, where evaluations may complete at different times, could lead to further improvements in optimization throughput and performance.

In conclusion, the parallel knowledge gradient method represents a substantial improvement for batch Bayesian optimization, with significant gains in computational efficiency and robustness, making it an asset for researchers and practitioners aiming to optimize complex, noisy systems.