不依赖模型的在线预测方法，实现对稳定系统误差的对数级累积损失控制。
Online Nonstochastic Prediction: Logarithmic Regret via Predictive Online Least Squares
- 通过自适应预测提示构造无约束在线最小二乘法，避免传统方法对有界性的依赖。
- 证明任意稳定李雅普诺夫预测器生成的提示可使残差一致有界，实现对数级后悔率。
- 适用于非随机扰动下的动态系统，特别适合轨迹可能发散但系统稳定的场景。
我们研究在非随机扰动下，对边缘稳定、部分可观测线性动态系统进行在线预测的问题。目标是最小化累积平方预测损失，并与最优事后李雅普诺夫预测器竞争。传统在线学习方法通常依赖有界域/梯度，因此在边缘稳定系统中可能出现轨迹无界时失效。本文提出一种无约束在线最小二乘法，通过量身定制的预测提示稳定学习过程。在已知模型的情况下，我们证明：任意稳定李雅普诺夫预测器构造的提示能使提示残差一致有界，即使轨迹无界增长，仍能实现对数级后悔率。此外，我们还讨论了无模型预测，引入一个适用于对称系统的通用提示，在无需模型知识的情况下依然保持对数级后悔率。结果表明，该方法相比经典固定增益观测器，在非随机扰动下提供了自适应且实例最优的在线预测器。
原文摘要 · Abstract (English)
We study online prediction for marginally stable, partially observed linear dynamical systems under nonstochastic disturbances. Our objective is to minimize the cumulative squared prediction loss and compete with the best-in-hindsight Luenberger predictor. Standard online learning methods typically rely on bounded domains/gradients, and thus their guarantees may fail to deal with potentially unbounded trajectories in marginally stable systems. In this paper, we introduce an unconstrained online least squares method that stabilizes the learning process via tailored predictive hints. With model knowledge, we prove that hints constructed from any stabilizing Luenberger predictor render the hint residuals uniformly bounded, achieving logarithmic regret despite unbounded trajectory growth. We also discuss model-free prediction and introduce a simple universal hint for symmetric systems, under which logarithmic regret is maintained without model knowledge. Our results provide an adaptive, instance-wise optimal online predictor compared to classical fixed-gain observers under nonstochastic disturbances.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。