Pith Number

pith:GPMBMTWM

pith:2026:GPMBMTWMT7I7VNR47GRCN7QI5M

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The Fragility of Learning LQG Controllers

Anastasios Tsiamis, Bruce D. Lee, John Lygeros, Manfred Morari, Nikolai Matni

Any algorithm turning offline trajectories into a stabilizing LQG controller faces an information-theoretic excess-cost lower bound set by the cost Hessian and the exploration policy's Fisher information.

arxiv:2604.24442 v2 · 2026-04-27 · eess.SY · cs.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 prove an ε-local minimax excess-cost lower bound that applies to any algorithm mapping the offline dataset to a stabilizing linear controller. The bound is expressed in terms of the Hessian of the LQG cost with respect to model parameters and the inverse Fisher Information induced by the exploration policy.

C2weakest assumption

The analysis assumes linear dynamics, quadratic cost, and that all trajectories are generated offline by a known linear exploration policy; if the true system is nonlinear or the policy is nonlinear or adaptive, the bound may not apply.

C3one line summary

Proves an ε-local minimax excess-cost lower bound for any algorithm learning a stabilizing linear controller from offline data, expressed via the LQG cost Hessian and inverse Fisher information of the exploration policy, with high complexity for fragile systems.

Receipt and verification

First computed	2026-05-20T00:05:45.204725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33d8164ecc9fd1fab63cf9a226fe08eb15e0573c7759ef85e961178e53605910

Aliases

arxiv: 2604.24442 · arxiv_version: 2604.24442v2 · doi: 10.48550/arxiv.2604.24442 · pith_short_12: GPMBMTWMT7I7 · pith_short_16: GPMBMTWMT7I7VNR4 · pith_short_8: GPMBMTWM

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GPMBMTWMT7I7VNR47GRCN7QI5M \
  | 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: 33d8164ecc9fd1fab63cf9a226fe08eb15e0573c7759ef85e961178e53605910

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df9997c556a36aea71b3600fbc3a90b42f11e352a92654049524297d226c5d82",
    "cross_cats_sorted": [
      "cs.SY"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "eess.SY",
    "submitted_at": "2026-04-27T13:06:48Z",
    "title_canon_sha256": "43722b0a0966a10c36009e17182fa6d6d4a4bd6075e0491da54c2a17a12d12e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.24442",
    "kind": "arxiv",
    "version": 2
  }
}