Pith Number

pith:PE6GDVQI

pith:2026:PE6GDVQILL33ULI5PGEWLITCOO

not attested not anchored not stored refs pending

Swap Regret Minimization Through Response-Based Approachability

Gabriele Farina, Haipeng Luo, Ioannis Anagnostides, Jon Schneider, Maxwell Fishelson

A simpler algorithm achieves O(d^{3/2} √T) linear swap regret over general convex sets via response-based approachability.

arxiv:2602.06264 v3 · 2026-02-05 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PE6GDVQILL33ULI5PGEWLITCOO}

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

We develop a significantly simpler, computationally efficient algorithm that guarantees O(d^{3/2} √T) linear swap regret for a general convex set and O(d √T) when the set is centrally symmetric.

C2weakest assumption

The response-based approachability framework of Bernstein and Shimkin can be directly applied to linear swap regret minimization over convex sets after John ellipsoid preconditioning, without hidden computational costs or additional assumptions on the loss functions.

C3one line summary

New response-based approachability algorithm with John ellipsoid preconditioning achieves O(d^{3/2} √T) linear swap regret for general convex sets and O(d √T) for symmetric sets, with matching Ω(d √T) lower bound.

Cited by

1 paper in Pith

An Efficient Black-Box Reduction from Online Learning to Multicalibration, and a New Route to $\Phi$-Regret Minimization

Receipt and verification

First computed	2026-05-22T01:03:56.640521Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

793c61d6085af7ba2d1d798965a262739f94348c15342ff39e78da2b79659a5e

Aliases

arxiv: 2602.06264 · arxiv_version: 2602.06264v3 · doi: 10.48550/arxiv.2602.06264 · pith_short_12: PE6GDVQILL33 · pith_short_16: PE6GDVQILL33ULI5 · pith_short_8: PE6GDVQI

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/PE6GDVQILL33ULI5PGEWLITCOO \
  | 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: 793c61d6085af7ba2d1d798965a262739f94348c15342ff39e78da2b79659a5e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c3a3ec8dc5c35655afab124138db1d1265568b4f16454d77a9271f13908313d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-02-05T23:43:25Z",
    "title_canon_sha256": "0811e8ff099222e288d749a88e8a962181ae7b67f4bc115174fbf3b4a445933e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.06264",
    "kind": "arxiv",
    "version": 3
  }
}