Targeted Variance Reduction: Robust Bayesian Optimization of Black-Box Simulators with Noise Parameters

Khái niệm cốt lõi

The author proposes a new Bayesian optimization method, Targeted Variance Reduction (TVR), to address robust black-box optimization problems by leveraging joint acquisition functions over control and noise parameters.

Tóm tắt

Scientific computing advancements allow reliable simulation of complex phenomena via computer experiments. Bayesian optimization, particularly TVR, offers an effective solution for optimizing response surfaces over large parameter spaces in the presence of uncertainty.
Computer experiments incur high computational costs but can be optimized using Gaussian processes and acquisition functions like TVR. The TVR method targets variance reduction on the objective within the desired region of improvement by exploiting control-to-noise interactions effectively.
The TVR approach demonstrates improved performance over existing methods in numerical experiments and applications to robust design challenges under operational uncertainty. It provides insights into exploration-exploitation-precision trade-offs crucial for robust black-box optimization.
Robust optimization formulations like TVR are essential for addressing uncertainties in simulations and improving decision-making processes in various scientific applications.

Thống kê

Each simulation run may take thousands of CPU hours to perform [Yeh et al., 2018].
The first distribution has a probability mass function with values ranging from 0.0792 to 0.3561.
The second distribution has a probability mass function with values ranging from 0.0762 to 0.2509.

Trích dẫn

"The TVR leverages a novel joint acquisition function over (x, θ), which targets variance reduction on the objective within the desired region of improvement."
"TVR can further accommodate a broad class of non-Gaussian distributions on P via a careful integration of normalizing flows."
"The improved performance of TVR over the state-of-the-art is demonstrated in numerical experiments and applications to robust design challenges."

Thông tin chi tiết chính được chắt lọc từ

Targeted Variance Reduction

by John Joshua ... lúc arxiv.org 03-07-2024

https://arxiv.org/pdf/2403.03816.pdf

Yêu cầu sâu hơn

How does the TVR method compare to traditional two-stage approaches in terms of computational efficiency

The TVR method offers a significant improvement in computational efficiency compared to traditional two-stage approaches. In the TVR method, the joint acquisition function over both control and noise parameters allows for more effective leveraging of control-to-noise interactions. This results in better-informed decisions on selecting the next evaluation point, leading to potentially fewer iterations needed to reach an optimal solution. Additionally, the closed-form expression of the TVR acquisition function enables efficient optimization using gradient-based methods and automatic differentiation. This streamlined approach reduces computational overhead and enhances overall efficiency in robust black-box optimization.

What are the potential limitations or drawbacks of using normalizing flows for accommodating non-Gaussian distributions

While normalizing flows offer a powerful tool for accommodating non-Gaussian distributions in Bayesian optimization, there are potential limitations or drawbacks to consider. One limitation is related to scalability and complexity when dealing with high-dimensional data or complex distributions. Normalizing flows require careful design and training of neural network architectures, which can be computationally intensive and challenging for large datasets or intricate distribution shapes. Additionally, ensuring convergence and stability during training may pose challenges, especially with highly nonlinear or multimodal distributions. Furthermore, interpreting the learned transformations from normalizing flows can be complex, making it harder to understand how these transformations impact model performance.

How might the insights gained from robust parameter design contribute to enhancing the effectiveness of Bayesian optimization methods like TVR

Insights gained from robust parameter design can significantly contribute to enhancing the effectiveness of Bayesian optimization methods like TVR by emphasizing control-to-noise interactions for improved decision-making. Robust parameter design principles focus on reducing sensitivity to uncontrollable factors through strategic selection of controllable parameters—a concept directly relevant to robust optimization problems where uncertainty exists in practice conditions (e.g., environmental factors). By incorporating strategies from robust parameter design into Bayesian optimization algorithms like TVR, practitioners can better account for uncertainties while optimizing objective functions over varying input parameters effectively.