发表机构
Columbia University（哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究非平稳在线学习中重复参数环境下的数据重用，提出暴露上限重用（ECR）算法，结合变化检测与污染控制，实现遗憾随不同值数量而非变化次数扩展，并证明其近乎极小极大最优性。
AI 中文摘要
我们考虑非平稳环境中的在线学习，其目标是跟踪一个在有限个重复出现的值之间突然切换的未知参数。重复性为明智地重用过去的观测以提高算法性能提供了可能性。然而，底层信号的变化性质以及对这些动态缺乏信息可能限制“安全”重用数据的能力。在本文中，我们量化了此类问题中的一些基本权衡，并表明它们与经典的偏差-方差困境有某种相似之处。具体来说，我们提出了一类随时算法，称为暴露上限重用（Exposure-Capped Reuse，ECR），它结合了在线变化检测、兼容性测试和“污染”控制。我们刻画了ECR的遗憾随不同值的数量而非变化次数扩展的机制，并推导了一个新颖的信息论下界，确立了ECR的近乎极小极大最优性。这为数据重用的统计“价值”提供了严格的量化。
英文摘要
We consider online learning in non-stationary environments, where the goal is to track an unknown parameter that switches abruptly between a finite set of recurring values. Recurrence opens the possibility of judiciously reusing past observations to improve algorithm performance. However, the changing nature of the underlying signal and lack of information on these dynamics may limit the ability to "safely" reuse data. In this paper we quantify some of the fundamental tradeoffs in this class of problems, and show that they bear a certain resemblance to the classical bias-variance dilemma. Specifically, we propose a class of anytime algorithms, dubbed Exposure-Capped Reuse (ECR), that combine online change detection, compatibility testing, and "contamination" control. We characterize the regime in which ECR's regret scales with the number of distinct values rather than the number of changes, and derive a novel information-theoretic lower bound that establishes the near-minimax optimality of ECR. This provides rigorous quantification of the statistical "value" of data reuse.
