Pith Number

pith:J5AGE4GI

pith:2026:J5AGE4GIQF2GNBIID6IXVE3LII

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Stochastic Non-Smooth Convex Optimization with Unbounded Gradients

Dmitry Kovalev

AdamW with clipped updates outperforms SGD and AdaGrad on convex stochastic problems with unbounded gradients.

arxiv:2605.15522 v1 · 2026-05-15 · math.OC · cs.LG

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\pithnumber{J5AGE4GIQF2GNBIID6IXVE3LII}

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Record completeness

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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

AdamW with clipped updates theoretically outperforms other popular stochastic optimization methods, such as SGD and AdaGrad, for convex stochastic generalized Lipschitz optimization problems.

C2weakest assumption

Objective functions belong to the newly introduced generalized Lipschitz class in which gradient norms are bounded by an affine function of the optimality gap.

C3one line summary

Introduces generalized Lipschitz class and shows clipped AdamW outperforms SGD and AdaGrad for stochastic convex optimization under this and related assumptions.

References

22 extracted · 22 resolved · 5 Pith anchors

[1] Adam: A Method for Stochastic Optimization · arXiv:1412.6980

[2] Decoupled Weight Decay Regularization · arXiv:1711.05101

[3] Why gradient clipping accelerates training: A theoretical justification for adaptivity 1905

[4] Near-optimal methods for minimizing star-convex functions and beyond 1938

[5] Methods for convex (l_0, l_1)-smooth optimization: Clipping, acceleration, and adaptivity

Receipt and verification

First computed	2026-05-20T00:01:03.043859Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f406270c881746685081f917a936b423c573ec24ec739af48937a6a2c20c7d4

Aliases

arxiv: 2605.15522 · arxiv_version: 2605.15522v1 · doi: 10.48550/arxiv.2605.15522 · pith_short_12: J5AGE4GIQF2G · pith_short_16: J5AGE4GIQF2GNBII · pith_short_8: J5AGE4GI

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/J5AGE4GIQF2GNBIID6IXVE3LII \
  | 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: 4f406270c881746685081f917a936b423c573ec24ec739af48937a6a2c20c7d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45cce6e35ed59ada4f5a31b882ff6434d169dc2587a8748eb47e178a18505745",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-15T01:43:22Z",
    "title_canon_sha256": "36c1edce1ac2cb48ee65483611a8698eddc85430de0bb7b6fffaf5ab624d7fbc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15522",
    "kind": "arxiv",
    "version": 1
  }
}