Tsai, Chung EnChung EnTsaiLin, Ying TingYing TingLinYEN-HUAN LI2024-05-062024-05-062023-01-0110495258https://scholars.lib.ntu.edu.tw/handle/123456789/642297This 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.conference paper2-s2.0-85190819446https://api.elsevier.com/content/abstract/scopus_id/85190819446