{"paper":{"title":"Zeroth-Order Langevin Monte Carlo via SPSA under Noisy Function Measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.CO","stat.TH"],"primary_cat":"math.OC","authors_text":"Hongbo Li, James C. Spall","submitted_at":"2026-08-08T00:44:41Z","abstract_excerpt":"In sampling problems, gradient-based schemes such as Langevin Monte Carlo (LMC) mix faster than non-gradient-based methods, but their applicability is limited by access to the gradient of the target log-density. In practice, gradients are often unavailable and function evaluations are noisy, e.g., stochastic simulators or black-box simulators, so we propose LMC-SPSA with noise, which approximates the gradient of the target log-density using two noisy function evaluations per iteration. We prove, under noisy gradient estimates, that LMC-SPSA converges in distribution by proving the convergence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07837","kind":"arxiv","version":1},"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/2608.07837/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"}