标题： 在线凸规划中的动态模型和追踪遗憾 显示英文标题

标题： Dynamical Models and Tracking Regret in Online Convex Programming

摘要： 本文介绍了一种新的在线凸优化方法，该方法引入了一组候选动态模型，并建立了新颖的追踪遗憾界，这些界值与比较器相对于该族中最佳动态模型的偏差成比例。 先前的在线优化方法旨在使总累积损失与最佳比较器序列的损失相当，而现有的追踪或移动遗憾界值则与比较器序列的整体变化成比例。 然而，在许多实际场景中，环境是非平稳的，小变化的比较器序列相对较弱，导致较大的损失。 相比之下，所提出的动态镜像下降方法可以通过跟踪最佳动态模型并基于该模型形成预测，从而相对于高度可变的比较器序列获得较低的遗憾。 这一概念在动态场景的顺序压缩观测以及跟踪动态社交网络的情境下通过实证进行了验证。 显示英文摘要

摘要： This paper describes a new online convex optimization method which incorporates a family of candidate dynamical models and establishes novel tracking regret bounds that scale with the comparator's deviation from the best dynamical model in this family. Previous online optimization methods are designed to have a total accumulated loss comparable to that of the best comparator sequence, and existing tracking or shifting regret bounds scale with the overall variation of the comparator sequence. In many practical scenarios, however, the environment is nonstationary and comparator sequences with small variation are quite weak, resulting in large losses. The proposed Dynamic Mirror Descent method, in contrast, can yield low regret relative to highly variable comparator sequences by both tracking the best dynamical model and forming predictions based on that model. This concept is demonstrated empirically in the context of sequential compressive observations of a dynamic scene and tracking a dynamic social network.