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Non-stationary online Learning with memory and Non-stochastic Control

JOURNAL OF MACHINE LEARNING RESEARCH 2023年第1期24卷 1-70页

作者： Zhao, Peng Yan, Yu-Hu Wang, Yu -Xiang Zhou, Zhi-Hua Nanjing Univ Natl Key Lab Novel Software Technol Nanjing 210023 Peoples R China Univ Calif Santa Barbara Dept Comp Sci Santa Barbara CA 93106 USA

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.

关键词： online learning online convex optimization with memory online non-stochastic control non-stationary environments dynamic policy regret online ensemble

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Non-stationary online learning with memory and non-stochastic control

The Journal of Machine Learning Research

引用

The Journal of Machine Learning Research 2023年第1期24卷 9831-9900页

作者： Peng Zhao Yu-Hu Yan Yu-Xiang Wang Zhi-Hua Zhou National Key Laboratory for Novel Software Technology Nanjing University Nanjing China Department of Computer Science University of California Santa Barbara CA

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.

关键词： online learning online convex optimization with memory online non-stochastic control non-stationary environments dynamic policy regret online ensemble

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