{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZTCIIDU2KIKDXMLIPR5QIB52WA","short_pith_number":"pith:ZTCIIDU2","schema_version":"1.0","canonical_sha256":"ccc4840e9a52143bb1687c7b0407bab0314828d151f75d252370ef649bd88b80","source":{"kind":"arxiv","id":"1712.09007","version":2},"attestation_state":"computed","paper":{"title":"Stochastic Multi-armed Bandits in Constant Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"David Liau, Eric Price, Ger Yang, Zhao Song","submitted_at":"2017-12-25T05:04:35Z","abstract_excerpt":"We consider the stochastic bandit problem in the sublinear space setting, where one cannot record the win-loss record for all $K$ arms. We give an algorithm using $O(1)$ words of space with regret \\[\n  \\sum_{i=1}^{K}\\frac{1}{\\Delta_i}\\log \\frac{\\Delta_i}{\\Delta}\\log T \\] where $\\Delta_i$ is the gap between the best arm and arm $i$ and $\\Delta$ is the gap between the best and the second-best arms. If the rewards are bounded away from $0$ and $1$, this is within an $O(\\log 1/\\Delta)$ factor of the optimum regret possible without space constraints."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.09007","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2017-12-25T05:04:35Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"ace7934a12c1432b78b9bc1e3158f3159da0142128ac7bca8d0c5d262b674852","abstract_canon_sha256":"6fd325a183940be3f98ea861f1e91f385547b131af700401c36085e5e364a912"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:52.040731Z","signature_b64":"5rD2MEYNclKKXdIpbwyaFSUMIOrz89D2H+2SpD+jMV+jFLcIy0BD3z+TBIc7pZd2X+b1erjYRDDkmUsfFheQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccc4840e9a52143bb1687c7b0407bab0314828d151f75d252370ef649bd88b80","last_reissued_at":"2026-05-18T00:15:52.040064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:52.040064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic Multi-armed Bandits in Constant Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"David Liau, Eric Price, Ger Yang, Zhao Song","submitted_at":"2017-12-25T05:04:35Z","abstract_excerpt":"We consider the stochastic bandit problem in the sublinear space setting, where one cannot record the win-loss record for all $K$ arms. We give an algorithm using $O(1)$ words of space with regret \\[\n  \\sum_{i=1}^{K}\\frac{1}{\\Delta_i}\\log \\frac{\\Delta_i}{\\Delta}\\log T \\] where $\\Delta_i$ is the gap between the best arm and arm $i$ and $\\Delta$ is the gap between the best and the second-best arms. If the rewards are bounded away from $0$ and $1$, this is within an $O(\\log 1/\\Delta)$ factor of the optimum regret possible without space constraints."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09007","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1712.09007","created_at":"2026-05-18T00:15:52.040162+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.09007v2","created_at":"2026-05-18T00:15:52.040162+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09007","created_at":"2026-05-18T00:15:52.040162+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZTCIIDU2KIKD","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZTCIIDU2KIKDXMLI","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZTCIIDU2","created_at":"2026-05-18T12:31:59.375834+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZTCIIDU2KIKDXMLIPR5QIB52WA","json":"https://pith.science/pith/ZTCIIDU2KIKDXMLIPR5QIB52WA.json","graph_json":"https://pith.science/api/pith-number/ZTCIIDU2KIKDXMLIPR5QIB52WA/graph.json","events_json":"https://pith.science/api/pith-number/ZTCIIDU2KIKDXMLIPR5QIB52WA/events.json","paper":"https://pith.science/paper/ZTCIIDU2"},"agent_actions":{"view_html":"https://pith.science/pith/ZTCIIDU2KIKDXMLIPR5QIB52WA","download_json":"https://pith.science/pith/ZTCIIDU2KIKDXMLIPR5QIB52WA.json","view_paper":"https://pith.science/paper/ZTCIIDU2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.09007&json=true","fetch_graph":"https://pith.science/api/pith-number/ZTCIIDU2KIKDXMLIPR5QIB52WA/graph.json","fetch_events":"https://pith.science/api/pith-number/ZTCIIDU2KIKDXMLIPR5QIB52WA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZTCIIDU2KIKDXMLIPR5QIB52WA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZTCIIDU2KIKDXMLIPR5QIB52WA/action/storage_attestation","attest_author":"https://pith.science/pith/ZTCIIDU2KIKDXMLIPR5QIB52WA/action/author_attestation","sign_citation":"https://pith.science/pith/ZTCIIDU2KIKDXMLIPR5QIB52WA/action/citation_signature","submit_replication":"https://pith.science/pith/ZTCIIDU2KIKDXMLIPR5QIB52WA/action/replication_record"}},"created_at":"2026-05-18T00:15:52.040162+00:00","updated_at":"2026-05-18T00:15:52.040162+00:00"}