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

Core Concepts

Proposing a new method, Targeted Variance Reduction (TVR), for robust black-box optimization by leveraging joint acquisition over control and noise parameters.

Abstract

科学的なアプリケーションにおけるブラックボックスシミュレータの最適化は、不確かさを持つパラメータに対するロバストな最適化が重要である。既存の手法では、制御パラメータとノイズパラメータ間の相互作用を十分に活用していない。新しいBayesian最適化手法であるTargeted Variance Reduction (TVR)は、制御とノイズパラメータのジョイント獲得を通じて効果的なロバスト最適化を実現する。 TVRは、目的関数の分散削減をターゲットとし、望ましい改善領域内で目的関数の精度向上を図る。この新しい獲得関数は、制御とノイズパラメータの両方にわたってジョイント獲得を提供し、効果的なロバスト最適化に向けてフィットされた制御とノイズの相互作用をよりよく活用する。 TVR獲得は探索・活用・精度トレードオフを示し、探索・活用トレードオフを強調しつつも精度向上も促進する。これは強化学習における探索・活用トレードオフの新たな拡張であり、ロバストブラックボックス最適化における重要性が示されている。 TVRアルゴリズムは他の既存手法と比較して効果的であり、一連の数値実験や自動車ブレーキディスク設計への応用でその優れた性能が示されている。

Stats

TVR leverages joint acquisition over (x, θ). TVR targets variance reduction on the objective within the desired region of improvement. TVR reveals an exploration-exploitation-precision trade-off for robust black-box optimization.

Quotes

"Robust optimization aims to optimize the objective E[f(x, Θ)], where Θ ∼ P is a random variable that models uncertainty on θ." "The TVR leverages a novel joint acquisition function over (x, θ), which targets variance reduction on the objective within the desired region of improvement." "The TVR can further accommodate a broad class of non-Gaussian distributions on P via a careful integration of normalizing flows."

Key Insights Distilled From

Targeted Variance Reduction

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

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

Deeper Inquiries

How does TVR address the limitations of existing two-stage approaches in robust optimization

TVR addresses the limitations of existing two-stage approaches in robust optimization by introducing a joint acquisition function over both control parameters x and noise parameters θ. Unlike the two-stage methods that optimize x and θ separately based on different criteria, TVR leverages the fitted control-to-noise interactions in f for guiding sequential queries more effectively. By targeting variance reduction within the desired region of improvement, TVR ensures that both exploration and exploitation are considered simultaneously, leading to better decision-making on selecting the next evaluation point (xn+1, θn+1). This joint acquisition function allows TVR to fully exploit the underlying interactions between control and noise parameters for more efficient robust optimization.

What are the implications of leveraging control-to-noise interactions for effective robust parameter design

Leveraging control-to-noise interactions is crucial for effective robust parameter design as it enables a better understanding of how changes in controllable factors impact responses under uncertain conditions represented by noise parameters. By considering these interactions, designers can identify optimal settings for control parameters that minimize sensitivity to variations in noise factors. This approach helps improve product quality and performance by ensuring stability and reliability even in the presence of uncertainties or fluctuations in external conditions. Ultimately, leveraging control-to-noise interactions leads to more resilient designs that can withstand real-world variability.

How can normalizing flows enhance the flexibility and performance of Bayesian optimization methods like TVR

Normalizing flows enhance the flexibility and performance of Bayesian optimization methods like TVR by providing a powerful tool for modeling complex distributions with continuous variables such as uncertain parameters Θ. Normalizing flows allow for learning invertible transformations from known distributions like Gaussian processes to arbitrary target distributions specified by P without requiring explicit knowledge of their c.d.f.s. This capability enables practitioners to handle diverse types of uncertainty efficiently while maintaining tractability in model training and inference processes. By incorporating normalizing flows into Bayesian optimization frameworks like TVR, researchers can achieve greater adaptability and accuracy when dealing with challenging simulation environments involving intricate probabilistic structures.