Gradient-based Sample Selection for Faster Bayesian Optimization (2504.07742v2)

Abstract: Bayesian optimization (BO) is an effective technique for black-box optimization. However, its applicability is typically limited to moderate-budget problems due to the cubic complexity in computing the Gaussian process (GP) surrogate model. In large-budget scenarios, directly employing the standard GP model faces significant challenges in computational time and resource requirements. In this paper, we propose a novel approach, gradient-based sample selection Bayesian Optimization (GSSBO), to enhance the computational efficiency of BO. The GP model is constructed on a selected set of samples instead of the whole dataset. These samples are selected by leveraging gradient information to maintain diversity and representation. We provide a theoretical analysis of the gradient-based sample selection strategy and obtain explicit sublinear regret bounds for our proposed framework. Extensive experiments on synthetic and real-world tasks demonstrate that our approach significantly reduces the computational cost of GP fitting in BO while maintaining optimization performance comparable to baseline methods.

Gradient-based Sample Selection for Faster Bayesian Optimization

The paper presents a novel approach to Bayesian Optimization (BO), addressing computational challenges associated with large-scale datasets. Bayesian Optimization is a popular method for optimizing black-box functions, but it faces computational limitations due to the cubic complexity of Gaussian Process (GP) models when handling extensive data sets.

Key Contributions

The core contribution of this paper is the introduction of Gradient-based Sample Selection Bayesian Optimization (GSSBO). This method aims to enhance BO's computational efficiency by introducing a mechanism for intelligent sample selection based on gradient information. The main contributions are:

1. Efficient Computation: A practical algorithm, GSSBO, is developed to reduce the cost of GP fitting. This algorithm selects a subset of data points instead of using the entire dataset, hence reducing the computational load.
2. Theoretical Analysis: The paper provides a rigorous analysis, demonstrating that the regret bounds of GSSBO are kept sublinear, similar to traditional BO strategies without sample reduction. This ensures that GSSBO maintains optimization performance while decreasing computational complexity.
3. Empirical Validation: Extensive experiments with synthetic and real-world datasets prove that GSSBO significantly reduces computational costs while delivering performance comparable to existing methods.

Theoretical Framework

The authors propose a gradient-based sample selection strategy, which uses gradient information to select the most representative subset of samples. Theoretical results demonstrate that this method does not compromise the BO's ability to model the objective function accurately. The use of regret bounds reinforces the reliability of the method compared to standard GP-UCB algorithms.

Empirical Results

The empirical section highlights experiments on both synthetic benchmark functions and a real-world application involving Neural Architecture Search (NAS) for diabetes detection. Key findings include:

• Computational Efficiency: GSSBO substantially reduces computational times across all tested functions compared to several baseline methods, including standard GP-UCB, SVIGP, and VecchiaBO.
• Optimization Performance: GSSBO's performance in terms of cumulative regret follows a comparable trajectory to standard GP-UCB, maintaining effectiveness throughout the optimization process.
• Gradient-based Selection Benefits: The gradient-based selection method effectively maintains focus on informative and diverse sample subsets, avoiding redundant samples and thus promoting efficient exploration and exploitation cycles during optimization.

Practical Implications and Future Work

This research has significant implications for scaling BO to larger problems in practical settings, such as machine learning hyperparameter tuning and real-time optimization tasks. GSSBO could be especially relevant in applications where computational resources are a constraint.

Future developments could explore adaptive strategies for buffer size, refined techniques for estimating gradients in noisy settings, and integration with other scalable BO methods, potentially expanding its applicability to more complex, high-dimensional black-box functions.

In summary, this paper presents a substantial improvement in the computational efficiency of Bayesian Optimization by leveraging gradient-based sample selection. It expands the practical usability of BO in real-world applications, demonstrating the method’s potential to adapt classical optimization techniques to modern computational challenges.