{"paper":{"title":"Convergence of Markovian Stochastic Approximation with discontinuous dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Amandine Schreck (LTCI), Eric Moulines (LTCI), Gersende Fort (LTCI), Matti Vihola","submitted_at":"2014-03-26T19:27:33Z","abstract_excerpt":"This paper is devoted to the convergence analysis of stochastic approximation  algorithms of the form $\\theta\\_{n+1} = \\theta\\_n + \\gamma\\_{n+1}  H\\_{\\theta\\_n}(X\\_{n+1})$ where $\\{\\theta\\_nn, n \\geq 0\\}$ is a $R^d$-valued sequence,  $\\{\\gamma, n \\geq 0\\}$ is a deterministic step-size sequence and $\\{X\\_n, n \\geq 0\\}$ is a  controlled Markov chain. We study the convergence under weak assumptions on  smoothness-in-$\\theta$ of the function $\\theta \\mapsto H\\_{\\theta}(x)$. It is  usually assumed that this function is continuous for any $x$; in this work,  we relax this condition. Our results are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6803","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}