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Feihu Huang

Publications and source records attributed to Feihu Huang.

At least 19 recordsLinked to original sources
arXiv2026

Efficient Hessian-Free Methods for Multi-Objective Bilevel Optimization with Nonconvex Lower Level

Multi-objective bilevel optimization has wide applications in the AI area such as automated learning and multi-task meta-learning. Although recently some works have been begun to study the multi-objective bilevel optimization, the proposed methods rely on the (strongly) convex lower level problems. In fact, these multi-objective bilevel learning problems are generally nonconvex, and particularly their lower level problems are nonconvex. To fill this gap, we propose a class of Multi-Objective Moreau Envelope based Hessian-free Algorithms (MOMEHA) for the multi-objective bilevel learning problems with nonconvex lower level. Specifically, our method uses the Moreau envelope to relax the original problem into a multi-objective single-level optimization with an envelope constraint. In particular, our method retains computational advantages of being single-loop and Hessian-free in the multi-objective setting by incorporating a smooth weighted Tchebycheff scalarization. Furthermore, we propose a momentum-based variant of MOMEHA (i.e., MB-MOMEHA) method for the stochastic multi-objective bilevel learning problems. In theory, we provide the convergence properties of our algorithms under both deterministic and stochastic setting. Some experiments on few-shot meta-learning and neural architecture search demonstrate that our methods outperform the existing approaches in Pareto front, validating its effectiveness and robustness.

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arXiv2026

Federated Compositional Muon Optimizer for Matrix-Wise Models

Muon, a more recently developed optimizer, is useful for matrix-wise models in AI areas. Although many works have studied Muon and its variants, these methods are still not particularly well-suited for hierarchical structured problems. To fill this gap, we propose an effective federated compositional Muon (FedCoMuon) optimizer to solve distributed matrix-wise compositional optimization problems. Specifically, our FedCoMuon optimizer builds on compositional gradient tracking and orthogonalized momentum. Moreover, we propose a variance reduced variant of FedCoMuon (FedCoMuon-VR) based on a momentum-based variance reduced technique. In theory, we analyze the convergence properties of our algorithms under the non-i.i.d. and non-convex settings. In particular, we prove that our FedCoMuon-VR obtains a lower sample complexity of $O(\epsilon^{-3})$ for finding an $\epsilon$-stationary solution than the existing FedMuon algorithms. Extensive numerical experiments on robust federated learning and task-distributed risk-sensitive meta learning show that our proposed methods are competitive with existing compositional baselines and achieve the best reported accuracy in several settings.

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arXiv2026

MiMuon: Mixed Muon Optimizer with Improved Generalization for Large Models

Matrix-structured parameters frequently appear in many artificial intelligence models such as large language models. More recently, an efficient Muon optimizer is designed for matrix parameters of large-scale models, and shows markedly faster convergence than the vector-wise algorithms. Although some works have begun to study convergence properties (i.e., optimization error) of the Muon optimizer, its generalization properties (i.e., generalization error) is still not established. Thus, in this paper, we study generalization error of the Muon optimizer based on algorithmic stability and mathematical induction, and prove that the Muon has a generalization error of $O\big(\frac{1}{N\kappa^{T}}\big)$, where $N$ is training sample size, and $T$ denotes iteration number, and $\kappa>0$ denotes minimum difference between singular values of gradient estimate. To enhance generalization of the Muon, we propose an effective mixed Muon (MiMuon) optimizer by cautiously using orthogonalization of gradient, which is a hybrid of Muon and momentum-based SGD optimizers. Then we prove that our MiMuon optimizer has a lower generalization error of $O\big(\frac{1}{N}\big)$ than $O\big(\frac{1}{N\kappa^{T}}\big)$ of Muon optimizer, since $\kappa$ generally is very small. Meanwhile, we also studied the convergence properties of our MiMuon algorithm, and prove that our MiMuon algorithm has the same convergence rate of $O(\frac{1}{T^{1/4}})$ as the Muon algorithm. Some numerical experimental results on training large models including Qwen3-0.6B and YOLO26m demonstrate efficiency of the MiMuon optimizer.

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arXiv2026

AdaBFL: Multi-Layer Defensive Adaptive Aggregation for Bzantine-Robust Federated Learning

Federated learning (FL) is a popular distributed learning paradigm in machine learning, which enables multiple clients to collaboratively train models under the guidance of a server without exposing private client data. However, FL's decentralized nature makes it vulnerable to poisoning attacks, where malicious clients can submit corrupted models to manipulate the system. To counter such attacks, although various Byzantine-robust methods have been proposed, these methods struggle to provide balanced defense against multiple types of attacks or rely on possessing the dataset in the server. To deal with these drawbacks, thus, we propose an effective multi-layer defensive adaptive aggregation for Bzantine-robust federated learning (AdaBFL) based on a novel three-layer defensive mechanism, which can adaptively adjust the weights of defense algorithms to counter complex attacks. Moreover, we provide convergence properties of our AdaBFL method under the non-convex setting on non-iid data. Comprehensive experiments across multiple datasets validate the superiority of our AdaBFL over the comparable algorithms.

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arXiv2026

CLion: Efficient Cautious Lion Optimizer with Enhanced Generalization

Lion optimizer is a popular learning-based optimization algorithm in machine learning, which shows impressive performance in training many deep learning models. Although convergence property of the Lion optimizer has been studied, its generalization analysis is still missing. To fill this gap, we study generalization property of the Lion via algorithmic stability based on the mathematical induction. Specifically, we prove that the Lion has a generalization error of $O(\frac{1}{N\tau^T})$, where $N$ is training sample size, and $\tau>0$ denotes the smallest absolute value of non-zero element in gradient estimator, and $T$ is the total iteration number. In addition, we obtain an interesting byproduct that the SignSGD algorithm has the same generalization error as the Lion. To enhance generalization of the Lion, we design a novel efficient Cautious Lion (i.e., CLion) optimizer by cautiously using sign function. Moreover, we prove that our CLion has a lower generalization error of $O(\frac{1}{N})$ than $O(\frac{1}{N\tau^T})$ of the Lion, since the parameter $\tau$ generally is very small. Meanwhile, we study convergence property of our CLion optimizer, and prove that our CLion has a fast convergence rate of $O(\frac{\sqrt{d}}{T^{1/4}})$ under $\ell_1$-norm of gradient for nonconvex stochastic optimization, where $d$ denotes the model dimension. Extensive numerical experiments demonstrate effectiveness of our CLion optimizer.

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arXiv2026

HomeAdam: Adam and AdamW Algorithms Sometimes Go Home to Obtain Better Provable Generalization

Adam and AdamW are a class of default optimizers for training deep learning models in machine learning. These adaptive algorithms converge faster but generalize worse compared to SGD. In fact, their proved generalization error $O(\frac{1}{\sqrt{N}})$ also is larger than $O(\frac{1}{N})$ of SGD, where $N$ denotes training sample size. Recently, although some variants of Adam have been proposed to improve its generalization, their improved generalizations are still unexplored in theory. To fill this gap, in the paper, we restudy generalization of Adam and AdamW via algorithmic stability, and first prove that Adam and AdamW without square-root (i.e., Adam(W)-srf) have a generalization error $O(\frac{\hat{\rho}^{-2T}}{N})$, where $T$ denotes iteration number and $\hat{\rho}>0$ denotes the smallest element of second-order momentum plus a small positive number. To improve generalization, we propose a class of efficient clever Adam (i.e., HomeAdam(W)) algorithms via sometimes returning momentum-based SGD. Moreover, we prove that our HomeAdam(W) have a smaller generalization error $O(\frac{1}{N})$ than $O(\frac{\hat{\rho}^{-2T}}{N})$ of Adam(W)-srf, since $\hat{\rho}$ is generally very small. In particular, it is also smaller than the existing $O(\frac{1}{\sqrt{N}})$ of Adam(W). Meanwhile, we prove our HomeAdam(W) have a faster convergence rate of $O(\frac{1}{T^{1/4}})$ than $O(\frac{\breve{\rho}^{-1}}{T^{1/4}})$ of the Adam(W)-srf, where $\breve{\rho}\leq\hat{\rho}$ also is very small. Extensive numerical experiments demonstrate efficiency of our HomeAdam(W) algorithms.

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arXiv2025

LiMuon: Light and Fast Muon Optimizer for Large Models

Large models recently are widely applied in machine learning, so efficient training of large models has received widespread attention. More recently, the useful Muon optimizer is specifically designed for matrix-structured parameters of large models. Although some works have begun to study the Muon optimizer, the existing Muon and its variants still suffer from high sample complexity or high memory for large models. To fill this gap, we propose a light and fast Muon (LiMuon) optimizer for training large models, which builds on the momentum-based variance reduced technique and randomized Singular Value Decomposition (SVD). In particular, our LiMuon simultaneously has a lower memory and lower sample complexity than the Muon and its variants. Moreover, we prove that our LiMuon with lower memory has a lower sample complexity of $O(\epsilon^{-3})$ for finding an $\epsilon$-stationary solution of non-convex stochastic optimization under the generalized smoothness condition. To further narrow practice and theory gap, we also prove that our LiMuon with Newton-Schulz steps has a lower sample complexity than the Muon with Newton-Schulz steps. Numerical experimental results on pre-training Mamba-130M, Qwen2.5-0.5B and ViT models demonstrate effectiveness of our LiMuon.

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arXiv2024

Faster Adaptive Decentralized Learning Algorithms

Decentralized learning recently has received increasing attention in machine learning due to its advantages in implementation simplicity and system robustness, data privacy. Meanwhile, the adaptive gradient methods show superior performances in many machine learning tasks such as training neural networks. Although some works focus on studying decentralized optimization algorithms with adaptive learning rates, these adaptive decentralized algorithms still suffer from high sample complexity. To fill these gaps, we propose a class of faster adaptive decentralized algorithms (i.e., AdaMDOS and AdaMDOF) for distributed nonconvex stochastic and finite-sum optimization, respectively. Moreover, we provide a solid convergence analysis framework for our methods. In particular, we prove that our AdaMDOS obtains a near-optimal sample complexity of $\tilde{O}(\epsilon^{-3})$ for finding an $\epsilon$-stationary solution of nonconvex stochastic optimization. Meanwhile, our AdaMDOF obtains a near-optimal sample complexity of $O(\sqrt{n}\epsilon^{-2})$ for finding an $\epsilon$-stationary solution of nonconvex finite-sum optimization, where $n$ denotes the sample size. To the best of our knowledge, our AdaMDOF algorithm is the first adaptive decentralized algorithm for nonconvex finite-sum optimization. Some experimental results demonstrate efficiency of our algorithms.

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arXiv2024

Optimal Hessian/Jacobian-Free Nonconvex-PL Bilevel Optimization

Bilevel optimization is widely applied in many machine learning tasks such as hyper-parameter learning, meta learning and reinforcement learning. Although many algorithms recently have been developed to solve the bilevel optimization problems, they generally rely on the (strongly) convex lower-level problems. More recently, some methods have been proposed to solve the nonconvex-PL bilevel optimization problems, where their upper-level problems are possibly nonconvex, and their lower-level problems are also possibly nonconvex while satisfying Polyak-{\L}ojasiewicz (PL) condition. However, these methods still have a high convergence complexity or a high computation complexity such as requiring compute expensive Hessian/Jacobian matrices and its inverses. In the paper, thus, we propose an efficient Hessian/Jacobian-free method (i.e., HJFBiO) with the optimal convergence complexity to solve the nonconvex-PL bilevel problems. Theoretically, under some mild conditions, we prove that our HJFBiO method obtains an optimal convergence rate of $O(\frac{1}{T})$, where $T$ denotes the number of iterations, and has an optimal gradient complexity of $O(\epsilon^{-1})$ in finding an $\epsilon$-stationary solution. We conduct some numerical experiments on the bilevel PL game and hyper-representation learning task to demonstrate efficiency of our proposed method.

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arXiv2024

Adaptive Federated Minimax Optimization with Lower Complexities

Federated learning is a popular distributed and privacy-preserving learning paradigm in machine learning. Recently, some federated learning algorithms have been proposed to solve the distributed minimax problems. However, these federated minimax algorithms still suffer from high gradient or communication complexity. Meanwhile, few algorithm focuses on using adaptive learning rate to accelerate these algorithms. To fill this gap, in the paper, we study a class of nonconvex minimax optimization, and propose an efficient adaptive federated minimax optimization algorithm (i.e., AdaFGDA) to solve these distributed minimax problems. Specifically, our AdaFGDA builds on the momentum-based variance reduced and local-SGD techniques, and it can flexibly incorporate various adaptive learning rates by using the unified adaptive matrices. Theoretically, we provide a solid convergence analysis framework for our AdaFGDA algorithm under non-i.i.d. setting. Moreover, we prove our AdaFGDA algorithm obtains a lower gradient (i.e., stochastic first-order oracle, SFO) complexity of $\tilde{O}(ε^{-3})$ with lower communication complexity of $\tilde{O}(ε^{-2})$ in finding $ε$-stationary point of the nonconvex minimax problems. Experimentally, we conduct some experiments on the deep AUC maximization and robust neural network training tasks to verify efficiency of our algorithms.

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arXiv2024

Communication-Efficient Federated Bilevel Optimization with Local and Global Lower Level Problems

Bilevel Optimization has witnessed notable progress recently with new emerging efficient algorithms. However, its application in the Federated Learning setting remains relatively underexplored, and the impact of Federated Learning's inherent challenges on the convergence of bilevel algorithms remain obscure. In this work, we investigate Federated Bilevel Optimization problems and propose a communication-efficient algorithm, named FedBiOAcc. The algorithm leverages an efficient estimation of the hyper-gradient in the distributed setting and utilizes the momentum-based variance-reduction acceleration. Remarkably, FedBiOAcc achieves a communication complexity $O(ε^{-1})$, a sample complexity $O(ε^{-1.5})$ and the linear speed up with respect to the number of clients. We also analyze a special case of the Federated Bilevel Optimization problems, where lower level problems are locally managed by clients. We prove that FedBiOAcc-Local, a modified version of FedBiOAcc, converges at the same rate for this type of problems. Finally, we validate the proposed algorithms through two real-world tasks: Federated Data-cleaning and Federated Hyper-representation Learning. Empirical results show superior performance of our algorithms.

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arXiv2023

Nonconvex Zeroth-Order Stochastic ADMM Methods with Lower Function Query Complexity

Zeroth-order (a.k.a, derivative-free) methods are a class of effective optimization methods for solving complex machine learning problems, where gradients of the objective functions are not available or computationally prohibitive. Recently, although many zeroth-order methods have been developed, these approaches still have two main drawbacks: 1) high function query complexity; 2) not being well suitable for solving the problems with complex penalties and constraints. To address these challenging drawbacks, in this paper, we propose a class of faster zeroth-order stochastic alternating direction method of multipliers (ADMM) methods (ZO-SPIDER-ADMM) to solve the nonconvex finite-sum problems with multiple nonsmooth penalties. Moreover, we prove that the ZO-SPIDER-ADMM methods can achieve a lower function query complexity of $O(nd+dn^{\frac{1}{2}}ε^{-1})$ for finding an $ε$-stationary point, which improves the existing best nonconvex zeroth-order ADMM methods by a factor of $O(d^{\frac{1}{3}}n^{\frac{1}{6}})$, where $n$ and $d$ denote the sample size and data dimension, respectively. At the same time, we propose a class of faster zeroth-order online ADMM methods (ZOO-ADMM+) to solve the nonconvex online problems with multiple nonsmooth penalties. We also prove that the proposed ZOO-ADMM+ methods achieve a lower function query complexity of $O(dε^{-\frac{3}{2}})$, which improves the existing best result by a factor of $O(ε^{-\frac{1}{2}})$. Extensive experimental results on the structure adversarial attack on black-box deep neural networks demonstrate the efficiency of our new algorithms.

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arXiv2023

On Momentum-Based Gradient Methods for Bilevel Optimization with Nonconvex Lower-Level

Bilevel optimization is a popular two-level hierarchical optimization, which has been widely applied to many machine learning tasks such as hyperparameter learning, meta learning and continual learning. Although many bilevel optimization methods recently have been developed, the bilevel methods are not well studied when the lower-level problem is nonconvex. To fill this gap, in the paper, we study a class of nonconvex bilevel optimization problems, where both upper-level and lower-level problems are nonconvex, and the lower-level problem satisfies Polyak-Łojasiewicz (PL) condition. We propose an efficient momentum-based gradient bilevel method (MGBiO) to solve these deterministic problems. Meanwhile, we propose a class of efficient momentum-based stochastic gradient bilevel methods (MSGBiO and VR-MSGBiO) to solve these stochastic problems. Moreover, we provide a useful convergence analysis framework for our methods. Specifically, under some mild conditions, we prove that our MGBiO method has a sample (or gradient) complexity of $O(ε^{-2})$ for finding an $ε$-stationary solution of the deterministic bilevel problems (i.e., $\|\nabla F(x)\|\leq ε$), which improves the existing best results by a factor of $O(ε^{-1})$. Meanwhile, we prove that our MSGBiO and VR-MSGBiO methods have sample complexities of $\tilde{O}(ε^{-4})$ and $\tilde{O}(ε^{-3})$, respectively, in finding an $ε$-stationary solution of the stochastic bilevel problems (i.e., $\mathbb{E}\|\nabla F(x)\|\leq ε$), which improves the existing best results by a factor of $\tilde{O}(ε^{-3})$. Extensive experimental results on bilevel PL game and hyper-representation learning demonstrate the efficiency of our algorithms. This paper commemorates the mathematician Boris Polyak (1935 -2023).

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arXiv2023

Adaptive Mirror Descent Bilevel Optimization

In the paper, we propose a class of efficient adaptive bilevel methods based on mirror descent for nonconvex bilevel optimization, where its upper-level problem is nonconvex possibly with nonsmooth regularization, and its lower-level problem is also nonconvex while satisfies Polyak-Łojasiewicz (PL) condition. To solve these deterministic bilevel problems, we present an efficient adaptive projection-aid gradient (i.e., AdaPAG) method based on mirror descent, and prove that it obtains the best known gradient complexity of $O(ε^{-1})$ for finding an $ε$-stationary solution of nonconvex bilevel problems. To solve these stochastic bilevel problems, we propose an efficient adaptive stochastic projection-aid gradient (i.e., AdaVSPAG) methods based on mirror descent and variance-reduced techniques, and prove that it obtains the best known gradient complexity of $O(ε^{-3/2})$ for finding an $ε$-stationary solution. Since the PL condition relaxes the strongly convex, our algorithms can be used to nonconvex strongly-convex bilevel optimization. Theoretically, we provide a useful convergence analysis framework for our methods under some mild conditions, and prove that our methods have a fast convergence rate of $O(\frac{1}{T})$, where $T$ denotes the number of iterations.

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arXiv2023

Compositional federated learning: Applications in distributionally robust averaging and meta learning

In the paper, we propose an effective and efficient Compositional Federated Learning (ComFedL) algorithm for solving a new compositional Federated Learning (FL) framework, which frequently appears in many data mining and machine learning problems with a hierarchical structure such as distributionally robust FL and model-agnostic meta learning (MAML). Moreover, we study the convergence analysis of our ComFedL algorithm under some mild conditions, and prove that it achieves a convergence rate of $O(\frac{1}{\sqrt{T}})$, where $T$ denotes the number of iteration. To the best of our knowledge, our new Compositional FL framework is the first work to bridge federated learning with composition stochastic optimization. In particular, we first transform the distributionally robust FL (i.e., a minimax optimization problem) into a simple composition optimization problem by using KL divergence regularization. At the same time, we also first transform the distribution-agnostic MAML problem (i.e., a minimax optimization problem) into a simple yet effective composition optimization problem. Finally, we apply two popular machine learning tasks, i.e., distributionally robust FL and MAML to demonstrate the effectiveness of our algorithm.

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arXiv2023

Near-Optimal Decentralized Momentum Method for Nonconvex-PL Minimax Problems

Minimax optimization plays an important role in many machine learning tasks such as generative adversarial networks (GANs) and adversarial training. Although recently a wide variety of optimization methods have been proposed to solve the minimax problems, most of them ignore the distributed setting where the data is distributed on multiple workers. Meanwhile, the existing decentralized minimax optimization methods rely on the strictly assumptions such as (strongly) concavity and variational inequality conditions. In the paper, thus, we propose an efficient decentralized momentum-based gradient descent ascent (DM-GDA) method for the distributed nonconvex-PL minimax optimization, which is nonconvex in primal variable and is nonconcave in dual variable and satisfies the Polyak-Lojasiewicz (PL) condition. In particular, our DM-GDA method simultaneously uses the momentum-based techniques to update variables and estimate the stochastic gradients. Moreover, we provide a solid convergence analysis for our DM-GDA method, and prove that it obtains a near-optimal gradient complexity of $O(ε^{-3})$ for finding an $ε$-stationary solution of the nonconvex-PL stochastic minimax problems, which reaches the lower bound of nonconvex stochastic optimization. To the best of our knowledge, we first study the decentralized algorithm for Nonconvex-PL stochastic minimax optimization over a network.

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arXiv2023

Faster Adaptive Momentum-Based Federated Methods for Distributed Composition Optimization

Federated Learning is a popular distributed learning paradigm in machine learning. Meanwhile, composition optimization is an effective hierarchical learning model, which appears in many machine learning applications such as meta learning and robust learning. More recently, although a few federated composition optimization algorithms have been proposed, they still suffer from high sample and communication complexities. In the paper, thus, we propose a class of faster federated compositional optimization algorithms (i.e., MFCGD and AdaMFCGD) to solve the nonconvex distributed composition problems, which builds on the momentum-based variance reduced and local-SGD techniques. In particular, our adaptive algorithm (i.e., AdaMFCGD) uses a unified adaptive matrix to flexibly incorporate various adaptive learning rates. Moreover, we provide a solid theoretical analysis for our algorithms under non-i.i.d. setting, and prove our algorithms obtain a lower sample and communication complexities simultaneously than the existing federated compositional algorithms. Specifically, our algorithms obtain lower sample complexity of $\tilde{O}(ε^{-3})$ with lower communication complexity of $\tilde{O}(ε^{-2})$ in finding an $ε$-stationary solution. We conduct the numerical experiments on robust federated learning and distributed meta learning tasks to demonstrate the efficiency of our algorithms.

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arXiv2023

Faster Adaptive Federated Learning

Federated learning has attracted increasing attention with the emergence of distributed data. While extensive federated learning algorithms have been proposed for the non-convex distributed problem, federated learning in practice still faces numerous challenges, such as the large training iterations to converge since the sizes of models and datasets keep increasing, and the lack of adaptivity by SGD-based model updates. Meanwhile, the study of adaptive methods in federated learning is scarce and existing works either lack a complete theoretical convergence guarantee or have slow sample complexity. In this paper, we propose an efficient adaptive algorithm (i.e., FAFED) based on the momentum-based variance-reduced technique in cross-silo FL. We first explore how to design the adaptive algorithm in the FL setting. By providing a counter-example, we prove that a simple combination of FL and adaptive methods could lead to divergence. More importantly, we provide a convergence analysis for our method and prove that our algorithm is the first adaptive FL algorithm to reach the best-known samples $O(ε^{-3})$ and $O(ε^{-2})$ communication rounds to find an $ε$-stationary point without large batches. The experimental results on the language modeling task and image classification task with heterogeneous data demonstrate the efficiency of our algorithms.

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