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...Onmarkovchaingradientdescent taosun yuejiao sun college of computer department mathematics national university defense technology california los angeles changsha hunan china losangeles ca usa nudtsuntao com sunyj math ucla edu wotaoyin abstract stochastic gradient methods are the workhorse algorithms large scale opti mization problems in machine learning signal processing and other computational sciences engineering this paper studies markov chain descent a variant where random samples taken on trajectory existing results method assume convex objec tives reversible thus have their limitations we establish newnon ergodic convergence under wider step sizes for nonconvex non nite state chains nonconvexity makes our applicable to broader problem classes hand can mix substatially faster obtain these introduce new technique that varies mixing levels reported numerical validate contributions introduction consider minimization let be statistical sample space with probability distribution omit ...