{"ID":2850132,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.22819","arxiv_id":"2510.22819","title":"Last-Iterate Analyses of FTRL with the 1/2-Tsallis Entropy in Stochastic Bandits","abstract":"The convergence analysis of online learning algorithms is central to machine learning theory, where the last-iterate convergence is particularly important, as it captures the learner's actual decisions and describes the evolution of the learning process over time. However, in multi-armed bandits, most existing algorithmic analyses mainly focus on the order of regret, while the last-iterate (simple regret) convergence rate remains less explored -- especially for the widely studied Follow-the-Regularized-Leader (FTRL) algorithms. Recently, FTRL with the $1/2$-Tsallis entropy regularizer $Ψ(p) = -4\\sum_{i=1}^d \\sqrt{p_i}$ (the $1/2$-Tsallis-INF algorithm, by arXiv:1807.07623) was shown to achieve logarithmic regret in stochastic bandits. Nevertheless, its last-iterate convergence rate has not yet been studied. Intuitively, logarithmic regret should correspond to a $t^{-1}$ last-iterate convergence rate. This paper studies the $1/2$-Tsallis-INF algorithm and partially confirms this intuition through theoretical analysis, showing that the Bregman divergence, defined by $Ψ(p)$, between the point mass on the optimal arm and the probability distribution over the arm set obtained at iteration $t$, decays at a rate of $t^{-1/2}$.","short_abstract":"The convergence analysis of online learning algorithms is central to machine learning theory, where the last-iterate convergence is particularly important, as it captures the learner's actual decisions and describes the evolution of the learning process over time. However, in multi-armed bandits, most existing algorith...","url_abs":"https://arxiv.org/abs/2510.22819","url_pdf":"https://arxiv.org/pdf/2510.22819v2","authors":"[\"Jingxin Zhan\",\"Yuze Han\",\"Zhihua Zhang\"]","published":"2025-10-26T20:20:10Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}