{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:RAPIYXPD3W32G56UPIHWZUPXH7","short_pith_number":"pith:RAPIYXPD","canonical_record":{"source":{"id":"2602.01453","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-01T21:44:11Z","cross_cats_sorted":[],"title_canon_sha256":"86271ab381b69e0d5f4c664f5e0125f946e799b1753f745e712a834545ba03ba","abstract_canon_sha256":"3d0557f081da79de65c4311622df0fb86b19b47ef16d67a1b66d86da095ae2db"},"schema_version":"1.0"},"canonical_sha256":"881e8c5de3ddb7a377d47a0f6cd1f73fc67feb293447cad0304f97dfb52f3891","source":{"kind":"arxiv","id":"2602.01453","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.01453","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"2602.01453v3","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.01453","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"RAPIYXPD3W32","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"RAPIYXPD3W32G56U","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"RAPIYXPD","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:RAPIYXPD3W32G56UPIHWZUPXH7","target":"record","payload":{"canonical_record":{"source":{"id":"2602.01453","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-01T21:44:11Z","cross_cats_sorted":[],"title_canon_sha256":"86271ab381b69e0d5f4c664f5e0125f946e799b1753f745e712a834545ba03ba","abstract_canon_sha256":"3d0557f081da79de65c4311622df0fb86b19b47ef16d67a1b66d86da095ae2db"},"schema_version":"1.0"},"canonical_sha256":"881e8c5de3ddb7a377d47a0f6cd1f73fc67feb293447cad0304f97dfb52f3891","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:24.034421Z","signature_b64":"0baniJUPwneyNV54NSxMXPqUQluiO5xudlubddH7Vk9/28hvapTLXAmIyqYi2XW5N1b2oBVGHXEuZj5Mbqy4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"881e8c5de3ddb7a377d47a0f6cd1f73fc67feb293447cad0304f97dfb52f3891","last_reissued_at":"2026-05-18T03:09:24.033584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:24.033584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.01453","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:09:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M4JeEPbh0h3d+hAd9Z/GbZ88NnqUU4wtIhl8F7sgJ5+fypbtCAGbhAppENQZu1mXI/85GhAa0s7eNm3cv5I5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:58:10.094201Z"},"content_sha256":"018756a9c02a6d38bfd48b37d67580439d2a104ace62538453449cffc6005178","schema_version":"1.0","event_id":"sha256:018756a9c02a6d38bfd48b37d67580439d2a104ace62538453449cffc6005178"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:RAPIYXPD3W32G56UPIHWZUPXH7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Horizon Threshold in Cooperative Multi-Agent Reward-Free Exploration","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Setting learning phases equal to the horizon H allows polynomial agents to approximate MDP dynamics in multi-agent reward-free exploration.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Idan Barnea, Orin Levy, Yishay Mansour","submitted_at":"2026-02-01T21:44:11Z","abstract_excerpt":"We study cooperative multi-agent reinforcement learning in the setting of reward-free exploration, where multiple agents jointly explore an unknown MDP in order to learn its dynamics (without observing rewards). We focus on a tabular finite-horizon MDP and adopt a phased learning framework. In each learning phase, multiple agents independently interact with the environment. More specifically, in each learning phase, each agent is assigned a policy, executes it, and observes the resulting trajectory. Our primary goal is to characterize the tradeoff between the number of learning phases and the "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"When the number of learning phases equals H, we present a computationally efficient algorithm that uses only Õ(S^6 H^6 A / ε²) agents to obtain an ε approximation of the dynamics (i.e., yields an ε-optimal policy for any reward function). We complement our algorithm with a lower bound showing that any algorithm restricted to ρ < H phases requires at least A^{H/ρ} agents to achieve constant accuracy.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The MDP is tabular and finite-horizon, and the learning proceeds in independent phases where each agent is assigned a policy and executes it without intra-phase communication.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Θ(H) learning phases are necessary and sufficient for polynomial-agent ε-accurate dynamics estimation in multi-agent reward-free exploration of finite-horizon tabular MDPs.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Setting learning phases equal to the horizon H allows polynomial agents to approximate MDP dynamics in multi-agent reward-free exploration.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c61aa029dd055e9c47650591034855f998106fa4bcd6ee21871edefc8d840819"},"source":{"id":"2602.01453","kind":"arxiv","version":3},"verdict":{"id":"b648f2b2-d099-41cd-92be-ef7266ab6a15","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T08:22:30.324972Z","strongest_claim":"When the number of learning phases equals H, we present a computationally efficient algorithm that uses only Õ(S^6 H^6 A / ε²) agents to obtain an ε approximation of the dynamics (i.e., yields an ε-optimal policy for any reward function). We complement our algorithm with a lower bound showing that any algorithm restricted to ρ < H phases requires at least A^{H/ρ} agents to achieve constant accuracy.","one_line_summary":"Θ(H) learning phases are necessary and sufficient for polynomial-agent ε-accurate dynamics estimation in multi-agent reward-free exploration of finite-horizon tabular MDPs.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The MDP is tabular and finite-horizon, and the learning proceeds in independent phases where each agent is assigned a policy and executes it without intra-phase communication.","pith_extraction_headline":"Setting learning phases equal to the horizon H allows polynomial agents to approximate MDP dynamics in multi-agent reward-free exploration."},"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"},"verdict_id":"b648f2b2-d099-41cd-92be-ef7266ab6a15"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:09:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cx/4a4N/ZjJm6IsLIfZv5HBHfZz3ggX1LR/o0QUxxMA6ajCdzIhOw4zV9TP+9IuyGpqDCg2aK0MCsDQpbZwlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:58:10.094773Z"},"content_sha256":"62c18ccc4d0e3a53d694a707adbc07bf75bd75ba13ec270ebef1335bba8435ab","schema_version":"1.0","event_id":"sha256:62c18ccc4d0e3a53d694a707adbc07bf75bd75ba13ec270ebef1335bba8435ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RAPIYXPD3W32G56UPIHWZUPXH7/bundle.json","state_url":"https://pith.science/pith/RAPIYXPD3W32G56UPIHWZUPXH7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RAPIYXPD3W32G56UPIHWZUPXH7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T04:58:10Z","links":{"resolver":"https://pith.science/pith/RAPIYXPD3W32G56UPIHWZUPXH7","bundle":"https://pith.science/pith/RAPIYXPD3W32G56UPIHWZUPXH7/bundle.json","state":"https://pith.science/pith/RAPIYXPD3W32G56UPIHWZUPXH7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RAPIYXPD3W32G56UPIHWZUPXH7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RAPIYXPD3W32G56UPIHWZUPXH7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3d0557f081da79de65c4311622df0fb86b19b47ef16d67a1b66d86da095ae2db","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-01T21:44:11Z","title_canon_sha256":"86271ab381b69e0d5f4c664f5e0125f946e799b1753f745e712a834545ba03ba"},"schema_version":"1.0","source":{"id":"2602.01453","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.01453","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"2602.01453v3","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.01453","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"RAPIYXPD3W32","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"RAPIYXPD3W32G56U","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"RAPIYXPD","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:62c18ccc4d0e3a53d694a707adbc07bf75bd75ba13ec270ebef1335bba8435ab","target":"graph","created_at":"2026-05-18T03:09:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"When the number of learning phases equals H, we present a computationally efficient algorithm that uses only Õ(S^6 H^6 A / ε²) agents to obtain an ε approximation of the dynamics (i.e., yields an ε-optimal policy for any reward function). We complement our algorithm with a lower bound showing that any algorithm restricted to ρ < H phases requires at least A^{H/ρ} agents to achieve constant accuracy."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The MDP is tabular and finite-horizon, and the learning proceeds in independent phases where each agent is assigned a policy and executes it without intra-phase communication."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Θ(H) learning phases are necessary and sufficient for polynomial-agent ε-accurate dynamics estimation in multi-agent reward-free exploration of finite-horizon tabular MDPs."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Setting learning phases equal to the horizon H allows polynomial agents to approximate MDP dynamics in multi-agent reward-free exploration."}],"snapshot_sha256":"c61aa029dd055e9c47650591034855f998106fa4bcd6ee21871edefc8d840819"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study cooperative multi-agent reinforcement learning in the setting of reward-free exploration, where multiple agents jointly explore an unknown MDP in order to learn its dynamics (without observing rewards). We focus on a tabular finite-horizon MDP and adopt a phased learning framework. In each learning phase, multiple agents independently interact with the environment. More specifically, in each learning phase, each agent is assigned a policy, executes it, and observes the resulting trajectory. Our primary goal is to characterize the tradeoff between the number of learning phases and the ","authors_text":"Idan Barnea, Orin Levy, Yishay Mansour","cross_cats":[],"headline":"Setting learning phases equal to the horizon H allows polynomial agents to approximate MDP dynamics in multi-agent reward-free exploration.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-01T21:44:11Z","title":"The Horizon Threshold in Cooperative Multi-Agent Reward-Free Exploration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.01453","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-16T08:22:30.324972Z","id":"b648f2b2-d099-41cd-92be-ef7266ab6a15","model_set":{"reader":"grok-4.3"},"one_line_summary":"Θ(H) learning phases are necessary and sufficient for polynomial-agent ε-accurate dynamics estimation in multi-agent reward-free exploration of finite-horizon tabular MDPs.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Setting learning phases equal to the horizon H allows polynomial agents to approximate MDP dynamics in multi-agent reward-free exploration.","strongest_claim":"When the number of learning phases equals H, we present a computationally efficient algorithm that uses only Õ(S^6 H^6 A / ε²) agents to obtain an ε approximation of the dynamics (i.e., yields an ε-optimal policy for any reward function). We complement our algorithm with a lower bound showing that any algorithm restricted to ρ < H phases requires at least A^{H/ρ} agents to achieve constant accuracy.","weakest_assumption":"The MDP is tabular and finite-horizon, and the learning proceeds in independent phases where each agent is assigned a policy and executes it without intra-phase communication."}},"verdict_id":"b648f2b2-d099-41cd-92be-ef7266ab6a15"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:018756a9c02a6d38bfd48b37d67580439d2a104ace62538453449cffc6005178","target":"record","created_at":"2026-05-18T03:09:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3d0557f081da79de65c4311622df0fb86b19b47ef16d67a1b66d86da095ae2db","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-01T21:44:11Z","title_canon_sha256":"86271ab381b69e0d5f4c664f5e0125f946e799b1753f745e712a834545ba03ba"},"schema_version":"1.0","source":{"id":"2602.01453","kind":"arxiv","version":3}},"canonical_sha256":"881e8c5de3ddb7a377d47a0f6cd1f73fc67feb293447cad0304f97dfb52f3891","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"881e8c5de3ddb7a377d47a0f6cd1f73fc67feb293447cad0304f97dfb52f3891","first_computed_at":"2026-05-18T03:09:24.033584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:24.033584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0baniJUPwneyNV54NSxMXPqUQluiO5xudlubddH7Vk9/28hvapTLXAmIyqYi2XW5N1b2oBVGHXEuZj5Mbqy4Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:24.034421Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.01453","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:018756a9c02a6d38bfd48b37d67580439d2a104ace62538453449cffc6005178","sha256:62c18ccc4d0e3a53d694a707adbc07bf75bd75ba13ec270ebef1335bba8435ab"],"state_sha256":"9fd8a0d6f6553f9bda8c07153ea7a79c4ba4803830ad9881f6bdad224f174417"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fyiEJX5IyGyQJ0o5q7LtFyByNrZN8BLMJCREM6F/ULu0b1OwpQVtcXp43fUqAoHLrq385DVA1G12Z77cdHFvAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T04:58:10.097404Z","bundle_sha256":"81b7562846f82b3efe2e377f78ba0542ee5d8172d280e96b0516612dadbc3176"}}