Pith Number

pith:Z3MN3YHF

pith:2026:Z3MN3YHFXKHP3KRB4ZZVHW4JA6

not attested not anchored not stored refs pending

Adaptive Calibration in Non-Stationary Environments

Haipeng Luo, Junyan Liu, Lillian J. Ratliff

Online algorithms achieve calibration errors that adapt to the unknown degree of non-stationarity in the outcome sequence.

arxiv:2605.11490 v2 · 2026-05-12 · cs.LG · stat.ML

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z3MN3YHFXKHP3KRB4ZZVHW4JA6}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

our algorithms attain Õ(√T+(TC)^{1/3}) for ℓ1 calibration error and Õ((1+C)^{1/3}) for both ℓ2 and pseudo KL calibration error. These bounds match the optimal rates in the stationary case (C=0) and recover known guarantees in the fully adversarial regime (C=T).

C2weakest assumption

The non-stationarity of the environment can be captured by the minimal ℓ1 deviation C of mean outcomes, and epoch-based scheduling combined with a non-uniform partition of the prediction space suffices to achieve the stated adaptive bounds without knowledge of C.

C3one line summary

Online algorithms achieve adaptive calibration bounds of Õ(√T + (TC)^{1/3}) for ℓ1 error and Õ((1+C)^{1/3}) for ℓ2 and pseudo-KL error, matching stationary and adversarial extremes via epoch scheduling and non-uniform prediction partitioning.

Cited by

1 paper in Pith

Instance-Adaptive Online Multicalibration

Receipt and verification

First computed	2026-05-25T02:01:23.163616Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ced8dde0e5ba8efdaa21e67353db8907813696aaf3f8b6be7e51ec7aaeafdc0b

Aliases

arxiv: 2605.11490 · arxiv_version: 2605.11490v2 · doi: 10.48550/arxiv.2605.11490 · pith_short_12: Z3MN3YHFXKHP · pith_short_16: Z3MN3YHFXKHP3KRB · pith_short_8: Z3MN3YHF

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Z3MN3YHFXKHP3KRB4ZZVHW4JA6 \
  | 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: ced8dde0e5ba8efdaa21e67353db8907813696aaf3f8b6be7e51ec7aaeafdc0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f77f7aa49fa0be81992d67f2e15b1ff58d58f26a49d88c3eb5d7b2fa3c8cfdde",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-12T04:06:40Z",
    "title_canon_sha256": "652bb2e580b68c23aa1ee55a250cbd1422f8e052e4e993dc37ef35be28587f49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11490",
    "kind": "arxiv",
    "version": 2
  }
}