Decentralized Min-Max Optimization with Gradient Tracking

Kun Huang; Runze You; Shi Pu

REVIEW 2 major objections 5 minor 41 references

Decentralized Min-Max Optimization with Gradient Tracking

T0 review · 2 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Decentralized min-max optimization matches centralized convergence rates.

desk verdict A genuinely new per-agent-y formulation with a solid deterministic analysis, but the constant-batch-size stochastic claim is not supported by the paper's own bound. read the letter →

arxiv 2505.10631 v1 pith:2TYIJWHC submitted 2025-05-15 math.OC

Runze You , Kun Huang , Shi Pu This is my paper · ORCID

classification math.OC MSC 90C2690C4768W15

keywords decentralizedmin-maxoptimizationgradienttrackingnonconvexstronglyconcavestochasticmethoditerationcomplexitysampleheterogeneousconstraintsets

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proposes a distributed formulation of min-max optimization in which each agent optimizes its own maximization variable under its own constraint set, while agents coordinate only on the shared minimization variable. The authors present two gradient-tracking algorithms—DGTA with full gradients and DSGTA with stochastic gradients—and prove that, for nonconvex strongly concave objectives, they reach an $\varepsilon$-first-order stationary point with iteration complexity $O(\kappa^2\varepsilon^{-2})$ and sample complexity $O(\kappa^3\varepsilon^{-4})$, matching centralized gradient descent ascent up to network-dependent constants. If correct, decentralized training can accommodate heterogeneous local adversaries or data domains without giving up centralized convergence guarantees.

What carries the argument

The engine is the gradient tracker, updated in DGTA by $g_i^{t+1} = \sum_{j \in \mathcal{N}_i} w_{ij}(g_j^t + \nabla_x f_i(x_i^{t+1}, y_i^{t+1}) - \nabla_x f_i(x_i^t, y_i^t))$, which lets every agent estimate the average of the local $x$-gradients without a coordinator. Around it, the paper builds the Lyapunov function $\mathcal{L}^t = \Phi(\bar{x}^t) - \Phi^* + \frac{300\kappa^2 L^2 \eta_x}{n(1-\lambda^2)}\|x^t - \bar{x}^t\|^2 + \frac{8\eta_x L^2}{n\eta_y \mu}\delta^t + \frac{2400\eta_x^3\kappa^2 L^2}{n(1-\lambda^2)^3}\|g^t - \bar{g}^t\|^2$. The coefficients are chosen so that Lemmas 3.1–3.4 combine into a single contraction (Lemma 3.5), turning the four coupled error terms into one step-size-dependent descent on the smoothed function $\Phi$.

What would settle it

Use Corollary 4.1.1 to compute the iteration bound on a family of graphs with shrinking spectral gap (e.g., rings of increasing size). If the number of iterations to reach $\|\nabla\Phi(\bar{x})\|^2 \le \varepsilon^2$ scales like $\kappa^2/\varepsilon^2$ times a constant independent of $n$, the headline claim is exactly right; if it scales like $n^2\kappa^2/\varepsilon^2$, then the graph dependence is a genuine factor, not a constant. This is a direct check from the displayed bounds in the paper.

Watch

Extended reading notes

Core claim

The central claim is that problem (1.1) — $\min_x \max_{\{y_i\}} \frac{1}{n} \sum_{i=1}^n f_i(x,y_i)$ with agent-specific $y_i$ and constraint sets $Y_i$ — can be solved by a single-loop decentralized method in which only $x$ is averaged over the network while each $y_i$ is updated by one projected gradient ascent step and never communicated. The paper proves this through a Lyapunov analysis: the gradient tracker keeps each agent's $g_i$ close to the average $x$-gradient, and the coupled recursions for the function value, consensus gap, maximizer gap $\delta^t = \sum_i \|\hat{y}_i(\bar{x}^t) - y_i^t\|^2$, and tracker disagreement all contract together. The resulting rates match the centralized GDA/SGDA results in [17] up to factors involving the spectral gap $1-\lambda$ of the mixing matrix, and the analysis requires no bounded-heterogeneity or bounded-second-moment assumptions.

Load-bearing premise

The load-bearing assumption is that every local constraint set $Y_i$ is convex, compact, and has a common finite diameter $D$; if any $Y_i$ were unbounded, the initial distance from $y_i^0$ to its argmax could be infinite and the finite-time bound would not close.

Editorial extensions

If this is right

DGTA attains iteration complexity $O(\kappa^2\varepsilon^{-2})$ for full gradients, the same order as centralized GDA, with the network entering only through spectral-gap factors.
DSGTA with batch size $b = \kappa\sigma^2/\varepsilon^2$ attains sample complexity $O(\kappa^3\varepsilon^{-4})$, matching centralized SGDA.
With batch size $b=1$, DSGTA attains sample complexity $O(\kappa^2\varepsilon^{-4})$ for small $\varepsilon$, independent of the graph and better in $\kappa$ than the large-batch regime.
The methods handle heterogeneous constraint sets $Y_i$ across agents without consensus constraints on $y$ and without bounded gradient dissimilarity.
A trade-off emerges: large batches reduce iteration count, while small batches reduce dependence on the communication graph.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

I infer that the advertised 'match up to constant factors' should be read with the spectral gap in mind: Corollary 4.1.1 contains $1/(1-\lambda)^2$ terms, so on a sparse ring with $1-\lambda = O(1/n^2)$ the complexity can degrade like $n^2\kappa^2/\varepsilon^2$, which is more than a constant-factor gap.
I infer the heterogeneous-$y_i$ formulation is a natural fit for personalized federated learning and multi-domain GANs, where a single shared discriminator variable is unrealistic; the single-loop projected ascent on $y_i$ is what makes the method practical.
A testable extension is to replace the deterministic projection step with variance-reduced stochastic updates for $y_i$; the Lyapunov recursion suggests $O(\varepsilon^{-3})$ sample complexity might be reachable.
Because the paper's $b=1$ sample complexity loses the $1/(1-\lambda)$ factor, I infer that in communication-heavy regimes small or moderate batch sizes are preferable even if iteration counts rise.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The new formulation in Problem (1.1) is real: letting each agent have its own y_i and its own constraint set Y_i is a meaningful departure from the consensus-y setup in earlier decentralized min-max papers, and it fits applications like distributed GANs and WRM. The deterministic algorithm DGTA is also well designed: single-loop, gradient tracking on x, projected ascent on each local y, and the Lyapunov analysis in Section 3 is coherent and detailed. I believe the deterministic rate in Corollary 4.1.1, with its explicit 1/(1-λ) factors, is essentially correct. The large-batch stochastic result (Corollary 4.1.3) also looks like a valid consequence of Theorem 4.1 when η_y is constant and b = O(κσ²/ε²), giving the advertised O(κ³ε⁻⁴) sample complexity. That part is worth a serious referee.

The soft spots are real and one is load-bearing. First, the abstract overclaims: it says O(κ²ε⁻²) and O(κ³ε⁻⁴) matching centralized methods, but the theorems carry spectral-gap terms 1/(1-λ) and 1/(1-λ)². For sparse graphs with 1-λ ~ 1/n², those are not constant factors. The tables in the body are honest, but the abstract and Remark 4.3 should be aligned with the theorems. Second, and more concretely, Corollary 4.1.2 (b = 1) is not established. Theorem 4.1 contains the variance floor F = [1/(nη_y²μ²) + ...] · 64η_x²κ²L²σ²/b. Under the b = 1 step sizes, both η_x and η_y decay as T^{-1/2}, so the 1/(nη_y²μ²) term times η_x² is O(1), not O(1/T). The proof of Corollary 4.1.2 replaces this expression with O(1/T) terms, and to do that it needs a lower bound on η_y μ that is false for large T. So the constant-batch-size O(κ²ε⁻⁴) sample complexity does not follow. The typos (e.g., ∇Φ(¯x²) in Lemma 3.5) and the missing error bars and code are minor by comparison.

My bottom line: the paper deserves peer review because the deterministic contribution and the large-batch stochastic analysis are valuable and likely correct, and the new formulation is worth citing. But the b = 1 result should be corrected, weakened, or removed, and the abstract should state the network dependence. I would send it to referees with that expectation.

Referee Report

2 major / 5 minor

Summary. The paper studies the decentralized min-max problem (1.1), in which agents jointly minimize a shared variable x while maximizing their own local variables y_i over possibly heterogeneous constraint sets Y_i, under nonconvex-strongly-concave (NC-SC) smooth objectives. Two algorithms are proposed: DGTA, which uses full gradients with gradient tracking, and DSGTA, which uses mini-batched stochastic gradients. The authors claim that DGTA reaches an ε-first-order stationary point in O(κ^2 ε^{-2}) iterations and that DSGTA has sample complexity O(κ^3 ε^{-4}) with large batches and O(κ^2 ε^{-4}) with constant batch size b=1, matching centralized GDA/SGDA up to network-dependent constants. The analysis is based on a Lyapunov function combining the primal descent, the errors δ^t = sum_i ||\hat y_i(\bar x^t) - y_i^t||^2, the consensus error, and the gradient-tracking error. Numerical experiments on an empirical Wasserstein robustness model with MNIST data compare DGTA with GT/DA and study DSGTA under different step sizes. The appendix contains detailed proofs of the lemmas and corollaries.

Significance. The paper's formulation with heterogeneous y_i and Y_i is a genuine extension of the common decentralized min-max formulation, and the proposed algorithms avoid bounded-heterogeneity assumptions on stochastic gradients. The Lyapunov analysis is systematic, and the appendix provides full finite-time proofs for the deterministic and large-batch stochastic results. If the advertised constant-batch (b=1) complexity were correct, it would be a notable improvement in the dependence on the network spectral gap. However, the proof of Corollary 4.1.2 contains a substantial gap: a variance term that is asymptotically a positive constant is bounded as if it were O(1/T). In addition, the abstract's κ-only rates omit explicit spectral-gap factors that appear in the paper's own tables and corollaries. These issues affect central claims and must be fixed before the paper is suitable for publication.

major comments (2)

[Corollary 4.1.2 / Theorem 4.1] The claimed O(κ^2 ε^{-4}) sample complexity with b=1 is not established. Under the step sizes stated in Corollary 4.1.2, for large T one has η_y ≈ D/√(3σ^2 T) and η_x ≈ √(n Δ_Φ/(L κ σ^2 T)). Substituting these into the first additive variance term of (4.1), namely (1/(n η_y^2 μ^2)) · 64 η_x^2 κ^2 L^2 σ^2, gives an asymptotic constant of order Δ_Φ κ L σ^2/(μ^2 D^2), not a vanishing term. Hence the right-hand side of (4.1) has a positive limit as T→∞, so the bound cannot imply E‖∇Φ(\bar x^t)‖^2 ≤ ε^2 with T = O(κ^2 ε^{-4}). In the proof of Corollary 4.1.2 this term is replaced by a multiple of n Δ_Φ κ L / T; that replacement requires 1/(η_y^2 μ^2) = O(1), whereas the chosen η_y satisfies η_y^2 μ^2 = O(1/T). Because the b=1 row of Table 2 and Remark 4.3 depend directly on this step, the proof must be corrected or the step-size choices revised.
[Abstract / Remark 4.2 / Table 1] The abstract and Section 1.2 state that DGTA achieves O(κ^2 ε^{-2}) and that both algorithms match centralized counterparts up to constant factors related to the communication network. However, Corollary 4.1.1 and Remark 4.2, as well as Table 1, give rates containing explicit factors such as 1/(1−λ)^2 and 1/√(1−λ). For sparse graphs 1/(1−λ) can grow as O(n^2), so these factors are not bounded by a constant independent of the network size. The headline complexity statements should either explicitly include the spectral-gap dependence or clearly specify the class of graphs over which the stated constants are uniform.

minor comments (5)

[Lemma 3.5 and Appendix A.5] In the statement of Lemma 3.5, Eq. (3.4), and the final display of Appendix A.5, the expression ∇Φ(\bar x^2) should be ∇Φ(\bar x^t); the superscript t is missing.
[End of Section 3] The sentence before Lemma 3.4 says 'whose recursion is stated in Lemma 3.3' but should refer to Lemma 3.4.
[Corollary 4.1.1] The heading of Corollary 4.1.1 says 'DSGT' instead of 'DGTA'.
[Section 5] In the discussion of Figure 1b, the sentence 'since the full gradient computation requires.' is incomplete and should be finished.
[Remark 4.3, Eq. (4.9)] The claim that (4.9) reduces to O(Δ_Φ L κ σ^2/(n ε^4) + D^2 σ^2 L^2 κ^2/ε^4) when ε is small should state the threshold condition on ε relative to the other terms in the bound.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: the convergence and complexity claims follow from self-contained Lyapunov recursions; only minor, non-load-bearing self-citations appear.

full rationale

The paper's derivation chain is self-contained. Lemmas 3.1-3.4 establish recursions for Phi(bar x^t), delta^t, ||x^t - bar x^t||^2, and ||g^t - bar g^t||^2 using Assumptions 2.1-2.5, and Lemma 3.5 combines them into a Lyapunov function with explicit constants. The constants in the Lyapunov function are chosen algebraically in Appendix A.5 to satisfy inequalities (A.28a)-(A.28c), not fitted to any target complexity or empirical data. Theorem 4.1 then averages the Lyapunov recursion, and Corollaries 4.1.1-4.1.3 substitute explicit stepsizes and batch sizes and solve for T. Thus the claimed O(kappa^2 epsilon^{-2}) and O(kappa^3 epsilon^{-4}) rates are consequences of the stated bounds, not restatements of the desired rates. The abstract's omission of spectral-gap factors is an imprecise presentation of Corollary 4.1.1, which explicitly contains 1/(1-lambda) and 1/(1-lambda)^2 terms; this is a presentation concern, not circularity. The support of the b=1 sample complexity in Corollary 4.1.2 may be questionable because the variance floor in Theorem 4.1 need not vanish with the stated T-dependent stepsizes, but that is a proof-gap/correctness issue, not a circularity: the claim is not obtained by defining a quantity in terms of itself or by renaming a fitted parameter. Self-citations appear, for example [27] and [11], for gradient tracking and variance assumptions, but the proofs in the appendix do not rely on those citations; they are background references, so they are not load-bearing. Hence no specific circular step can be exhibited, and the circularity score is minimal.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The analysis rests on standard assumptions for decentralized optimization and NC-SC min-max problems. No free parameters are fitted to data; the algorithm step sizes and Lyapunov coefficients are chosen analytically. No new entities are introduced.

assumptions (6)

domain assumption Assumption 2.1: The graph is undirected, connected, and the mixing matrix W is nonnegative, symmetric, and doubly stochastic, with spectral gap 1-λ > 0.
The gradient tracking recursions and consensus-like updates rely on the contraction property of W - 11^T/n.
domain assumption Assumption 2.2: Each f_i is L-smooth and μ-strongly concave in y.
Defines the NC-SC regime and is used to bound the smoothness of Φ_i and the Lipschitz continuity of the argmax y_i(x).
domain assumption Assumption 2.3: Each Y_i is convex and compact with diameter D.
Used in the projection step and to bound δ_0 and the term D^2 in the final complexity.
domain assumption Assumption 2.4: Φ is lower bounded.
Needed so the Lyapunov function is bounded from below and the telescoping sum yields a finite bound.
domain assumption Assumption 2.5: Stochastic gradients are unbiased with bounded variance σ².
Controls the noise terms in the recursion and appears in the DSGTA bounds.
standard math Lemma 2.1: Φ_i is 2κL-smooth and the argmax y_i(x) is κ-Lipschitz.
Cited from [19]; central to converting the min-max problem into a smooth minimization problem.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Decentralized Min-Max Optimization with Gradient Tracking." pith.science (2026). https://pith.science/paper/2TYIJWHC

@misc{pith2026250510631,
  author       = {Pith},
  title        = {Pith review of: Decentralized Min-Max Optimization with Gradient Tracking},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2TYIJWHC}},
  note         = {Machine review of arXiv:2505.10631}
}

abstract

This paper presents a novel distributed formulation of the min-max optimization problem. Such a formulation enables enhanced flexibility among agents when optimizing their maximization variables. To address the problem, we propose two distributed gradient methods over networks, termed Distributed Gradient Tracking Ascent (DGTA) and Distributed Stochastic Gradient Tracking Ascent (DSGTA). We demonstrate that DGTA achieves an iteration complexity of $\mathcal{O}(\kappa^2\varepsilon^{-2})$, and DSGTA attains a sample complexity of $\mathcal{O}(\kappa^3\varepsilon^{-4})$ for nonconvex strongly concave (NC-SC) objective functions. Both results match those of their centralized counterparts up to constant factors related to the communication network. Numerical experiments further demonstrate the superior empirical performance of the proposed algorithms compared to existing methods.

Figures

Figures reproduced from arXiv: 2505.10631 by the authors.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

41 extracted references · 32 canonical work pages

[1]

A RJOVSKY , S

M. A RJOVSKY , S. C HINTALA , AND L. B OTTOU , Wasserstein generative adversarial networks, in International conference on machine learning, PMLR, 2017, pp. 214–223

work page 2017
[2]

B ECK, First-order methods in optimization, SIAM, 2017

A. B ECK, First-order methods in optimization, SIAM, 2017

2017
[3]

B OTTOU , F

L. B OTTOU , F. E. C URTIS , AND J. N OCEDAL , Optimization methods for large-scale machine learning, SIAM review, 60 (2018), pp. 223–311

work page 2018
[4]

C HEN , H

L. C HEN , H. Y E, AND L. L UO, An efficient stochastic algorithm for decentralized nonconvex-strongly-concave minimax optimization, in Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, S. Dasgupta, S. Mandt, and Y . Li, eds., vol. 238 of Proceedings of Machine Learning Research, PMLR, 02–04 May 2024, pp. 1990–199...

work page 2024
[5]

C UTKOSKY AND F

A. C UTKOSKY AND F. ORABONA , Momentum-based variance reduction in non-convex sgd, Advances in neural information processing systems, 32 (2019)

work page 2019
[6]

B. D AI, A. S HAW, L. L I, L. X IAO, N. H E, Z. L IU, J. C HEN , AND L. S ONG, Sbeed: Convergent reinforcement learning with nonlinear function approximation, in International Conference on Machine Learning, PMLR, 2018, pp. 1125–1134

work page 2018
[7]

DI LORENZO AND G

P. DI LORENZO AND G. S CUTARI , Next: In-network nonconvex optimization, IEEE Transactions on Signal and Information Processing over Networks, 2 (2016), pp. 120–136

2016
[8]

F ANG , C

C. F ANG , C. J. L I, Z. L IN, AND T. Z HANG , Spider: Near-optimal non-convex optimization via stochastic path-integrated differential estimator, Advances in Neural Information Processing Systems, 31 (2018)

work page 2018

Show all 41 references

[9]

G OODFELLOW , J

I. G OODFELLOW , J. P OUGET -A BADIE , M. M IRZA , B. X U, D. WARDE -FARLEY , S. O ZAIR , A. C OURVILLE , AND Y. BENGIO , Generative adversarial nets, in Advances in Neural Information Processing Systems, Z. Ghahra- mani, M. Welling, C. Cortes, N. Lawrence, and K. Weinberger, ...

2014
[10]

HUANG , S

F. HUANG , S. G AO, J. P EI, AND H. H UANG , Accelerated zeroth-order and first-order momentum methods from mini to minimax optimization, The Journal of Machine Learning Research, 23 (2022), pp. 1616–1685

2022
[11]

H UANG , X

K. H UANG , X. L I, AND S. P U, Distributed stochastic optimization under a general variance condition, IEEE Transactions on Automatic Control, (2024)

2024
[12]

C. J IN, P. N ETRAPALLI , AND M. J ORDAN , What is local optimality in nonconvex-nonconcave minimax optimization?, in International conference on machine learning, PMLR, 2020, pp. 4880–4889

2020
[13]

J. J IN, B. Z HANG , H. WANG , AND L. WANG, Non-convex distributionally robust optimization: Non-asymptotic analysis, Advances in Neural Information Processing Systems, 34 (2021), pp. 2771–2782

2021
[14]

K ANG , J.-Y

M. K ANG , J.-Y. Z HU, R. Z HANG , J. P ARK , E. S HECHTMAN , S. P ARIS , AND T. PARK, Scaling up gans for text-to-image synthesis, in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2023, pp. 10124–10134. 15 Decentralized Min-Max Optimizatio...

2023
[15]

L ECUN, C

Y. L ECUN, C. C ORTES , C. B URGES , ET AL ., Mnist handwritten digit database, 2010

2010
[16]

L IAN , C

X. L IAN , C. Z HANG , H. Z HANG , C.-J. H SIEH , W. Z HANG , AND J. L IU, Can decentralized algorithms outperform centralized algorithms? a case study for decentralized parallel stochastic gradient descent, Advances in Neural Information Processing Systems, 30 (2017)

2017
[17]

T. L IN, C. J IN, AND M. J ORDAN , On gradient descent ascent for nonconvex-concave minimax problems, in International Conference on Machine Learning, PMLR, 2020, pp. 6083–6093

2020
[18]

T. L IN, C. J IN, AND M. I. J ORDAN , Near-optimal algorithms for minimax optimization, in Conference on Learning Theory, PMLR, 2020, pp. 2738–2779

2020
[19]

T. LIN, C. J IN, AND M. I. J ORDAN , A nonasymptotic analysis of gradient descent ascent for nonconvex-concave minimax problems, Available at SSRN, (2022)

2022
[20]

M. L IU, W. Z HANG , Y. MROUEH , X. C UI, J. R OSS , T. YANG , AND P. DAS, A decentralized parallel algorithm for training generative adversarial nets, Advances in Neural Information Processing Systems, 33 (2020), pp. 11056– 11070

2020
[21]

Z. L IU, X. Z HANG , S. L U, AND J. L IU, Precision: Decentralized constrained min-max learning with low communication and sample complexities, arXiv preprint arXiv:2303.02532, (2023)

2023 arXiv
[22]

L. L UO, H. Y E, Z. H UANG , AND T. Z HANG , Stochastic recursive gradient descent ascent for stochastic nonconvex-strongly-concave minimax problems, Advances in Neural Information Processing Systems, 33 (2020), pp. 20566–20577

2020
[23]

M ADRY, A

A. M ADRY, A. M AKELOV , L. S CHMIDT , D. T SIPRAS , AND A. V LADU , Towardsdeep learning models resistant to adversarial attacks, arXiv preprint arXiv:1706.06083, (2017)

2017 arXiv
[24]

M ANCINO -BALL AND Y

G. M ANCINO -BALL AND Y. X U, Variance-reduced accelerated methods for decentralized stochastic double-regularized nonconvex strongly-concave minimax problems, arXiv preprint arXiv:2307.07113, (2023)

2023 arXiv
[25]

M CMAHAN , E

B. M CMAHAN , E. M OORE , D. R AMAGE , S. H AMPSON , AND B. A. Y ARCAS , Communication-efficient learning of deep networks from decentralized data, in Artificial intelligence and statistics, PMLR, 2017, pp. 1273– 1282

2017
[26]

N OUIEHED , M

M. N OUIEHED , M. S ANJABI , T. H UANG , J. D. L EE, AND M. R AZAVIYAYN , Solving a class of non-convex min-max games using iterative first order methods, Advances in Neural Information Processing Systems, 32 (2019)

2019
[27]

P U AND A

S. P U AND A. N EDI ´C, Distributed stochastic gradient tracking methods, Mathematical Programming, 187 (2021), pp. 409–457

2021
[28]

R EISIZADEH , F

A. R EISIZADEH , F. F ARNIA , R. P EDARSANI , AND A. J ADBABAIE , Robust federated learning: The case of affine distribution shifts, Advances in Neural Information Processing Systems, 33 (2020), pp. 21554–21565

2020
[29]

SHARMA , R

P. SHARMA , R. PANDA , G. J OSHI , AND P. VARSHNEY , Federated minimax optimization: Improved convergence analyses and algorithms, in International Conference on Machine Learning, PMLR, 2022, pp. 19683–19730

2022
[30]

SHEN , M

W. SHEN , M. H UANG , J. Z HANG , AND C. S HEN, Stochastic smoothed gradient descent ascent for federated minimax optimization, arXiv preprint arXiv:2311.00944, (2023). 16 Decentralized Min-Max Optimization with Gradient Tracking A PREPRINT

2023 arXiv
[31]

S INHA , H

A. S INHA , H. N AMKOONG , R. V OLPI , AND J. D UCHI , Certifying some distributional robustness with principled adversarial training, arXiv preprint arXiv:1710.10571, (2017)

2017 arXiv
[32]

T SAKNAKIS , M

I. T SAKNAKIS , M. H ONG , AND S. L IU, Decentralized min-max optimization: Formulations, algorithms and applications in network poisoning attack, in ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 2020, pp. 5755–5759

2020
[33]

T SAKNAKIS , M

I. T SAKNAKIS , M. H ONG , AND S. L IU, Decentralized min-max optimization: Formulations, algorithms and applications in network poisoning attack, in ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020, pp. 5755–5759, http...

2020
[34]

X. W U, J. S UN, Z. H U, A. Z HANG , AND H. H UANG , Solving a class of non-convex minimax optimization in federated learning, Advances in Neural Information Processing Systems, 36 (2024)

2024
[35]

XIAN , F

W. XIAN , F. H UANG , Y. Z HANG , AND H. H UANG , A faster decentralized algorithm for nonconvex minimax problems, Advances in Neural Information Processing Systems, 34 (2021), pp. 25865–25877

2021
[36]

J. X U, S. Z HU, Y. C. S OH, AND L. X IE, Augmented distributed gradient methods for multi-agent optimization under uncoordinated constant stepsizes, in 2015 54th IEEE Conference on Decision and Control (CDC), IEEE, 2015, pp. 2055–2060

2015
[37]

Y ANG , N

J. Y ANG , N. K IYAVASH, AND N. H E, Global convergence and variance reduction for a class of nonconvex-nonconcave minimax problems, Advances in Neural Information Processing Systems, 33 (2020), pp. 1153–1165

2020
[38]

Y ANG , A

J. Y ANG , A. O RVIETO , A. L UCCHI , AND N. H E, Faster single-loop algorithms for minimax optimization without strong concavity, in International Conference on Artificial Intelligence and Statistics, PMLR, 2022, pp. 5485–5517

2022
[39]

Z HANG , P

J. Z HANG , P. X IAO, R. S UN, AND Z. L UO, A single-loop smoothed gradient descent-ascent algorithm for nonconvex-concavemin-max problems, Advances in neural information processing systems, 33 (2020), pp. 7377– 7389

2020
[40]

Z HANG , J

S. Z HANG , J. YANG , C. G UZMÁN , N. K IYAVASH, AND N. H E, The complexity of nonconvex-strongly-concave minimax optimization, in Uncertainty in Artificial Intelligence, PMLR, 2021, pp. 482–492

2021
[41]

Z HANG , G

X. Z HANG , G. M ANCINO -BALL , N. S. A YBAT, AND Y. XU, Jointly improving the sample and communication complexities in decentralized stochastic minimax optimization, arXiv preprint arXiv:2307.09421, (2023). 17 Decentralized Min-Max Optimization with Gradient Tracking A PREPRI...

2023 arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

A RJOVSKY , S

M. A RJOVSKY , S. C HINTALA , AND L. B OTTOU , Wasserstein generative adversarial networks, in International conference on machine learning, PMLR, 2017, pp. 214–223

work page 2017

[2] [2]

B ECK, First-order methods in optimization, SIAM, 2017

A. B ECK, First-order methods in optimization, SIAM, 2017

2017

[3] [3]

B OTTOU , F

L. B OTTOU , F. E. C URTIS , AND J. N OCEDAL , Optimization methods for large-scale machine learning, SIAM review, 60 (2018), pp. 223–311

work page 2018

[4] [4]

C HEN , H

L. C HEN , H. Y E, AND L. L UO, An efficient stochastic algorithm for decentralized nonconvex-strongly-concave minimax optimization, in Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, S. Dasgupta, S. Mandt, and Y . Li, eds., vol. 238 of Proceedings of Machine Learning Research, PMLR, 02–04 May 2024, pp. 1990–199...

work page 2024

[5] [5]

C UTKOSKY AND F

A. C UTKOSKY AND F. ORABONA , Momentum-based variance reduction in non-convex sgd, Advances in neural information processing systems, 32 (2019)

work page 2019

[6] [6]

B. D AI, A. S HAW, L. L I, L. X IAO, N. H E, Z. L IU, J. C HEN , AND L. S ONG, Sbeed: Convergent reinforcement learning with nonlinear function approximation, in International Conference on Machine Learning, PMLR, 2018, pp. 1125–1134

work page 2018

[7] [7]

DI LORENZO AND G

P. DI LORENZO AND G. S CUTARI , Next: In-network nonconvex optimization, IEEE Transactions on Signal and Information Processing over Networks, 2 (2016), pp. 120–136

2016

[8] [8]

F ANG , C

C. F ANG , C. J. L I, Z. L IN, AND T. Z HANG , Spider: Near-optimal non-convex optimization via stochastic path-integrated differential estimator, Advances in Neural Information Processing Systems, 31 (2018)

work page 2018