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• W3081736962 abstract "In online convex optimization (OCO), Lipschitz of the functions is commonly assumed in order to obtain sublinear regret. Moreover, many algorithms have only logarithmic regret when these functions are also strongly convex. Recently, researchers from convex optimization proposed the notions of Lipschitz continuity and strong convexity. Both of the notions are generalizations of their classical counterparts. It has been shown that subgradient methods in the relative setting have performance analogous to their performance in the classical setting. In this work, we consider OCO for relative Lipschitz and relative strongly convex functions. We extend the known regret bounds for classical OCO algorithms to the relative setting. Specifically, we show regret bounds for the follow the regularized leader algorithms and a variant of online mirror descent. Due to the generality of these methods, these results yield regret bounds for a wide variety of OCO algorithms. Furthermore, we further extend the results to algorithms with extra regularization such as regularized dual averaging." @default.
• W3081736962 created "2020-09-08" @default.
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• W3081736962 date "2020-10-22" @default.
• W3081736962 modified "2023-09-26" @default.
• W3081736962 title "Regret Bounds without Lipschitz Continuity: Online Learning with Relative-Lipschitz Losses" @default.
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• W3081736962 hasPublicationYear "2020" @default.
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