{"paper":{"title":"Cost-Aware Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"By accounting for different sampling costs, cost-aware stochastic gradient descent reaches target accuracy at lower total cost and reduces token usage by up to 30 percent in LLM policy optimization.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Amir Globerson, Clara Mohri, Haim Kaplan, Tomer Koren, Yishay Mansour","submitted_at":"2026-04-30T15:39:09Z","abstract_excerpt":"We consider the problem of Cost-Aware Learning, where sampling different components of a finite-sum objective incurs different costs. The objective is to reach a target error while minimizing the total cost. We propose Cost-Aware SGD, which uses a distribution based on gradient norms and costs to sample components. We provide a thorough analysis of this algorithm, including cost-improvement bounds over baselines, a characterization of distribution proxy sub-optimality, and a lower bound. We apply our theoretical insights to reinforcement learning with language models, where the computational c"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Empirical results on 1.5B and 8B LLMs demonstrate that our approach reduces the tokens used in policy optimization by up to about 30% while matching or exceeding baseline accuracy.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The per-component sampling costs are known in advance and can be used to set sampling probabilities without introducing bias that harms convergence; this is stated implicitly in the cost-aware SGD derivation and the GRPO adaptation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Cost-aware SGD achieves target error with lower total sampling cost than standard methods, and Cost-Aware GRPO reduces token usage by up to 30% in LLM reinforcement learning while matching baseline performance.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"By accounting for different sampling costs, cost-aware stochastic gradient descent reaches target accuracy at lower total cost and reduces token usage by up to 30 percent in LLM policy optimization.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9490acccddeb05ab3d7e0e2d4accb8b6f60bc06438e4cfa77fbd02f8b118e23b"},"source":{"id":"2604.28020","kind":"arxiv","version":2},"verdict":{"id":"b34bcc42-13f1-456f-8a51-02a3738b6194","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T05:01:06.202809Z","strongest_claim":"Empirical results on 1.5B and 8B LLMs demonstrate that our approach reduces the tokens used in policy optimization by up to about 30% while matching or exceeding baseline accuracy.","one_line_summary":"Cost-aware SGD achieves target error with lower total sampling cost than standard methods, and Cost-Aware GRPO reduces token usage by up to 30% in LLM reinforcement learning while matching baseline performance.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The per-component sampling costs are known in advance and can be used to set sampling probabilities without introducing bias that harms convergence; this is stated implicitly in the cost-aware SGD derivation and the GRPO adaptation.","pith_extraction_headline":"By accounting for different sampling costs, cost-aware stochastic gradient descent reaches target accuracy at lower total cost and reduces token usage by up to 30 percent in LLM policy optimization."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.28020/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T20:42:12.032805Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:41:30.656157Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"2edd81f7537ba101f25a5110eb2e237f033fd9e99a20aa2e221961cb7c58f48f"},"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"}