Pith Number

pith:VOH7P5BM

pith:2026:VOH7P5BMHVBK7HCTR6B5FLOO4O

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Stochastic Compositional Optimization via Hybrid Momentum Frank--Wolfe

El Mahdi Chayti

A hybrid momentum Frank-Wolfe algorithm achieves the optimal O(K^{-1/4}) convergence rate for stochastic compositional problems with merely Lipschitz outer functions.

arxiv:2605.15350 v1 · 2026-05-14 · math.OC · cs.LG

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Claims

C1strongest claim

We establish an O(K^{-1/4}) convergence rate in the generalized Frank-Wolfe gap for non-convex objectives with L_F-Lipschitz outer functions, matching the optimal complexity for projection-free single-sample stochastic methods under expected smoothness.

C2weakest assumption

The outer function F is L_F-Lipschitz (but not necessarily differentiable), and the stochastic oracles satisfy expected smoothness or bounded r-th moments for r in (1,2]. This premise enters in the convergence analysis that bounds the generalized Frank-Wolfe gap.

C3one line summary

The Hybrid Momentum Stochastic Frank-Wolfe algorithm achieves O(K^{-1/4}) convergence in the generalized Frank-Wolfe gap for non-convex stochastic compositional optimization with Lipschitz outer functions.

References

32 extracted · 32 resolved · 0 Pith anchors

[1] Conference on Learning Theory , pages= 2023

[2] 2024 , url = 2024

[3] IEEE Transactions on Signal Processing , volume= 2021

[4] Mathematical Programming , volume= 2017

[5] Journal of Machine Learning Research , volume=

Formal links

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Receipt and verification

First computed	2026-05-20T00:00:53.836646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab8ff7f42c3d42af9c538f83d2adcee38821c02839b848ee8eb0511545f584ac

Aliases

arxiv: 2605.15350 · arxiv_version: 2605.15350v1 · doi: 10.48550/arxiv.2605.15350 · pith_short_12: VOH7P5BMHVBK · pith_short_16: VOH7P5BMHVBK7HCT · pith_short_8: VOH7P5BM

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/VOH7P5BMHVBK7HCTR6B5FLOO4O \
  | 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: ab8ff7f42c3d42af9c538f83d2adcee38821c02839b848ee8eb0511545f584ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4df34068a89c803490e19e2cc5fd4292d1ef0035f5329b947d65b1533053058c",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-14T19:20:22Z",
    "title_canon_sha256": "609c2a39fee63bf4345ea361eb8c20988033413f11d7492d64d032bc2a1de815"
  },
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  "source": {
    "id": "2605.15350",
    "kind": "arxiv",
    "version": 1
  }
}