Pith Number

pith:JXL4H4BW

pith:2026:JXL4H4BW6PHSIROKSGWUO2333W

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A PAC-Bayes Approach for Controlling Unknown Linear Discrete-time Systems

Jingge Zhu, Jonathan H. Manton, Ye Pu, Yujia Luo

A PAC-Bayes bound gives high-probability performance guarantees for any stochastic controller learned on unknown linear discrete-time systems.

arxiv:2605.10493 v2 · 2026-05-11 · math.OC · cs.SY · eess.SY · stat.ML

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Claims

C1strongest claim

We derive a data-dependent high probability bound on the performance of any learned (stochastic) controller, and propose novel efficient learning algorithms with theoretical guarantees, which can be implemented for both finite and infinite controller spaces. Compared to prior work, our bound holds for unbounded quadratic cost.

C2weakest assumption

The system parameters are drawn from a fixed but unknown distribution, and the controller is allowed to be stochastic; if the true parameter distribution changes over time or if only deterministic controllers are permitted, the derived bound and algorithms no longer apply.

C3one line summary

A PAC-Bayes method supplies high-probability bounds on the cost of any learned stochastic controller for unknown linear systems and gives efficient algorithms that work for both finite and infinite controller sets, including unbounded quadratic costs.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-22T01:03:20.127932Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4dd7c3f036f3cf2445ca91ad476b7bddae2eb9923a71f4bdcc8c73f5488e23d6

Aliases

arxiv: 2605.10493 · arxiv_version: 2605.10493v2 · doi: 10.48550/arxiv.2605.10493 · pith_short_12: JXL4H4BW6PHS · pith_short_16: JXL4H4BW6PHSIROK · pith_short_8: JXL4H4BW

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JXL4H4BW6PHSIROKSGWUO2333W \
  | 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: 4dd7c3f036f3cf2445ca91ad476b7bddae2eb9923a71f4bdcc8c73f5488e23d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "deaf1ca73ddb14fba7ec8c4a1c5333ec960dac5fedcd8cb46cb2f4bce9d74935",
    "cross_cats_sorted": [
      "cs.SY",
      "eess.SY",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-11T12:51:13Z",
    "title_canon_sha256": "6d72184e0ab33cde3ca6d29048eb457709801f43b14419d2ef63f3fabcca642d"
  },
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  "source": {
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    "kind": "arxiv",
    "version": 2
  }
}