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pith:SZRBQK25

pith:2025:SZRBQK25IGU622WI7VGQCFN7RA

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Why Goal-Conditioned Reinforcement Learning Works: Relation to Dual Control

Ali Mesbah, Nathan P. Lawrence

Goal-conditioned reinforcement learning succeeds because its reward represents the probability of reaching target states, yielding a smaller optimality gap than classical quadratic objectives and suiting it to dual control.

arxiv:2512.06471 v2 · 2025-12-06 · cs.LG · cs.AI

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Claims

C1strongest claim

we derive an optimality gap between more classical, often quadratic, objectives and the goal-conditioned reward, elucidating the success of goal-conditioned RL and why classical ``dense'' rewards can falter. We then consider the partially observed Markov decision setting and connect state estimation to our probabilistic reward, making the goal-conditioned reward well suited to dual control problems.

C2weakest assumption

The analysis assumes that the goal-conditioned reward can be interpreted directly as a probability of reaching target states and that this interpretation transfers without additional unstated restrictions on the system dynamics or observation model when moving to the POMDP and dual-control setting.

C3one line summary

Goal-conditioned RL succeeds over dense rewards because its probabilistic goal-reaching objective aligns naturally with dual control requirements in uncertain, partially observed systems.

References

3 extracted · 3 resolved · 0 Pith anchors

[1] Bar-Shalom, Y. and Tse, E. (1974). Dual effect, certainty equivalence, and separation in stochastic control.IEEE Transactions on Automatic Control, 19(5), 494–500. Bayard, D.S. and Schumitzky, A. (201 1974

[2] Athena scientific. Chen, Z. (2003). Bayesian filtering: From Kalman filters to particle filters, and beyond.Statistics, 182(1), 1–69. Drgoˇ na, J., Kiˇ s, K., Tuor, A., Vrabie, D., and Klauˇ co, M. (2 2003

[3] Vyas, N., Morwani, D., Zhao, R., Kwun, M., Shapira, I., Brandfonbrener, D., Janson, L., and Kakade, S 2025

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First computed	2026-05-17T23:39:00.583124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9662182b5d41a9ed6ac8fd4d0115bf880df3d8e6348c8d1eac64231669893571

Aliases

arxiv: 2512.06471 · arxiv_version: 2512.06471v2 · doi: 10.48550/arxiv.2512.06471 · pith_short_12: SZRBQK25IGU6 · pith_short_16: SZRBQK25IGU622WI · pith_short_8: SZRBQK25

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SZRBQK25IGU622WI7VGQCFN7RA \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9662182b5d41a9ed6ac8fd4d0115bf880df3d8e6348c8d1eac64231669893571

Canonical record JSON

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    "abstract_canon_sha256": "1f3dee88a1f7937337015abb3a085ed697aca02282d04d6ee24436c3c0418f41",
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      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-12-06T15:28:35Z",
    "title_canon_sha256": "72b7a0aead423de5ff3232f497621bb6590a182c6b94f97156784ac26df32b67"
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