{"paper":{"title":"The ODE Method for Asymptotic Statistics in Stochastic Approximation and Reinforcement Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","stat.TH"],"primary_cat":"math.ST","authors_text":"Adithya Devraj, Ioannis Kontoyiannis, Sean Meyn, Shuhang Chen, Vivek Borkar","submitted_at":"2021-10-27T13:38:25Z","abstract_excerpt":"The paper concerns the $d$-dimensional stochastic approximation recursion, $$ \\theta_{n+1}= \\theta_n + \\alpha_{n + 1} f(\\theta_n, \\Phi_{n+1}) $$ where $ \\{ \\Phi_n \\}$ is a stochastic process on a general state space, satisfying a conditional Markov property that allows for parameter-dependent noise. The main results are established under additional conditions on the mean flow and a version of the Donsker-Varadhan Lyapunov drift condition known as (DV3):\n  (i) An appropriate Lyapunov function is constructed that implies convergence of the estimates in $L_4$.\n  (ii) A functional central limit th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14427","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.14427/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}