Online Convex Optimization in Dynamic Environments

By Eric C. Hall, Rebecca M. Willett. 2015

238 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering, Management Science and Operations Research

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Citations in the corpus

Decentralized Online Learning: Take Benefits from Others’ Data without Sharing Your Own to Track Global Trend (2019, neutral): “For example, References [10, 11] choose the reference points {x∗ t }t=1 satisfying ∑T−1 t=1 ‖x∗ t+1 − Φ(x∗ t )‖ ≤ M , where Φ(x∗ t ) is the predictive optimal model.”
Online Meta-Learning (2019, neutral): “To overcome these limitations, prior work has placed restrictions on how quickly the loss functions or the comparator model can change (Hazan & Comandur, 2009; Hall & Willett, 2015; Herbster & Warmuth, 1995).”
Distributed Online Optimization in Dynamic Environments Using Mirror Descent (2016, methodology): “In parallel to studies of centralized online optimization [14], [15], [26], the hardness of the problem should be characterized via a complexity measure that captures the variation in the minimizer sequence {x t }t=1 .”
Markov Decision Processes with Time-varying Transition Probabilities and Rewards (2019, unknown): “…(Hazan, 2016; Shalev-Shwartz, 2012; Zinkevich, 2003; Mokhtari et al., 2016; Jadbabaie et al., 2015; Li et al., 2018; Besbes et al., 2015; Hall & Willett, 2015; 2013; Zhang et al., 2017), in prediction with expert advice (Cesa-Bianchi & Lugosi, 2006; Herbster & Warmuth, 1998; Adamskiy et…”
Optimization in Dynamic Environments : Improved Regret Rates for Strongly Convex Problems (2016, unknown): “where Φt(ut−1) is the predicted reference point for step t evaluated at step t− 1 by the learner [10].”
Proximal Online Gradient Is Optimum for Dynamic Regret: A General Lower Bound (2021, background): “When Φ(yt) predict the dynamic environment accurately, [22], [23] obtain a better regret than [1], but it is still bounded by O (√ TD0 + √ T ) .”
Tracking Moving Agents via Inexact Online Gradient Descent Algorithm (2017, methodology): “Different from the vast majority of literature on online convex optimization, the gradient bound allows us to forgo the assumption on the boundedness of the set X [8], [9], [17].”
Understand Dynamic Regret with Switching Cost for Online Decision Making (2019, background): “[21, 22] use similar but more general denitions of dynamic regret, and still achieves O (√ TD + √ T ) regret.”
Proximal Online Gradient is Optimum for Dynamic Regret (2018, background): “Then, set the learning rate η t by Letting β = 0, our upper bound is O (cid:16)p T D 0 ( T ) + √ T (cid:17) , which slightly improves the known regret (cid:16) [Zinkevich, 2003, Hall and Willett, 2013, 2015] in the sense that it has a better dependence on D 0 ( T ).”
Incremental learning algorithms and applications (2016, methodology): “Second order numeric optimisation methods and advanced optimisation schemes can be extended as well, such as variational Bayes, convex optimization, second order perceptron learning based on higher order statistics in primal or dual space, and online realisations of the quasi-Newton Broyden-Fletcher”