论文标题
在线凸优化具有可预测序列的长期约束
Online Convex Optimization with Long Term Constraints for Predictable Sequences
论文作者
论文摘要
在本文中,我们研究了用于在线学习的在线凸优化(OCO)的框架。 OCO为许多应用程序提供了非常强大的在线学习框架。在这种情况下,我们研究了一个名为{\ it oco具有长期约束}的OCO的特定框架。长期限制通常是作为在在线优化的每个更新步骤中降低投影复杂性的替代方案。尽管已经通过长期限制进行了许多算法进步,但这些算法通常假定一定$ t $有限步骤的成本功能的顺序确定了对在线学习者的成本的对抗性。在许多情况下,成本函数的顺序可能不会无关,因此可以从观察到的那些时间点来预测。在本文中,我们研究了序列可预测的设置。我们提出了一种新颖的在线优化算法,用于在线优化,并具有可以利用这种可预测性的长期限制。我们表明,借助可以在序列中提供下一个功能的梯度信息的预测变量,我们的算法可以实现总体的遗憾和约束违规率,严格少于没有预测而无法实现的速率。
In this paper, we investigate the framework of Online Convex Optimization (OCO) for online learning. OCO offers a very powerful online learning framework for many applications. In this context, we study a specific framework of OCO called {\it OCO with long term constraints}. Long term constraints are introduced typically as an alternative to reduce the complexity of the projection at every update step in online optimization. While many algorithmic advances have been made towards online optimization with long term constraints, these algorithms typically assume that the sequence of cost functions over a certain $T$ finite steps that determine the cost to the online learner are adversarially generated. In many circumstances, the sequence of cost functions may not be unrelated, and thus predictable from those observed till a point of time. In this paper, we study the setting where the sequences are predictable. We present a novel online optimization algorithm for online optimization with long term constraints that can leverage such predictability. We show that, with a predictor that can supply the gradient information of the next function in the sequence, our algorithm can achieve an overall regret and constraint violation rate that is strictly less than the rate that is achievable without prediction.