{"paper":{"title":"Stochastic Zeroth-Order Optimization Under Heavy-Tailed Noise","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Clipped scalar directional estimates let zeroth-order methods find stationary points under heavy-tailed noise with near-optimal query rates.","cross_cats":[],"primary_cat":"math.OC","authors_text":"El Mahdi Chayti, Imane Rahali, Omar Saadi, Qiuyi Zhang, Taha El Bakkali","submitted_at":"2026-05-17T11:24:17Z","abstract_excerpt":"We study stochastic zeroth-order (ZO) optimization of smooth nonconvex objectives under heavy-tailed sample-gradient noise. This regime is motivated by empirical evidence that gradient noise in modern machine learning can violate the bounded-variance assumptions used in classical ZO theory. While first-order methods have optimal rates under bounded $p$-th moment noise for $p\\in(1,2]$, analogous high-probability guarantees for nonconvex ZO methods are much less understood.\n  The ZO setting is not a direct corollary of first-order theory. First-order methods observe stochastic gradients, whereas"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under sample-wise smoothness and a weak-L_p tail condition on sample-gradient noise, RSC-ZO finds an ε-stationary point with high probability using Õ(d^{p/2(p-1)} ε^{-(3p-2)/(p-1)}) noisy function evaluations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That weak-L_p control of the sample gradient noise can be transferred to the scalar directional finite-difference estimates without additional assumptions that would invalidate the high-probability bound (abstract states this transfer is nontrivial and is the key technical step).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"RSC-ZO achieves high-probability ε-stationary points for stochastic ZO optimization under weak-L_p heavy-tailed noise with Õ(d^{p/2(p-1)} ε^{-(3p-2)/(p-1)}) function queries.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Clipped scalar directional estimates let zeroth-order methods find stationary points under heavy-tailed noise with near-optimal query rates.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"79a150f9e734365e86422916db9d5a52495e15bc9ee72fba29186922b1b08195"},"source":{"id":"2605.17394","kind":"arxiv","version":1},"verdict":{"id":"3d4ec52f-535b-4b57-b4d9-8fde0af799be","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T23:15:27.794078Z","strongest_claim":"Under sample-wise smoothness and a weak-L_p tail condition on sample-gradient noise, RSC-ZO finds an ε-stationary point with high probability using Õ(d^{p/2(p-1)} ε^{-(3p-2)/(p-1)}) noisy function evaluations.","one_line_summary":"RSC-ZO achieves high-probability ε-stationary points for stochastic ZO optimization under weak-L_p heavy-tailed noise with Õ(d^{p/2(p-1)} ε^{-(3p-2)/(p-1)}) function queries.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That weak-L_p control of the sample gradient noise can be transferred to the scalar directional finite-difference estimates without additional assumptions that would invalidate the high-probability bound (abstract states this transfer is nontrivial and is the key technical step).","pith_extraction_headline":"Clipped scalar directional estimates let zeroth-order methods find stationary points under heavy-tailed noise with near-optimal query rates."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17394/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:31:19.996843Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:21:01.388141Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.759395Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.700780Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"87e26984513dbb483bc059a3185e00eff338da2f9ea433e8d1a91debc37f1de1"},"references":{"count":41,"sample":[{"doi":"","year":2013,"title":"SIAM journal on optimization , volume=","work_id":"24af5e2b-15c0-406e-9ad5-9306210b5b2e","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Proceedings of The 28th International Conference on Artificial Intelligence and Statistics , pages =","work_id":"01c87699-f318-48dd-9f0f-7cda26422959","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Foundations of Computational Mathematics , volume =","work_id":"267d2ff9-d074-4c40-9dc8-ca62ca2104df","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2015,"title":"and Jordan, Michael I","work_id":"069fadda-34b5-42b4-8d34-b0f919c0c0e7","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Proceedings of the 10th ACM Workshop on Artificial Intelligence and Security (AISec) , pages =","work_id":"577c2471-428f-4d93-9708-c9e737b149a7","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":41,"snapshot_sha256":"c81b9e9fff25e22d3803e0cd73865c6b05eec4e3d005f54f3311f1628f252ec2","internal_anchors":2},"formal_canon":{"evidence_count":2,"snapshot_sha256":"4447c55ddb545b7e10d393937797f84ba90be5e0d67cc500b2b0c2c060b8ee83"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}