Pith Number

pith:ZCVZIOXA

pith:2026:ZCVZIOXALTXE3BLDU4NWNOWOJ4

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Achieving $\epsilon^{-2}$ Sample Complexity for Single-Loop Actor-Critic under Minimal Assumptions

Ishaq Hamza, Zaiwei Chen

Single-loop off-policy actor-critic reaches an ε-optimal policy with Õ(ε^{-2}) samples under only irreducibility of one policy.

arxiv:2605.13639 v1 · 2026-05-13 · cs.LG · math.OC · stat.ML

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Claims

C1strongest claim

we prove the first Õ(ε^{-2}) sample complexity guarantee for finding an ε-optimal policy under minimal assumptions, namely, the existence of a policy that induces an irreducible Markov chain.

C2weakest assumption

the existence of a policy that induces an irreducible Markov chain; the coupled Lyapunov drift framework and cross-domination property hold for the single-loop off-policy updates with unbounded iterates.

C3one line summary

Single-loop actor-critic achieves the first Õ(ε^{-2}) sample complexity for ε-optimal policies under minimal irreducibility assumptions.

References

69 extracted · 69 resolved · 2 Pith anchors

[1] Agarwal, A., Kakade, S. M., Lee, J. D., and Mahajan, G. (2021). On the theory of policy gra- dient methods: Optimality, approximation, and distribution shift.Journal of Machine Learning Research, 22(9 2021

[2] Alacaoglu, A., Viano, L., He, N., and Cevher, V. (2022). A natural actor-critic framework for zero-sum Markov games. InInternational Conference on Machine Learning, pages 307–366. PMLR 2022

[3] Banach, S. (1922). Sur les op´ erations dans les ensembles abstraits et leur application aux ´ equations int´ egrales.Fund. Math, 3(1):133–181 1922

[4] Bertsekas, D. P. (2011). Approximate policy iteration: A survey and some new methods. Journal of Control Theory and Applications, 9(3):310–335 2011

[5] Bhandari, J., Russo, D., and Singal, R. (2018). A finite-time analysis of temporal difference learning with linear function approximation. InConference On Learning Theory, pages 1691– 1692 2018

Receipt and verification

First computed	2026-05-18T02:44:17.625374Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8ab943ae05cee4d8563a71b66bace4f214166effee64669864687fd34d7d3c3

Aliases

arxiv: 2605.13639 · arxiv_version: 2605.13639v1 · doi: 10.48550/arxiv.2605.13639 · pith_short_12: ZCVZIOXALTXE · pith_short_16: ZCVZIOXALTXE3BLD · pith_short_8: ZCVZIOXA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZCVZIOXALTXE3BLDU4NWNOWOJ4 \
  | 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: c8ab943ae05cee4d8563a71b66bace4f214166effee64669864687fd34d7d3c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "830565cf23fce4613fb81e2d6bcf04b77a035b7089f1d5861f7b20360b186c66",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T15:04:59Z",
    "title_canon_sha256": "03845fc45ceec497163534ed0e97652299513e483cff184f975b34cbf0f568a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13639",
    "kind": "arxiv",
    "version": 1
  }
}