Paper Citation Record · LEDGER

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning

As of 16 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2508.21443.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2508.21443 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T14:23:12.792191Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

33 of 33 outbound references displayed

verified exact2
verified fuzzy23
unresolved8
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 99c67e3f-93a2-4f96-ad99-6f4c30902898 · outbound

This paper cites Human- level control through deep reinforcement learning,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Human- level control through deep reinforcement learning,

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:16.727422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4f849639-2619-4e83-a01b-bd67c1b4310c · outbound

This paper cites Benchmarking deep reinforcement learning for continuous control,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Benchmarking deep reinforcement learning for continuous control,

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:16.518368Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e88dae6b-4ef8-43df-a770-9381aeba42f5 · outbound

This paper cites Research priorities for robust and beneficial artificial intelligence,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Research priorities for robust and beneficial artificial intelligence,

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:16.375126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8b4efd2d-524a-437c-aca8-8bd0763ecbee · outbound

This paper cites Concrete Problems in AI Safety.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Concrete Problems in AI Safety

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:10.073115Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 29b1a652-9c0a-4afd-8728-4f4773efaf9d · outbound

This paper cites Rigorous Agent Evaluation: An Adversarial Approach to Uncover Catastrophic Failures.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Rigorous Agent Evaluation: An Adversarial Approach to Uncover Catastrophic Failures

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:10.172323Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f5870618-a950-4566-b73e-3cc5c7324a69 · outbound

This paper cites an unresolved cited work.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:10.288361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0b4b4b84-1086-4b56-a809-c853c4c5293f · outbound

This paper cites Bertsekas, Reinforcement Learning and Optimal Control.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Bertsekas, Reinforcement Learning and Optimal Control

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:10.405961Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f2ee9982-9bc0-4cee-8352-15813493aff4 · outbound

This paper cites Reinforcement learning with non-ergodic reward in- crements: robustness via ergodicity transformations,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Reinforcement learning with non-ergodic reward in- crements: robustness via ergodicity transformations,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:16.263825Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5b91cb89-0bfe-46c0-b32c-929af9a18041 · outbound

This paper cites Linearly-solvable markov decision problems,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Linearly-solvable markov decision problems,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:16.162010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9a1d85f1-1d73-4396-985a-fb0d9b0e7f7e · outbound

This paper cites A theory of regularized Markov decision processes,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning A theory of regularized Markov decision processes,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:16.032142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e77cda3b-c52f-4351-84de-5f764dbd789d · outbound

This paper cites Approximate modified policy iteration and its application to the game of tetris.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Approximate modified policy iteration and its application to the game of tetris

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:15.881505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3b2f7ae1-5ec8-449b-90df-fff9d6b77d6b · outbound

This paper cites Munchausen reinforcement learning,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Munchausen reinforcement learning,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:15.762341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fe9d1c02-fa7a-405a-aacf-8bc83e35b612 · outbound

This paper cites Maximum a Posteriori Policy Optimisation.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Maximum a Posteriori Policy Optimisation

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:11.102414Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 37475928-ea80-4620-b75d-a97fed392256 · outbound

This paper cites Leverage the average: an analysis of KL regularization in reinforcement learning,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Leverage the average: an analysis of KL regularization in reinforcement learning,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:15.633431Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d340f80d-c6b6-4000-a8ef-b7a9cd3b862a · outbound

This paper cites Incremental multi-step q-learning,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Incremental multi-step q-learning,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:15.516046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9d80eb6e-7a80-493b-94db-6a6d18fb2dd8 · outbound

This paper cites Multi- step reinforcement learning: A unifying algorithm,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Multi- step reinforcement learning: A unifying algorithm,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:15.406979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d44e8e4c-aef5-45a9-9d6d-861a865a1590 · outbound

This paper cites Multi-Bellman operator for convergence of $Q$-learning with linear function approximation.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Multi-Bellman operator for convergence of $Q$-learning with linear function approximation

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-05T14:23:13.133448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 176002bd-bd9d-46f3-8e54-c5231c0efe9b · outbound

This paper cites A novel multi-step q-learning method to improve data efficiency for deep reinforcement learning,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning A novel multi-step q-learning method to improve data efficiency for deep reinforcement learning,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:15.292218Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9ead2d0e-8c2c-4029-a97a-f9adbda5bed2 · outbound

This paper cites Rainbow: Combining improvements in deep reinforcement learning,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Rainbow: Combining improvements in deep reinforcement learning,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:15.176986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8b2937fa-e06b-47d8-9fb3-80102323141c · outbound

This paper cites Policy invariance under reward transformations: Theory and application to reward shaping,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Policy invariance under reward transformations: Theory and application to reward shaping,

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:15.033813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b115652d-26c2-4aaa-9bf6-ad36573eec73 · outbound

This paper cites Self- supervised online reward shaping in sparse-reward environments,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Self- supervised online reward shaping in sparse-reward environments,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:14.907088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation cfc613d6-3c2c-4231-a5ce-395deac298a2 · outbound

This paper cites On learning intrinsic rewards for policy gradient methods,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning On learning intrinsic rewards for policy gradient methods,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:14.705725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 63a95a3f-c7cf-41c3-8739-cd423be75372 · outbound

This paper cites Microfoun- dations of discounting,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Microfoun- dations of discounting,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:14.508866Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 51f104c9-7e90-4b61-b2c8-39faabb455d8 · outbound

This paper cites The time interpretation of expected utility theory.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning The time interpretation of expected utility theory

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-05T14:23:12.989244Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0d7c7bd7-6180-4222-b328-314c3c7ec392 · outbound

This paper cites On-policy deep reinforcement learning for the average-reward criterion,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning On-policy deep reinforcement learning for the average-reward criterion,

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:14.318428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fca3c8ce-c7e5-424c-a0f9-526e21c89b17 · outbound

This paper cites A provably-efficient model-free algo- rithm for infinite-horizon average-reward constrained markov decision processes,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning A provably-efficient model-free algo- rithm for infinite-horizon average-reward constrained markov decision processes,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:14.193869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1f56c440-556a-4953-9a7a-3bd54f3c865a · outbound

This paper cites Robust average-reward markov decision processes,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Robust average-reward markov decision processes,

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:14.026163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5631c70d-22e9-478c-b473-ccc365ac65df · outbound

This paper cites Proof of the ergodic theorem,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Proof of the ergodic theorem,

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:13.832657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7942132c-9b81-4527-b2ba-087db936646b · outbound

This paper cites an unresolved cited work.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-05T14:23:13.646460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8eb43f76-1e2c-411e-b29c-d9923c1b49fc · outbound

This paper cites Finite-time analysis of natural actor- critic for POMDPs,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Finite-time analysis of natural actor- critic for POMDPs,

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:13.471063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f10314ca-72c1-4a23-894e-793bd3b5506b · outbound

This paper cites The ergodicity solution of the cooperation puzzle,.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning The ergodicity solution of the cooperation puzzle,

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:13.314948Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6e6a2025-1cc9-4354-bdb9-4830d8a86c19 · outbound

This paper cites OpenAI Gym.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning OpenAI Gym

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:12.734177Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d3fdd08-294a-437c-bd82-77dfd1264619 · outbound

This paper cites Playing Atari with Deep Reinforcement Learning.

Beyond expected value: geometric mean optimization for long-term policy performance in reinforcement learning Playing Atari with Deep Reinforcement Learning

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:12.792191Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.