为学习型控制器提供在分布偏移下的性能保障方法
Distributionally Robust PAC-Bayesian Control
- 结合PAC-Bayes与Wasserstein距离，处理无界损失和训练部署分布差异
- 导出基于闭环映射算子范数的性能损失上界，具有高概率保证
- 适用于线性时不变系统，可生成真实环境部署的安全证书
我们提出一种分布鲁棒的PAC-Bayesian框架，用于认证基于学习的有限时域控制器的性能。现有PAC-Bayes控制研究通常假设损失有界且训练与部署分布一致，而本文明确处理无界损失和环境分布偏移（仿真到现实的差距）。通过结合现代两项研究：PAC-Bayes泛化理论与基于类型1 Wasserstein距离的分布鲁棒优化，利用系统层级合成（SLS）重参数化，推导出一个次高斯损失代理，并得到由分布偏移导致的性能损失上界。该上界直接关联闭环映射的算子范数。对于线性时不变系统，该方法可实现计算上可行的优化框架，并为在不同于训练环境的真实世界部署提供高概率安全证书。
原文摘要 · Abstract (English)
We present a distributionally robust PAC-Bayesian framework for certifying the performance of learning-based finite-horizon controllers. While existing PAC-Bayes control literature typically assumes bounded losses and matching training and deployment distributions, we explicitly address unbounded losses and environmental distribution shifts (the sim-to-real gap). We achieve this by drawing on two modern lines of research, namely the PAC-Bayes generalization theory and distributionally robust optimization via the type-1 Wasserstein distance. By leveraging the System Level Synthesis (SLS) reparametrization, we derive a sub-Gaussian loss proxy and a bound on the performance loss due to distribution shift. Both are tied directly to the operator norm of the closed-loop map. For linear time-invariant systems, this yields a computationally tractable optimization-based framework together with high-probability safety certificates for deployment in real-world environments that differ from those used in training.
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