[论文] [论文] PAC-Bayesian Certificates for Quadratic Closed-Loop Control

论文概要

研究领域: ML 作者: Domagoj Herceg 发布时间: 2026-06-26 arXiv: 2606.28281

中文摘要

PAC-Bayesian界限为数据依赖的随机预测器提供有限样本保证，但将其应用于基于学习的控制是困难的，因为自然目标是二次轨迹成本。此类损失是无界的、非Lipschitz的。我们采用系统级综合参数化，它直接暴露线性系统的闭环轨迹映射，并使二次控制损失适用于显式认证。此外，我们为可行闭环响应上的后验分布提供一组PAC-Bayes-Chernoff证书。对于具有任意协方差的高斯扰动轨迹，我们推导精确的单边高斯变换和通过闭环灵敏度量表达的易处理的二次上界。尽管PAC-Bayes认证非退化的后验，SLS损失的凸二次形式将证书转移到后验均值响应。我们提出一个特别适合控制同时保留随机后验在界限中的确定性均值响应部署结果。此外，我们为此部署提供数据驱动的界限。双积分器上的数值实验表明，该算法作为灵敏度感知的有限样本正则化器，在低数据状态下改善保留成本并降低闭环灵敏度。

原文摘要

PAC-Bayesian bounds provide finite-sample guarantees for data-dependent randomized predictors, but applying them to learning-based control is difficult because the natural objective is a quadratic trajectory cost. Such losses are unbounded, non-Lipschitz , and lead to response-dependent Chernoff terms. We employ System Level Synthesis parameterization, which exposes the closed-loop trajectory map of a linear system directly and makes the quadratic control loss amenable to explicit certification. Moreover, we provide a set of PAC-Bayes-Chernoff certificates for posterior distributions over feasible closed-loop responses. For Gaussian disturbance trajectories with arbitrary covariance, we derive an exact one-sided Gaussian transform and a tractable quadratic upper bound expressed through clo...

--- *自动采集于 2026-06-30*

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