{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:XKXGWYFCB2KJWHMB3JG4ZZB4DS","short_pith_number":"pith:XKXGWYFC","canonical_record":{"source":{"id":"2008.07773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2020-08-18T07:17:53Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"2e68a7c5e9dd0c0fa8fd635c55ea159b84a5637006fac447da8425aa896aefc8","abstract_canon_sha256":"6c73ac6ff3b8fcd6a5ff7001101cea03877fa42c07ffc4b00c08e86139226c57"},"schema_version":"1.0"},"canonical_sha256":"baae6b60a20e949b1d81da4dcce43c1c835c1608a7c029c59fea99f448264ae4","source":{"kind":"arxiv","id":"2008.07773","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.07773","created_at":"2026-07-05T01:27:55Z"},{"alias_kind":"arxiv_version","alias_value":"2008.07773v1","created_at":"2026-07-05T01:27:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.07773","created_at":"2026-07-05T01:27:55Z"},{"alias_kind":"pith_short_12","alias_value":"XKXGWYFCB2KJ","created_at":"2026-07-05T01:27:55Z"},{"alias_kind":"pith_short_16","alias_value":"XKXGWYFCB2KJWHMB","created_at":"2026-07-05T01:27:55Z"},{"alias_kind":"pith_short_8","alias_value":"XKXGWYFC","created_at":"2026-07-05T01:27:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:XKXGWYFCB2KJWHMB3JG4ZZB4DS","target":"record","payload":{"canonical_record":{"source":{"id":"2008.07773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2020-08-18T07:17:53Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"2e68a7c5e9dd0c0fa8fd635c55ea159b84a5637006fac447da8425aa896aefc8","abstract_canon_sha256":"6c73ac6ff3b8fcd6a5ff7001101cea03877fa42c07ffc4b00c08e86139226c57"},"schema_version":"1.0"},"canonical_sha256":"baae6b60a20e949b1d81da4dcce43c1c835c1608a7c029c59fea99f448264ae4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:27:55.220370Z","signature_b64":"vC2jLlKMIwUpN/siDOw6k9PP0qmxph8Xka1P+Jg5vJApMdcHZVe3+Q2VgZ9Y260fnZFk2pcsomoamnPbSVKnAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"baae6b60a20e949b1d81da4dcce43c1c835c1608a7c029c59fea99f448264ae4","last_reissued_at":"2026-07-05T01:27:55.219921Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:27:55.219921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.07773","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:27:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aHiT3HogTq5OQ3DMLKeEiWPpD3Cq4CBUpp1cWQLRC6r4EiJkuvaZ0KFcyA8OuaFt2Reevxmd0zmMpG+Hv5htAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T20:41:33.983019Z"},"content_sha256":"5b218df3e47cae012a0e03af68f51897a50228c70c268af8ff512dc65e0ab573","schema_version":"1.0","event_id":"sha256:5b218df3e47cae012a0e03af68f51897a50228c70c268af8ff512dc65e0ab573"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:XKXGWYFCB2KJWHMB3JG4ZZB4DS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Fair Policies in Multiobjective (Deep) Reinforcement Learning with Average and Discounted Rewards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.AI","authors_text":"Matthieu Zimmer, Paul Weng, Umer Siddique","submitted_at":"2020-08-18T07:17:53Z","abstract_excerpt":"As the operations of autonomous systems generally affect simultaneously several users, it is crucial that their designs account for fairness considerations. In contrast to standard (deep) reinforcement learning (RL), we investigate the problem of learning a policy that treats its users equitably. In this paper, we formulate this novel RL problem, in which an objective function, which encodes a notion of fairness that we formally define, is optimized. For this problem, we provide a theoretical discussion where we examine the case of discounted rewards and that of average rewards. During this an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.07773","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.07773/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:27:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L2RUCjX/jQ/g8+OQm+C5WJdKOX//kdDqIuCj2jlal3VJ418bQxBU2eeTh0ruXiihnXonvx+Z4vZ0PV7P+4OIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T20:41:33.983564Z"},"content_sha256":"742a48720ffbca6372ca326f219cc38a56709deef947bae422cd7aecf2e5d223","schema_version":"1.0","event_id":"sha256:742a48720ffbca6372ca326f219cc38a56709deef947bae422cd7aecf2e5d223"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XKXGWYFCB2KJWHMB3JG4ZZB4DS/bundle.json","state_url":"https://pith.science/pith/XKXGWYFCB2KJWHMB3JG4ZZB4DS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XKXGWYFCB2KJWHMB3JG4ZZB4DS/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":"2026-07-31T20:41:33Z","links":{"resolver":"https://pith.science/pith/XKXGWYFCB2KJWHMB3JG4ZZB4DS","bundle":"https://pith.science/pith/XKXGWYFCB2KJWHMB3JG4ZZB4DS/bundle.json","state":"https://pith.science/pith/XKXGWYFCB2KJWHMB3JG4ZZB4DS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XKXGWYFCB2KJWHMB3JG4ZZB4DS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:XKXGWYFCB2KJWHMB3JG4ZZB4DS","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":"6c73ac6ff3b8fcd6a5ff7001101cea03877fa42c07ffc4b00c08e86139226c57","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2020-08-18T07:17:53Z","title_canon_sha256":"2e68a7c5e9dd0c0fa8fd635c55ea159b84a5637006fac447da8425aa896aefc8"},"schema_version":"1.0","source":{"id":"2008.07773","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.07773","created_at":"2026-07-05T01:27:55Z"},{"alias_kind":"arxiv_version","alias_value":"2008.07773v1","created_at":"2026-07-05T01:27:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.07773","created_at":"2026-07-05T01:27:55Z"},{"alias_kind":"pith_short_12","alias_value":"XKXGWYFCB2KJ","created_at":"2026-07-05T01:27:55Z"},{"alias_kind":"pith_short_16","alias_value":"XKXGWYFCB2KJWHMB","created_at":"2026-07-05T01:27:55Z"},{"alias_kind":"pith_short_8","alias_value":"XKXGWYFC","created_at":"2026-07-05T01:27:55Z"}],"graph_snapshots":[{"event_id":"sha256:742a48720ffbca6372ca326f219cc38a56709deef947bae422cd7aecf2e5d223","target":"graph","created_at":"2026-07-05T01:27:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.07773/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"As the operations of autonomous systems generally affect simultaneously several users, it is crucial that their designs account for fairness considerations. In contrast to standard (deep) reinforcement learning (RL), we investigate the problem of learning a policy that treats its users equitably. In this paper, we formulate this novel RL problem, in which an objective function, which encodes a notion of fairness that we formally define, is optimized. For this problem, we provide a theoretical discussion where we examine the case of discounted rewards and that of average rewards. During this an","authors_text":"Matthieu Zimmer, Paul Weng, Umer Siddique","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2020-08-18T07:17:53Z","title":"Learning Fair Policies in Multiobjective (Deep) Reinforcement Learning with Average and Discounted Rewards"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.07773","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":"sha256:5b218df3e47cae012a0e03af68f51897a50228c70c268af8ff512dc65e0ab573","target":"record","created_at":"2026-07-05T01:27:55Z","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":"6c73ac6ff3b8fcd6a5ff7001101cea03877fa42c07ffc4b00c08e86139226c57","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2020-08-18T07:17:53Z","title_canon_sha256":"2e68a7c5e9dd0c0fa8fd635c55ea159b84a5637006fac447da8425aa896aefc8"},"schema_version":"1.0","source":{"id":"2008.07773","kind":"arxiv","version":1}},"canonical_sha256":"baae6b60a20e949b1d81da4dcce43c1c835c1608a7c029c59fea99f448264ae4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"baae6b60a20e949b1d81da4dcce43c1c835c1608a7c029c59fea99f448264ae4","first_computed_at":"2026-07-05T01:27:55.219921Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:27:55.219921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vC2jLlKMIwUpN/siDOw6k9PP0qmxph8Xka1P+Jg5vJApMdcHZVe3+Q2VgZ9Y260fnZFk2pcsomoamnPbSVKnAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:27:55.220370Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.07773","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b218df3e47cae012a0e03af68f51897a50228c70c268af8ff512dc65e0ab573","sha256:742a48720ffbca6372ca326f219cc38a56709deef947bae422cd7aecf2e5d223"],"state_sha256":"9d0f8e502b3a6fd29e3a5f31914b5326162225aa86e873380ef72c2de3274bcb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"npmHWSC/KUJOs5j9Kq+eTevuIHG7WtDwBwcIOOoy2JL5LgE4G5ay1PASLa7a0YrRDCzH8YLqOnBI2wYZfhR3AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-31T20:41:33.988500Z","bundle_sha256":"13322346a6cd2537d990a7ac9cb1e96c9e262f594375ccaf7564c82ae0dc70ab"}}