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Title: Second Order Path Variationals in Non-Stationary Online Learning
We consider the problem of universal dynamic regret minimization under exp-concave and smooth losses. We show that appropriately designed Strongly Adaptive algorithms achieve a dynamic regret of $\tilde O(d^2 n^{1/5} [\mathcal{TV}_1(w_{1:n})]^{2/5} \vee d^2)$, where $n$ is the time horizon and $\mathcal{TV}_1(w_{1:n})$ a path variational based on second order differences of the comparator sequence. Such a path variational naturally encodes comparator sequences that are piece-wise linear – a powerful family that tracks a variety of non-stationarity patterns in practice (Kim et al., 2009). The aforementioned dynamic regret is shown to be optimal modulo dimension dependencies and poly-logarithmic factors of $n$. To the best of our knowledge, this path variational has not been studied in the non-stochastic online learning literature before. Our proof techniques rely on analysing the KKT conditions of the offline oracle and requires several non-trivial generalizations of the ideas in Baby and Wang (2021) where the latter work only implies an $\tilde{O}(n^{1/3})$ regret for the current problem.  more » « less
Award ID(s):
2007117
NSF-PAR ID:
10466935
Author(s) / Creator(s):
;
Editor(s):
Ruiz, Francisco and
Publisher / Repository:
PMLR
Date Published:
Journal Name:
Proceedings of Machine Learning Research
Volume:
206
ISSN:
2640-3498
Page Range / eLocation ID:
9024--9075
Subject(s) / Keyword(s):
["Online learning","nonstationarity","dynamic regret","total variation"]
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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