Pith Number

pith:SW3MFUY7

pith:2026:SW3MFUY7E3GKINHIMFFDXQQHKX

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Policy Optimization in Hybrid Discrete-Continuous Action Spaces via Mixed Gradients

Daniel Russo, Matias Alvo, Yash Kanoria

Hybrid Policy Optimization mixes pathwise and score-function gradients to keep policy updates unbiased in hybrid discrete-continuous action spaces.

arxiv:2605.14297 v1 · 2026-05-14 · cs.LG · cs.AI · math.OC · stat.ML

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Claims

C1strongest claim

we propose Hybrid Policy Optimization (HPO), which backpropagates through the simulator wherever smoothness permits, using a mixed gradient estimator that combines pathwise and SF gradients while maintaining unbiasedness. We also show how problems with action discontinuities can be reformulated in hybrid form... Empirically, HPO substantially outperforms PPO on inventory control and switched linear-quadratic regulator problems, with performance gaps increasing as the continuous action dimension grows.

C2weakest assumption

The mixed gradient estimator maintains unbiasedness despite the combination of pathwise and score-function components, and that the simulator allows backpropagation where smoothness permits without introducing bias from discrete actions.

C3one line summary

HPO enables unbiased policy optimization in hybrid action spaces by mixing differentiable simulation gradients with score-function estimates, outperforming PPO as continuous dimensions increase.

References

118 extracted · 118 resolved · 12 Pith anchors

[1] Machine learning , volume= 1992

[2] International conference on machine learning , pages= 2015

[3] Dynamic programming and optimal control 3rd edition, volume ii , author=

[4] Advances in neural information processing systems , volume=

[5] Advances in neural information processing systems , volume=

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:10.132625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

95b6c2d31f26cca434e8614a3bc20755fd77a64cc1c201bead4661616441c705

Aliases

arxiv: 2605.14297 · arxiv_version: 2605.14297v1 · doi: 10.48550/arxiv.2605.14297 · pith_short_12: SW3MFUY7E3GK · pith_short_16: SW3MFUY7E3GKINHI · pith_short_8: SW3MFUY7

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SW3MFUY7E3GKINHIMFFDXQQHKX \
  | 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: 95b6c2d31f26cca434e8614a3bc20755fd77a64cc1c201bead4661616441c705

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "e02d514969680dbb6e652b72a68618d3483c1c5330c1af21e75c6a72910658bf",
    "cross_cats_sorted": [
      "cs.AI",
      "math.OC",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-14T02:59:45Z",
    "title_canon_sha256": "e1114d9c38f5a4309d09384a406f3e6b004dc368b29ae41ae882ac0db629b4f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14297",
    "kind": "arxiv",
    "version": 1
  }
}