Statistical Learning Theory for Control: A Finite-Sample Perspective
Statistical Learning Theory for Control: A Finite-Sample Perspective
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DOI：
10.1109/mcs.2023.3310345
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发表时间：
2022-09
期刊：
影响因子：
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通讯作者：
Anastasios Tsiamis;Ingvar M. Ziemann;N. Matni;George Pappas
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文献类型：
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作者：
Anastasios Tsiamis;Ingvar M. Ziemann;N. Matni;George Pappas
学习算法已成为现代工程解决方案不可或缺的组成部分。例子包括从自动驾驶汽车和推荐系统到金融甚至关键基础设施，其中许多通常属于控制理论的范围。虽然这些算法已经在某些应用中显示出巨大的前景[1]，但仍然存在相当大的挑战，特别是在保证安全性和衡量操作的基本限制方面。因此，当我们将机器学习工具集成到我们的系统中时，我们还需要对它们在动态和系统理论现象存在下如何运作有一个综合的理论理解。在过去的几年里，人们为实现这一目标——对学习、动力学和控制的综合理论理解——做出了巨大的努力。虽然还有很多工作要做，但（完全观察到的）线性动力系统的相对清晰和完整的图景已经开始出现。这些系统已经允许对具体故障模式进行推理，从而有助于指明前进的道路。此外，虽然这些系统乍一看很简单，但分析起来却很困难。最近，我们的社区引入了许多来自学习理论和高维统计的方法（通常不在控制理论工具箱中）。本教程调查介绍了这些结果，以便在未知线性动力系统的背景下进行学习（参见“摘要”）。我们回顾了当前的技术水平，并强调需要哪些工具才能达到这些结果。我们的重点是表征学习算法的样本效率和基本限制。在此过程中，我们还描述了一些悬而未决的问题。更具体地说，本文的结构如下。我们首先回顾系统识别有限样本分析的最新进展。接下来，我们讨论如何在下游使用这些有限样本范围来为基于学习的离线控制提供有保证的性能。最后的技术部分讨论更具挑战性的在线控制设置。最后，根据讨论的材料，我们概述了一些未来的方向。
Learning algorithms have become an integral component to modern engineering solutions. Examples range from self-driving cars and recommender systems to finance and even critical infrastructure, many of which are typically under the purview of control theory. While these algorithms have already shown tremendous promise in certain applications [1], there are considerable challenges, in particular, with respect to guaranteeing safety and gauging fundamental limits of operation. Thus, as we integrate tools from machine learning into our systems, we also require an integrated theoretical understanding of how they operate in the presence of dynamic and system-theoretic phenomena. Over the past few years, intense efforts toward this goal—an integrated theoretical understanding of learning, dynamics, and control—have been made. While much work remains to be done, a relatively clear and complete picture has begun to emerge for (fully observed) linear dynamical systems. These systems already allow for reasoning about concrete failure modes, thus helping to indicate a path forward. Moreover, while simple at a glance, these systems can be challenging to analyze. Recently, a host of methods from learning theory and high-dimensional statistics, not typically in the control-theoretic toolbox, have been introduced to our community. This tutorial survey serves as an introduction to these results for learning in the context of unknown linear dynamical systems (see “Summary”). We review the current state of the art and emphasize which tools are needed to arrive at these results. Our focus is on characterizing the sample efficiency and fundamental limits of learning algorithms. Along the way, we also delineate a number of open problems. More concretely, this article is structured as follows. We begin by revisiting recent advances in the finite-sample analysis of system identification. Next, we discuss how these finite-sample bounds can be used downstream to give guaranteed performance for learning-based offline control. The final technical section discusses the more challenging online control setting. Finally, in light of the material discussed, we outline a number of future directions.