arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2102.03758cs.LGstat.ML
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带记忆的非平稳在线学习与非随机控制

Non-stationary Online Learning with Memory and Non-stochastic Control

Nanjing University(南京大学);University of California, Santa Barbara(加州大学圣巴巴拉分校)

Peng Zhao, Yu-Hu Yan, Yu-Xiang Wang, Zhi-Hua Zhou

AI总结:

针对带记忆在线凸优化与非随机控制中的非平稳性,提出感知切换成本的在线集成算法及基于梯度的控制器,实现最优动态策略遗憾保证。

摘要:

我们研究带记忆的在线凸优化(Online Convex Optimization,OCO)问题,该问题允许损失函数依赖于过去的决策,因此能够刻画学习问题中的时间效应。本文引入动态策略遗憾作为性能度量,以设计对非平稳环境鲁棒的算法;该度量将算法的决策与一系列不断变化的比较器进行竞争。我们提出了一种用于带记忆 OCO 的新型算法,并证明该算法在时间范围、非平稳性度量和记忆长度方面享有最优的动态策略遗憾。关键技术挑战在于如何控制切换成本,即参与者决策的累积移动量;我们通过一种新颖的、感知切换成本的在线集成方法巧妙地解决了这一问题,该方法配备了动态策略遗憾的全新元—基分解,以及对元学习器和基学习器的精心设计,从而显式地正则化切换成本。这些结果进一步被应用于处理在线非随机控制(Agarwal 等人,2019)中的非平稳性,即在具有对抗性扰动和凸成本函数的情况下控制线性动力系统。我们推导了一种具有动态策略遗憾保证的新型基于梯度的控制器,这是首个被证明可与在线非随机控制中一系列不断变化的策略相竞争的控制器。

英文摘要:

We study the problem of Online Convex Optimization (OCO) with memory, which allows loss functions to depend on past decisions and thus captures temporal effects of learning problems. In this paper, we introduce dynamic policy regret as the performance measure to design algorithms robust to non-stationary environments, which competes algorithms' decisions with a sequence of changing comparators. We propose a novel algorithm for OCO with memory that provably enjoys an optimal dynamic policy regret in terms of time horizon, non-stationarity measure, and memory length. The key technical challenge is how to control the switching cost, the cumulative movements of player's decisions, which is neatly addressed by a novel switching-cost-aware online ensemble approach equipped with a new meta-base decomposition of dynamic policy regret and a careful design of meta-learner and base-learner that explicitly regularizes the switching cost. The results are further applied to tackle non-stationarity in online non-stochastic control (Agarwal et al., 2019), i.e., controlling a linear dynamical system with adversarial disturbance and convex cost functions. We derive a novel gradient-based controller with dynamic policy regret guarantees, which is the first controller provably competitive to a sequence of changing policies for online non-stochastic control.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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