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Weixin An

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4 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Tight High-Probability Bounds for Nonconvex Heavy-Tailed Scenario under Weaker Assumptions

Weixin An
Yuanyuan Liu
Fanhua Shang
Han Yu
Junkang Liu
Hongying Liu

Gradient clipping is increasingly important in centralized learning (CL) and federated learning (FL). Many works focus on its optimization properties under strong assumptions involving Gaussian noise and standard smoothness. However, practical machine learning tasks often only satisfy weaker conditions, such as heavy-tailed noise and $(L_0, L_1)$-smoothness. To bridge this gap, we propose a high-probability analysis for clipped Stochastic Gradient Descent (SGD) under these weaker assumptions. Our findings show a better convergence rate than existing ones can be achieved, and our high-probability analysis does not rely on the bounded gradient assumption. Moreover, we extend our analysis to FL, where a gap remains between expected and high-probability convergence, which the naive clipped SGD cannot bridge. Thus, we design a new \underline{Fed}erated \underline{C}lipped \underline{B}atched \underline{G}radient (FedCBG) algorithm, and prove the convergence and generalization bounds with high probability for the first time. Our analysis reveals the trade-offs between the optimization and generalization performance. Extensive experiments demonstrate that \methodname{} can generalize better to unseen client distributions than state-of-the-art baselines.

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NeurIPS Conference 2024 Conference Paper

Robust and Faster Zeroth-Order Minimax Optimization: Complexity and Applications

Weixin An
Yuanyuan Liu
Fanhua Shang
Hongying Liu

Many zeroth-order (ZO) optimization algorithms have been developed to solve nonconvex minimax problems in machine learning and computer vision areas. However, existing ZO minimax algorithms have high complexity and rely on some strict restrictive conditions for ZO estimations. To address these issues, we design a new unified ZO gradient descent extragradient ascent (ZO-GDEGA) algorithm, which reduces the overall complexity to $\mathcal{O}(d\epsilon^{-6})$ to find an $\epsilon$-stationary point of the function $\psi$ for nonconvex-concave (NC-C) problems, where $d$ is the variable dimension. To the best of our knowledge, ZO-GDEGA is the first ZO algorithm with complexity guarantees to solve stochastic NC-C problems. Moreover, ZO-GDEGA requires weaker conditions on the ZO estimations and achieves more robust theoretical results. As a by-product, ZO-GDEGA has advantages on the condition number for the NC-strongly concave case. Experimentally, ZO-GDEGA can generate more effective poisoning attack data with an average accuracy reduction of 5\%. The improved AUC performance also verifies the robustness of gradient estimations.

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NeurIPS Conference 2023 Conference Paper

A Single-Loop Accelerated Extra-Gradient Difference Algorithm with Improved Complexity Bounds for Constrained Minimax Optimization

Yuanyuan Liu
Fanhua Shang
Weixin An
Junhao Liu
Hongying Liu
Zhouchen Lin

In this paper, we propose a novel extra-gradient difference acceleration algorithm for solving constrained nonconvex-nonconcave (NC-NC) minimax problems. In particular, we design a new extra-gradient difference step to obtain an important quasi-cocoercivity property, which plays a key role to significantly improve the convergence rate in the constrained NC-NC setting without additional structural assumption. Then momentum acceleration is also introduced into our dual accelerating update step. Moreover, we prove that, to find an $\epsilon$-stationary point of the function $f$, our algorithm attains the complexity $\mathcal{O}(\epsilon^{-2})$ in the constrained NC-NC setting, while the best-known complexity bound is $\widetilde{\mathcal{O}}(\epsilon^{-4})$, where $\widetilde{\mathcal{O}}(\cdot)$ hides logarithmic factors compared to $\mathcal{O}(\cdot)$. As the special cases of the constrained NC-NC setting, our algorithm can also obtain the same complexity $\mathcal{O}(\epsilon^{-2})$ for both the nonconvex-concave (NC-C) and convex-nonconcave (C-NC) cases, while the best-known complexity bounds are $\widetilde{\mathcal{O}}(\epsilon^{-2. 5})$ for the NC-C case and $\widetilde{\mathcal{O}}(\epsilon^{-4})$ for the C-NC case. For fair comparison with existing algorithms, we also analyze the complexity bound to find $\epsilon$-stationary point of the primal function $\phi$ for the constrained NC-C problem, which shows that our algorithm can improve the complexity bound from $\widetilde{\mathcal{O}}(\epsilon^{-3})$ to $\mathcal{O}(\epsilon^{-2})$. To the best of our knowledge, this is the first time that the proposed algorithm improves the best-known complexity bounds from $\mathcal{O}(\epsilon^{-4})$ and $\widetilde{\mathcal{O}}(\epsilon^{-3})$ to $\mathcal{O}(\epsilon^{-2})$ in both the NC-NC and NC-C settings.

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ICML Conference 2022 Conference Paper

Kill a Bird with Two Stones: Closing the Convergence Gaps in Non-Strongly Convex Optimization by Directly Accelerated SVRG with Double Compensation and Snapshots

Yuanyuan Liu 0001
Fanhua Shang
Weixin An
Hongying Liu 0001
Zhouchen Lin

Recently, some accelerated stochastic variance reduction algorithms such as Katyusha and ASVRG-ADMM achieve faster convergence than non-accelerated methods such as SVRG and SVRG-ADMM. However, there are still some gaps between the oracle complexities and their lower bounds. To fill in these gaps, this paper proposes a novel Directly Accelerated stochastic Variance reductIon (DAVIS) algorithm with two Snapshots for non-strongly convex (non-SC) unconstrained problems. Our theoretical results show that DAVIS achieves the optimal convergence rate O(1/(nS^2)) and optimal gradient complexity O(n+\sqrt{nL/\epsilon}), which is identical to its lower bound. To the best of our knowledge, this is the first directly accelerated algorithm that attains the optimal lower bound and improves the convergence rate from O(1/S^2) to O(1/(nS^2)). Moreover, we extend DAVIS and theoretical results to non-SC problems with a structured regularizer, and prove that the proposed algorithm with double-snapshots also attains the optimal convergence rate O(1/(nS)) and optimal oracle complexity O(n+L/\epsilon) for such problems, and it is at least a factor n/S faster than existing accelerated stochastic algorithms, where n\gg S in general.

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