{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6ZBM56AIITSW3IJ2CMA5JJYWHR","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":"67872d1293eaafe9b65e644790015d2bfdd964ddc7a4ef239acaf74195c529a1","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-07-23T08:56:08Z","title_canon_sha256":"8d908ff9e2588f928479de5ad7b1985eb9030ea6f0e03cfc3f10804245aff2b1"},"schema_version":"1.0","source":{"id":"1907.09765","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.09765","created_at":"2026-05-17T23:39:50Z"},{"alias_kind":"arxiv_version","alias_value":"1907.09765v1","created_at":"2026-05-17T23:39:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09765","created_at":"2026-05-17T23:39:50Z"},{"alias_kind":"pith_short_12","alias_value":"6ZBM56AIITSW","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6ZBM56AIITSW3IJ2","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6ZBM56AI","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:9f1ea05c2b22628fcba8172e5d182834aba56279ee7912c420101c201ffcde93","target":"graph","created_at":"2026-05-17T23:39:50Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"After presenting Actor Critic Methods (ACM), we show ACM are control variate estimators. Using the projection theorem, we prove that the Q and Advantage Actor Critic (A2C) methods are optimal in the sense of the $L^2$ norm for the control variate estimators spanned by functions conditioned by the current state and action. This straightforward application of Pythagoras theorem provides a theoretical justification of the strong performance of QAC and AAC most often referred to as A2C methods in deep policy gradient methods. This enables us to derive a new formulation for Advantage Actor Critic m","authors_text":"Eric Benhamou","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-07-23T08:56:08Z","title":"Variance Reduction in Actor Critic Methods (ACM)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09765","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ee6e172dd5b95262291b46432b5967c4a614190bd7ed780c7f9e5755a6bc609a","target":"record","created_at":"2026-05-17T23:39:50Z","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":"67872d1293eaafe9b65e644790015d2bfdd964ddc7a4ef239acaf74195c529a1","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-07-23T08:56:08Z","title_canon_sha256":"8d908ff9e2588f928479de5ad7b1985eb9030ea6f0e03cfc3f10804245aff2b1"},"schema_version":"1.0","source":{"id":"1907.09765","kind":"arxiv","version":1}},"canonical_sha256":"f642cef80844e56da13a1301d4a7163c739d93c2eacdbe6686b20563e7f386d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f642cef80844e56da13a1301d4a7163c739d93c2eacdbe6686b20563e7f386d3","first_computed_at":"2026-05-17T23:39:50.100035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:50.100035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8kT6evpktZCANmin6btKAVYBnFtkDUef87d/Vz3vTR1uu5bt4tRenROeFHMndCA95Mc5E6iOxpZt1eE+33MLCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:50.100688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.09765","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee6e172dd5b95262291b46432b5967c4a614190bd7ed780c7f9e5755a6bc609a","sha256:9f1ea05c2b22628fcba8172e5d182834aba56279ee7912c420101c201ffcde93"],"state_sha256":"ad21dff423427d154b7c47d0a8d0620358735307a990775f22d2089d640b093b"}