Pith Number

pith:DVUUGUOY

pith:2026:DVUUGUOYKBRVQO2ZJKDQUSJOYC

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Distributionally Robust Regret Optimal LQR with Common Stage-Law Ambiguity

Jose Blanchet, Lukas-Benedikt Fiechtner

Multistage distributionally robust regret-optimal LQR under common stage-law ambiguity admits an exact SDP reformulation over linear disturbance-feedback policies.

arxiv:2604.06158 v2 · 2026-04-07 · math.OC · cs.SY · eess.SY

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We show that over linear disturbance-feedback policies the resulting multistage DRRO-LQR problem admits an exact semidefinite programming reformulation. The optimal controller is the nominal certainty-equivalent LQR law plus a strictly causal empirical-mean correction.

C2weakest assumption

The restriction to linear disturbance-feedback policies is sufficient to achieve both tractability and optimality, together with the common stage-law ambiguity model using a Gelbrich ball.

C3one line summary

The multistage DRRO-LQR problem over linear disturbance-feedback policies admits an exact SDP reformulation whose solution is the nominal certainty-equivalent LQR law plus a strictly causal empirical-mean correction.

Receipt and verification

First computed	2026-08-11T01:24:44.117344Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d694351d85063583b594a870a492ec08fcd3b343912a8787573b878ac81a7b2

Aliases

arxiv: 2604.06158 · arxiv_version: 2604.06158v2 · doi: 10.48550/arxiv.2604.06158 · pith_short_12: DVUUGUOYKBRV · pith_short_16: DVUUGUOYKBRVQO2Z · pith_short_8: DVUUGUOY

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DVUUGUOYKBRVQO2ZJKDQUSJOYC \
  | 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: 1d694351d85063583b594a870a492ec08fcd3b343912a8787573b878ac81a7b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "266fde08a4b667fd6ec81f68ed10352a7a437a4db0be6efcc1e863ea6e64e3d8",
    "cross_cats_sorted": [
      "cs.SY",
      "eess.SY"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-04-07T17:55:56Z",
    "title_canon_sha256": "f3f046c280204c59391e561e30df558ea484f99d0d2f824e73f00127c29aa6e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.06158",
    "kind": "arxiv",
    "version": 2
  }
}