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Data-Dependent Bounds for Online Portfolio Selection Without Lipschitzness and Smoothness

Chung-En Tsai · Ying-Ting Lin · Yen-Huan Li

Great Hall & Hall B1+B2 (level 1) #1820
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[ Paper [ Poster [ OpenReview
Tue 12 Dec 3:15 p.m. PST — 5:15 p.m. PST


This work introduces the first small-loss and gradual-variation regret bounds for online portfolio selection, marking the first instances of data-dependent bounds for online convex optimization with non-Lipschitz, non-smooth losses. The algorithms we propose exhibit sublinear regret rates in the worst cases and achieve logarithmic regrets when the data is "easy," with per-round time almost linear in the number of investment alternatives. The regret bounds are derived using novel smoothness characterizations of the logarithmic loss, a local norm-based analysis of following the regularized leader (FTRL) with self-concordant regularizers, which are not necessarily barriers, and an implicit variant of optimistic FTRL with the log-barrier.

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