Paper Citation Record · LEDGER

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness

As of 16 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 1 inbound Pith citation observation for arXiv:2505.04599.

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2505.04599 v1

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Source: pith, observed 2026-08-15T16:18:52.617155Z

Reference resolution

51 of 51 outbound references displayed

verified exact0
verified fuzzy29
unresolved22
parse uncertain0
malformed identifier0
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Outbound references

Observation a2694726-8f38-48c1-b075-4263af3617fb · outbound

This paper cites an unresolved cited work.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:30:25.769951Z

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Observation f1d6d86c-4b02-4429-b2b8-f7f311c05e42 · outbound

This paper cites Therefore, the effective learning rate of the algorithm at stept is ηt = η √ γ2 +∑ t−1 i=0 ‖F (xi,ξi)‖2 = η√ γ2 +t(ǫ2 +σ2) =αt+2.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Therefore, the effective learning rate of the algorithm at stept is ηt = η √ γ2 +∑ t−1 i=0 ‖F (xi,ξi)‖2 = η√ γ2 +t(ǫ2 +σ2) =αt+2

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.722252Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f71e23ea-10e6-4706-ac5e-30ff33ab47a8 · outbound

This paper cites We now bound the remaining constants.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness We now bound the remaining constants

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.510513Z

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Observation 162b8764-b904-4214-ab15-703b480c2980 · outbound

This paper cites an unresolved cited work.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:30:25.656138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5f2d3f58-2eb0-4417-b339-cf729753f331 · outbound

This paper cites Let algorithmADAN denote Decorrelated AdaGrad-Norm with parameters η >0 and 0<γ ≤ ∆ L1 8 log ( 1 + 48 ∆ L2 1 L0 ).

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Let algorithmADAN denote Decorrelated AdaGrad-Norm with parameters η >0 and 0<γ ≤ ∆ L1 8 log ( 1 + 48 ∆ L2 1 L0 )

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.688372Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 05d82fd6-c6b7-4986-abb3-0b577140bb86 · outbound

This paper cites Near -optimal non-convex stochastic opti- mization under generalized smoothness.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Near -optimal non-convex stochastic opti- mization under generalized smoothness

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-15T23:30:24.976572Z

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Observation fad08475-e6ef-4ba2-9812-fe6e7d8c2154 · outbound

This paper cites Adaptive Bound Optimization for Online Convex Optimization.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Adaptive Bound Optimization for Online Convex Optimization

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T23:30:24.980118Z

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Observation 70402f0a-9d47-4096-b2f3-c8db8dc97d71 · outbound

This paper cites Variance-reduced Clipping for Non-convex Optimization.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Variance-reduced Clipping for Non-convex Optimization

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T23:30:24.984392Z

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Observation fc002a4f-2e9b-478e-b4d3-98062730549d · outbound

This paper cites Adagrad stepsizes: Sharp convergence over nonconvex landscapes.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Adagrad stepsizes: Sharp convergence over nonconvex landscapes

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.789540Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation cdd59b75-7938-48fb-92d4-ce03865715d6 · outbound

This paper cites Suppose g ∈ Rd with ‖g‖ =ǫ.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Suppose g ∈ Rd with ‖g‖ =ǫ

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.555925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4bfd7057-a46e-485e-8197-b0daceca7bb4 · outbound

This paper cites an unresolved cited work.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:30:25.412347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 41c979b7-8086-4eeb-a316-0491e8f52aac · outbound

This paper cites (8) 15 Published as a conference paper at ICLR 2025 The RHS of Equation 7 can be bounded as 4 L1 log ( 1 + L1gt+1 L0 ) = 4 L1 log ( 1 + ∆ L2 1 L0 ( 576(t +.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness (8) 15 Published as a conference paper at ICLR 2025 The RHS of Equation 7 can be bounded as 4 L1 log ( 1 + L1gt+1 L0 ) = 4 L1 log ( 1 + ∆ L2 1 L0 ( 576(t +

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.760537Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 81248594-5734-4c61-8ff6-21b98f444777 · outbound

This paper cites f is informally pictured in Figure 1b of the main text.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness f is informally pictured in Figure 1b of the main text

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.750835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 03ce0f66-4c72-4d0f-b28c-2ef8ae9bc01c · outbound

This paper cites Thereforef (x0) − infxf (x) ≤ ∆.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Thereforef (x0) − infxf (x) ≤ ∆

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.741400Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 51b42532-16df-4479-9363-b0ce55b2b23a · outbound

This paper cites an unresolved cited work.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:30:25.732272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0dd5b158-8ee9-4016-80d8-dc3d403b0b16 · outbound

This paper cites Actually,f does not satisfy this condition becausef is not even lower bounded, due to the linear term ǫ⟨x, e1⟩.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Actually,f does not satisfy this condition becausef is not even lower bounded, due to the linear term ǫ⟨x, e1⟩

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.711410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 28da9ef0-af29-4dc3-839e-92775aa0863f · outbound

This paper cites Speciﬁcally, we need ˆf which is lower bounded and that satisﬁes: ∇ ˆf (xt) = ∇f (xt), ˆf (xt) = f (xt) for all 0 ≤t ≤T.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Speciﬁcally, we need ˆf which is lower bounded and that satisﬁes: ∇ ˆf (xt) = ∇f (xt), ˆf (xt) = f (xt) for all 0 ≤t ≤T

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.699836Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a0e8882c-eeb2-4dd2-a9ff-16b102a903de · outbound

This paper cites First, recall the deﬁnition of ψ: ˜ψ(x) = L0 L2 1 (exp (L1|x|) −L1|x| − 1).

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness First, recall the deﬁnition of ψ: ˜ψ(x) = L0 L2 1 (exp (L1|x|) −L1|x| − 1)

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.677814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e3562ffb-1431-458e-b79b-44c8185ca0ba · outbound

This paper cites an unresolved cited work.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:30:25.666623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7cdca7ed-d1b5-49ec-a00b-119708470b12 · outbound

This paper cites Therefore, with the initial point x0 =m + ∆ 2ǫ , the objective satisﬁes f (x0) − inf x f (x) = ǫ(x0 −m) +ψ(m) =ǫ ∆ 2ǫ + ∆ 2 = ∆.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Therefore, with the initial point x0 =m + ∆ 2ǫ , the objective satisﬁes f (x0) − inf x f (x) = ǫ(x0 −m) +ψ(m) =ǫ ∆ 2ǫ + ∆ 2 = ∆

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.645814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b84d0707-bf2e-4b9c-9461-5f94a4638b98 · outbound

This paper cites If η ≥ √ 2γ L1σ log ( 1 + L1ǫ L0 ) , then by Lemma 3 there exists a problem instance for which Dec orrelated AdaGrad will never ﬁnd an ǫ-approximate stationary point.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness If η ≥ √ 2γ L1σ log ( 1 + L1ǫ L0 ) , then by Lemma 3 there exists a problem instance for which Dec orrelated AdaGrad will never ﬁnd an ǫ-approximate stationary point

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.634333Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 297f349c-c3b1-4764-b5e4-2ad024615f47 · outbound

This paper cites an unresolved cited work.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:30:25.623723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7d83cb05-b831-4ea8-b494-0dea2b7ec6cc · outbound

This paper cites Recall the function ψ : R → R deﬁned as ψ(x) = L0 L2 1 (exp(L1|x|) −L1|x| − 1).

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Recall the function ψ : R → R deﬁned as ψ(x) = L0 L2 1 (exp(L1|x|) −L1|x| − 1)

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.612319Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8e5ee1b8-2362-45e8-9dc0-d76e99a1a971 · outbound

This paper cites In this case, the learning rate α(g) is large enough to ensure that f (xt+1) ≥ f (xt) for an exponentially increasing f.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness In this case, the learning rate α(g) is large enough to ensure that f (xt+1) ≥ f (xt) for an exponentially increasing f

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.600941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 04a1310b-39c7-43ed-b626-2dc68e25eca2 · outbound

This paper cites This completes the induction.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness This completes the induction

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.589932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3cc4a260-40a6-410a-ba46-11495783b782 · outbound

This paper cites Also, ‖g1 −ℓg‖ = |c1 −ℓ|‖g‖ =ℓ −c1 = 1 −p p (c2 −ℓ) ≤ 1 −p p (σ1 +σ2ℓ) ≤σ1 +σ2ℓ, where the last inequality uses p > 1 2.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Also, ‖g1 −ℓg‖ = |c1 −ℓ|‖g‖ =ℓ −c1 = 1 −p p (c2 −ℓ) ≤ 1 −p p (σ1 +σ2ℓ) ≤σ1 +σ2ℓ, where the last inequality uses p > 1 2

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.578621Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8edbb6e2-a660-464a-b4a4-dcee4a7d6676 · outbound

This paper cites The upper bound of ‖yi‖ in the deﬁnition of k1 ensures that Equation 31 is satisﬁed.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness The upper bound of ‖yi‖ in the deﬁnition of k1 ensures that Equation 31 is satisﬁed

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.543601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7251ec45-044a-4a1d-8e24-8563c5db5e59 · outbound

This paper cites an unresolved cited work.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:30:25.532573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 61092573-2b38-42db-acf3-14e22a087e98 · outbound

This paper cites We can also bound β(yk1 ) using the assumed condition α(g) < 4m |g| , since we previously showed that (yk1, yk+1) satisﬁes Equation 29 through Equation.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness We can also bound β(yk1 ) using the assumed condition α(g) < 4m |g| , since we previously showed that (yk1, yk+1) satisﬁes Equation 29 through Equation

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.521966Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 56975a94-a671-43bf-ba50-5c8f4124e53f · outbound

This paper cites an unresolved cited work.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:30:25.500610Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5fefb382-468e-4d51-b788-190b62a21471 · outbound

This paper cites For b1: b1 = 1−p1 p1 ( σ1 + ( σ2 − p1 1−p1 ) G ) ((σ2 + 1)(2p1 −.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness For b1: b1 = 1−p1 p1 ( σ1 + ( σ2 − p1 1−p1 ) G ) ((σ2 + 1)(2p1 −

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.489870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2ea15521-7d9a-4e13-95af-0e7976cf6cb1 · outbound

This paper cites Also as in the ﬁrst case, |c1 −ℓ| ≤ |c2 −ℓ|.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Also as in the ﬁrst case, |c1 −ℓ| ≤ |c2 −ℓ|

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.566506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 687c049a-651f-4bb9-8677-b92c85d43cbc · outbound

This paper cites an unresolved cited work.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:30:25.479666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5464baa6-62bf-43ff-ad3a-5ba9bc4cd8f8 · outbound

This paper cites 42 Published as a conference paper at ICLR 2025 Proof.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness 42 Published as a conference paper at ICLR 2025 Proof

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.469142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7ac47581-611f-4ff7-a90c-6d649946762a · outbound

This paper cites Therefore,t ≤ ∆ 2α(ǫ)ǫ2 implies thatt<t 0 + 1, so that ˆPg(xt) ≥a by the deﬁnition of t0, and ﬁnally ‖∇f (xt)‖ =ǫ.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Therefore,t ≤ ∆ 2α(ǫ)ǫ2 implies thatt<t 0 + 1, so that ˆPg(xt) ≥a by the deﬁnition of t0, and ﬁnally ‖∇f (xt)‖ =ǫ

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.457357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8374617c-f360-421f-9471-d76aa8a90d7b · outbound

This paper cites an unresolved cited work.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:30:25.445527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 274a6c48-0ec7-4c93-9646-07fa5a89247e · outbound

This paper cites Therefore ∇f (xt) = ǫe1.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Therefore ∇f (xt) = ǫe1

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.434670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 34f020d3-7745-4672-90f3-a910b0f0d246 · outbound

This paper cites Together, these three equations imply that ‖∇f (xt)‖ =ǫ for allt ≤T , which is the desired conclusion.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Together, these three equations imply that ‖∇f (xt)‖ =ǫ for allt ≤T , which is the desired conclusion

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.423850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1ab1cf66-ddda-4070-a7a1-1f7d0d62b3fd · outbound

This paper cites By the monotone convergence theorem, E[τ ] = limT →∞ E [Xτ ∧T ] − 1 (λ + 1)p − 1 We consider the following cases.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness By the monotone convergence theorem, E[τ ] = limT →∞ E [Xτ ∧T ] − 1 (λ + 1)p − 1 We consider the following cases

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.399789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 38ff7a7f-edb0-46fd-985b-c45f807c2ea0 · outbound

This paper cites Speciﬁcally, we need r(λ) is decreasing (59) lim λ→ 1−p p + r(λ) = 1 (60) lim λ→∞ r(λ) = 1 −p.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Speciﬁcally, we need r(λ) is decreasing (59) lim λ→ 1−p p + r(λ) = 1 (60) lim λ→∞ r(λ) = 1 −p

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.386052Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 227c42e6-5bb1-43d7-9daa-d3de12f41684 · outbound

This paper cites an unresolved cited work.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Unresolved cited work

Reference 49

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:30:25.372486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2a20dbf4-4857-4e3a-bccf-e81461d8b5dd · outbound

This paper cites If ∆ L2 1 ≥L0, then T (ADAN, Fdet,ǫ ) ≥ ˜Ω (∆ 2L2 1 ǫ2 ).

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness If ∆ L2 1 ≥L0, then T (ADAN, Fdet,ǫ ) ≥ ˜Ω (∆ 2L2 1 ǫ2 )

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.360829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5685fa76-27d4-4ab2-a9b7-f16a9e7e96e7 · outbound

This paper cites an unresolved cited work.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Unresolved cited work

Reference 51

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:30:25.348728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 60c35cc6-fae6-4f5b-9f98-d7a4822cc160 · outbound

This paper cites On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization

Reference 2010

Resolution: unresolved; no resolver link, observed 2026-08-15T23:30:24.853944Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0fb4aa0f-b843-4aef-822b-6b94177a9ecd · outbound

This paper cites A Novel Convergence Analysis for Algorithms of the Adam Family.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness A Novel Convergence Analysis for Algorithms of the Adam Family

Reference 2013

Resolution: unresolved; no resolver link, observed 2026-08-15T23:30:24.968099Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a5259fda-dac4-4253-a60d-3d3f72b8f65b · outbound

This paper cites The Min-Max Complexity of Distributed Stochastic Convex Optimization with Intermittent Communication.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness The Min-Max Complexity of Distributed Stochastic Convex Optimization with Intermittent Communication

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-15T23:30:24.995999Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0fbac585-7ee2-41da-baac-0a9bc7e863e5 · outbound

This paper cites Generalized-Smooth Nonconvex Optimization is As Efficient As Smooth Nonconvex Optimization.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Generalized-Smooth Nonconvex Optimization is As Efficient As Smooth Nonconvex Optimization

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-15T23:30:24.858567Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 169bd41b-dcaa-489f-a398-2a81204853fc · outbound

This paper cites Lower Bound for Randomized First Order Convex Optimization.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Lower Bound for Randomized First Order Convex Optimization

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-15T23:30:24.992058Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 394bb7db-b0e1-4562-9761-40089c868c0e · outbound

This paper cites Beyond Uniform Smoothness: A Stopped Analysis of Adaptive SGD.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Beyond Uniform Smoothness: A Stopped Analysis of Adaptive SGD

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-15T23:30:24.863084Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e80aaad8-bef7-4932-bbbd-146d406728ea · outbound

This paper cites Convergence of Adam Under Relaxed Assumptions.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Convergence of Adam Under Relaxed Assumptions

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-15T23:30:24.972422Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b56d61b4-c83b-44de-af95-3a3986ed3f10 · outbound

This paper cites Improved analysis of clipping algorithms for non-convex optimization.

Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness Improved analysis of clipping algorithms for non-convex optimization

Reference 2024

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:30:25.779616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

Observation 3e89b0cd-e87f-4110-b37e-38e86be44b1a · inbound

Decentralized Stochastic Nonconvex Optimization under the $(L_0,L_1)$-Smoothness cites this paper.

Decentralized Stochastic Nonconvex Optimization under the $(L_0,L_1)$-Smoothness Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:18:52.623130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.