{"paper":{"title":"Markovian Foundations for Quasi-Stochastic Approximation with Applications to Extremum Seeking Control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Caio Kalil Lauand, Sean Meyn","submitted_at":"2022-07-13T17:23:38Z","abstract_excerpt":"This paper concerns quasi-stochastic approximation (QSA) to solve root finding problems commonly found in applications to optimization and reinforcement learning. The general constant gain algorithm may be expressed as the time-inhomogeneous ODE $ \\frac{d}{dt}\\Theta_t=\\alpha f_t (\\Theta_t)$, with state process $\\Theta$ evolving on $\\mathbb{R}^d$. Theory is based on an almost periodic vector field, so that in particular the time average of $f_t(\\theta)$ defines the time-homogeneous mean vector field $\\bar{f} \\colon \\mathbb{R}^d \\to \\mathbb{R}^d$ with $\\bar{f}(\\theta^*)=0$. Under smoothness assu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.06371","kind":"arxiv","version":4},"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/2207.06371/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"}