2023/05/23 by Chung-En Tsai, Y. Lin, Tsai, Chung-En +3 · 2 citations
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Cognitive Radio Networks and Spectrum Sensing #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.2305.13946
openalex publication_date 2023/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.