Pith Number

pith:Z43LXKWP

pith:2026:Z43LXKWPAMDLOHNY4PQIQY6JLV

not attested not anchored not stored refs pending

A Switching System Theory of Q-Learning with Linear Function Approximation

Donghwan Lee, Han-Dong Lim

The mean dynamics of Q-learning with linear function approximation are exactly equivalent to a linear switched system whose stability determines convergence.

arxiv:2605.11021 v2 · 2026-05-10 · cs.LG

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\pithnumber{Z43LXKWPAMDLOHNY4PQIQY6JLV}

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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 derive an exact linear switched model for the mean dynamics and relate convergence to stability of the corresponding switched system.

C2weakest assumption

That the mean dynamics of Q-learning with linear function approximation admit an exact representation as a finite set of linear switching modes whose joint spectral radius governs convergence.

C3one line summary

Q-learning with linear function approximation is recast as a switched linear system whose mean dynamics converge precisely when the joint spectral radius of the switching matrices is less than one.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Geometrically Averaged Hard Target Updates for Linear Q-Learning

Receipt and verification

First computed	2026-05-20T01:05:16.522625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf36bbaacf0306b71db8e3e08863c95d6d665df4fce51a86f60fe5cac9432b80

Aliases

arxiv: 2605.11021 · arxiv_version: 2605.11021v2 · doi: 10.48550/arxiv.2605.11021 · pith_short_12: Z43LXKWPAMDL · pith_short_16: Z43LXKWPAMDLOHNY · pith_short_8: Z43LXKWP

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Z43LXKWPAMDLOHNY4PQIQY6JLV \
  | 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: cf36bbaacf0306b71db8e3e08863c95d6d665df4fce51a86f60fe5cac9432b80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50e911934cfb9d76dc0b2679b68867559464df43c129533a94dbdd78c07fee9c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-10T16:21:31Z",
    "title_canon_sha256": "1367a8f9dfe7deeb7b6cda9fc40c07ae986d30178b072d47d5f2fd1ecdc94c61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11021",
    "kind": "arxiv",
    "version": 2
  }
}