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

• URL: http://arxiv.org/abs/2305.13946v2
• Date: Sat, 4 Nov 2023 11:00:59 GMT
• Title: Data-Dependent Bounds for Online Portfolio Selection Without Lipschitzness and Smoothness
• Authors: Chung-En Tsai and Ying-Ting Lin and Yen-Huan Li
• Abstract summary: We introduce 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"
• Score: 2.315156126698557
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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-iteration 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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