Pith Number

pith:GPYEBFXJ

pith:2026:GPYEBFXJO5PAUJVRLJEQTZIJ2P

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Manifold-Aware Information Gain and Lower Bounds for Gaussian-Process Bandits on Riemannian Quotient Spaces

Changsheng Chen, Ning Xie, Yuriy Dorn

A regret lower bound for Gaussian-process bandits on Riemannian manifolds includes an explicit factor of the manifold volume raised to the power ν/(2ν+d).

arxiv:2605.13524 v1 · 2026-05-13 · eess.SP

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4 Citations 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

For any algorithm and time horizon T exceeding an explicit threshold, the worst-case expected regret over the RKHS-ball ||f||_{H_{k_ν}} ≤ B satisfies E[R_T(f)] ≥ c_*(d,ν) B^{d/(2ν+d)} σ_n^{2ν/(2ν+d)} · vol_g(M)^{ν/(2ν+d)} T^{(ν+d)/(2ν+d)} (log T)^{ν/(2ν+d)}.

C2weakest assumption

The unknown function f lies inside the RKHS ball of the intrinsic Matérn-ν kernel with ν > d/2 on a smooth compact Riemannian manifold; if the kernel does not faithfully encode the manifold geometry, the explicit volume factor may not hold.

C3one line summary

Derives an explicit volume-dependent lower bound on regret for GP bandits on Riemannian manifolds that matches the exponent of known upper bounds and includes a new geometric constant.

References

33 extracted · 33 resolved · 0 Pith anchors

[1] On information gain and regret bounds in Gaussian process bandits, 2021

[2] Stochastic multi-armed-bandit prob- lem with non-stationary rewards, 2014

[3] A domain-shrinking based Bayesian optimization algorithm with order-optimal regret performance, 2021

[4] Gaussian process optimization in the bandit setting: no regret and experimental design, 2010

[5] Mat´ern Gaussian processes on Riemannian manifolds, 2020

Receipt and verification

First computed	2026-05-18T02:44:24.333071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33f04096e9775e0a26b15a4909e509d3fcb284c3f3ae96a688fcab4c65c63e83

Aliases

arxiv: 2605.13524 · arxiv_version: 2605.13524v1 · doi: 10.48550/arxiv.2605.13524 · pith_short_12: GPYEBFXJO5PA · pith_short_16: GPYEBFXJO5PAUJVR · pith_short_8: GPYEBFXJ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GPYEBFXJO5PAUJVRLJEQTZIJ2P \
  | 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: 33f04096e9775e0a26b15a4909e509d3fcb284c3f3ae96a688fcab4c65c63e83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d5ab8315f10f536e82e7446c92142f34870925f8636df5524f7fc07d31724d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "eess.SP",
    "submitted_at": "2026-05-13T13:38:29Z",
    "title_canon_sha256": "c4a2e3746dce5160c35e1445a86352c0bd46eff5b84d2032583603c187056fa4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13524",
    "kind": "arxiv",
    "version": 1
  }
}