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Feihu Huang

Publications and source records attributed to Feihu Huang.

At least 37 records · Page 2Linked to original sources
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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arXiv2023

AdaGDA: Faster Adaptive Gradient Descent Ascent Methods for Minimax Optimization

In the paper, we propose a class of faster adaptive Gradient Descent Ascent (GDA) methods for solving the nonconvex-strongly-concave minimax problems by using the unified adaptive matrices, which include almost all existing coordinate-wise and global adaptive learning rates. In particular, we provide an effective convergence analysis framework for our adaptive GDA methods. Specifically, we propose a fast Adaptive Gradient Descent Ascent (AdaGDA) method based on the basic momentum technique, which reaches a lower gradient complexity of $\tilde{O}(κ^4ε^{-4})$ for finding an $ε$-stationary point without large batches, which improves the existing results of the adaptive GDA methods by a factor of $O(\sqrtκ)$. Moreover, we propose an accelerated version of AdaGDA (VR-AdaGDA) method based on the momentum-based variance reduced technique, which achieves a lower gradient complexity of $\tilde{O}(κ^{4.5}ε^{-3})$ for finding an $ε$-stationary point without large batches, which improves the existing results of the adaptive GDA methods by a factor of $O(ε^{-1})$. Moreover, we prove that our VR-AdaGDA method can reach the best known gradient complexity of $\tilde{O}(κ^{3}ε^{-3})$ with the mini-batch size $O(κ^3)$. The experiments on policy evaluation and fair classifier learning tasks are conducted to verify the efficiency of our new algorithms.

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arXiv2023

Dateformer: Time-modeling Transformer for Longer-term Series Forecasting

Transformers have demonstrated impressive strength in long-term series forecasting. Existing prediction research mostly focused on mapping past short sub-series (lookback window) to future series (forecast window). The longer training dataset time series will be discarded, once training is completed. Models can merely rely on lookback window information for inference, which impedes models from analyzing time series from a global perspective. And these windows used by Transformers are quite narrow because they must model each time-step therein. Under this point-wise processing style, broadening windows will rapidly exhaust their model capacity. This, for fine-grained time series, leads to a bottleneck in information input and prediction output, which is mortal to long-term series forecasting. To overcome the barrier, we propose a brand-new methodology to utilize Transformer for time series forecasting. Specifically, we split time series into patches by day and reform point-wise to patch-wise processing, which considerably enhances the information input and output of Transformers. To further help models leverage the whole training set's global information during inference, we distill the information, store it in time representations, and replace series with time representations as the main modeling entities. Our designed time-modeling Transformer -- Dateformer yields state-of-the-art accuracy on 7 real-world datasets with a 33.6\% relative improvement and extends the maximum forecast range to half-year.

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arXiv2023

BiAdam: Fast Adaptive Bilevel Optimization Methods

Bilevel optimization recently has attracted increased interest in machine learning due to its many applications such as hyper-parameter optimization and meta learning. Although many bilevel methods recently have been proposed, these methods do not consider using adaptive learning rates. It is well known that adaptive learning rates can accelerate optimization algorithms. To fill this gap, in the paper, we propose a novel fast adaptive bilevel framework to solve stochastic bilevel optimization problems that the outer problem is possibly nonconvex and the inner problem is strongly convex. Our framework uses unified adaptive matrices including many types of adaptive learning rates, and can flexibly use the momentum and variance reduced techniques. In particular, we provide a useful convergence analysis framework for the bilevel optimization. Specifically, we propose a fast single-loop adaptive bilevel optimization (BiAdam) algorithm, which achieves a sample complexity of $\tilde{O}(ε^{-4})$ for finding an $ε$-stationary solution. Meanwhile, we propose an accelerated version of BiAdam algorithm (VR-BiAdam), which reaches the best known sample complexity of $\tilde{O}(ε^{-3})$. To the best of our knowledge, we first study the adaptive bilevel optimization methods with adaptive learning rates. Experimental results on data hyper-cleaning and hyper-representation learning tasks demonstrate the efficiency of our algorithms.

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arXiv2023

FedDA: Faster Framework of Local Adaptive Gradient Methods via Restarted Dual Averaging

Federated learning (FL) is an emerging learning paradigm to tackle massively distributed data. In Federated Learning, a set of clients jointly perform a machine learning task under the coordination of a server. The FedAvg algorithm is one of the most widely used methods to solve Federated Learning problems. In FedAvg, the learning rate is a constant rather than changing adaptively. The adaptive gradient methods show superior performance over the constant learning rate schedule; however, there is still no general framework to incorporate adaptive gradient methods into the federated setting. In this paper, we propose \textbf{FedDA}, a novel framework for local adaptive gradient methods. The framework adopts a restarted dual averaging technique and is flexible with various gradient estimation methods and adaptive learning rate formulations. In particular, we analyze \textbf{FedDA-MVR}, an instantiation of our framework, and show that it achieves gradient complexity $\tilde{O}(ε^{-1.5})$ and communication complexity $\tilde{O}(ε^{-1})$ for finding a stationary point $ε$. This matches the best known rate for first-order FL algorithms and \textbf{FedDA-MVR} is the first adaptive FL algorithm that achieves this rate. We also perform extensive numerical experiments to verify the efficacy of our method.

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arXiv2023

Gradient Descent Ascent for Minimax Problems on Riemannian Manifolds

In the paper, we study a class of useful minimax problems on Riemanian manifolds and propose a class of effective Riemanian gradient-based methods to solve these minimax problems. Specifically, we propose an effective Riemannian gradient descent ascent (RGDA) algorithm for the deterministic minimax optimization. Moreover, we prove that our RGDA has a sample complexity of $O(κ^2ε^{-2})$ for finding an $ε$-stationary solution of the Geodesically-Nonconvex Strongly-Concave (GNSC) minimax problems, where $κ$ denotes the condition number. At the same time, we present an effective Riemannian stochastic gradient descent ascent (RSGDA) algorithm for the stochastic minimax optimization, which has a sample complexity of $O(κ^4ε^{-4})$ for finding an $ε$-stationary solution. To further reduce the sample complexity, we propose an accelerated Riemannian stochastic gradient descent ascent (Acc-RSGDA) algorithm based on the momentum-based variance-reduced technique. We prove that our Acc-RSGDA algorithm achieves a lower sample complexity of $\tilde{O}(κ^{4}ε^{-3})$ in searching for an $ε$-stationary solution of the GNSC minimax problems. Extensive experimental results on the robust distributional optimization and robust Deep Neural Networks (DNNs) training over Stiefel manifold demonstrate efficiency of our algorithms.

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arXiv2022

Fast Adaptive Federated Bilevel Optimization

Bilevel optimization is a popular hierarchical model in machine learning, and has been widely applied to many machine learning tasks such as meta learning, hyperparameter learning and policy optimization. Although many bilevel optimization algorithms recently have been developed, few adaptive algorithm focuses on the bilevel optimization under the distributed setting. It is well known that the adaptive gradient methods show superior performances on both distributed and non-distributed optimization. In the paper, thus, we propose a novel adaptive federated bilevel optimization algorithm (i.e.,AdaFBiO) to solve the distributed bilevel optimization problems, where the objective function of Upper-Level (UL) problem is possibly nonconvex, and that of Lower-Level (LL) problem is strongly convex. Specifically, our AdaFBiO algorithm builds on the momentum-based variance reduced technique and local-SGD to obtain the best known sample and communication complexities simultaneously. In particular, our AdaFBiO algorithm uses the unified adaptive matrices to flexibly incorporate various adaptive learning rates to update variables in both UL and LL problems. Moreover, we provide a convergence analysis framework for our AdaFBiO algorithm, and prove it needs the sample complexity of $\tilde{O}(ε^{-3})$ with communication complexity of $\tilde{O}(ε^{-2})$ to obtain an $ε$-stationary point. Experimental results on federated hyper-representation learning and federated data hyper-cleaning tasks verify efficiency of our algorithm.

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arXiv2022

Enhanced Bilevel Optimization via Bregman Distance

Bilevel optimization has been recently used in many machine learning problems such as hyperparameter optimization, policy optimization, and meta learning. Although many bilevel optimization methods have been proposed, they still suffer from the high computational complexities and do not consider the more general bilevel problems with nonsmooth regularization. In the paper, thus, we propose a class of enhanced bilevel optimization methods with using Bregman distance to solve bilevel optimization problems, where the outer subproblem is nonconvex and possibly nonsmooth, and the inner subproblem is strongly convex. Specifically, we propose a bilevel optimization method based on Bregman distance (BiO-BreD) to solve deterministic bilevel problems, which achieves a lower computational complexity than the best known results. Meanwhile, we also propose a stochastic bilevel optimization method (SBiO-BreD) to solve stochastic bilevel problems based on stochastic approximated gradients and Bregman distance. Moreover, we further propose an accelerated version of SBiO-BreD method (ASBiO-BreD) using the variance-reduced technique, which can achieve a lower computational complexity than the best known computational complexities with respect to condition number $κ$ and target accuracy $ε$ for finding an $ε$-stationary point. We conduct data hyper-cleaning task and hyper-representation learning task to demonstrate that our new algorithms outperform related bilevel optimization approaches.

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arXiv2022

Communication-Efficient Adam-Type Algorithms for Distributed Data Mining

Distributed data mining is an emerging research topic to effectively and efficiently address hard data mining tasks using big data, which are partitioned and computed on different worker nodes, instead of one centralized server. Nevertheless, distributed learning methods often suffer from the communication bottleneck when the network bandwidth is limited or the size of model is large. To solve this critical issue, many gradient compression methods have been proposed recently to reduce the communication cost for multiple optimization algorithms. However, the current applications of gradient compression to adaptive gradient method, which is widely adopted because of its excellent performance to train DNNs, do not achieve the same ideal compression rate or convergence rate as Sketched-SGD. To address this limitation, in this paper, we propose a class of novel distributed Adam-type algorithms (\emph{i.e.}, SketchedAMSGrad) utilizing sketching, which is a promising compression technique that reduces the communication cost from $O(d)$ to $O(\log(d))$ where $d$ is the parameter dimension. In our theoretical analysis, we prove that our new algorithm achieves a fast convergence rate of $O(\frac{1}{\sqrt{nT}} + \frac{1}{(k/d)^2 T})$ with the communication cost of $O(k \log(d))$ at each iteration. Compared with single-machine AMSGrad, our algorithm can achieve the linear speedup with respect to the number of workers $n$. The experimental results on training various DNNs in distributed paradigm validate the efficiency of our algorithms.

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arXiv2022

SUPER-ADAM: Faster and Universal Framework of Adaptive Gradients

Adaptive gradient methods have shown excellent performances for solving many machine learning problems. Although multiple adaptive gradient methods were recently studied, they mainly focus on either empirical or theoretical aspects and also only work for specific problems by using some specific adaptive learning rates. Thus, it is desired to design a universal framework for practical algorithms of adaptive gradients with theoretical guarantee to solve general problems. To fill this gap, we propose a faster and universal framework of adaptive gradients (i.e., SUPER-ADAM) by introducing a universal adaptive matrix that includes most existing adaptive gradient forms. Moreover, our framework can flexibly integrate the momentum and variance reduced techniques. In particular, our novel framework provides the convergence analysis support for adaptive gradient methods under the nonconvex setting. In theoretical analysis, we prove that our SUPER-ADAM algorithm can achieve the best known gradient (i.e., stochastic first-order oracle (SFO)) complexity of $\tilde{O}(ε^{-3})$ for finding an $ε$-stationary point of nonconvex optimization, which matches the lower bound for stochastic smooth nonconvex optimization. In numerical experiments, we employ various deep learning tasks to validate that our algorithm consistently outperforms the existing adaptive algorithms. Code is available at https://github.com/LIJUNYI95/SuperAdam

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arXiv2022

Local Stochastic Bilevel Optimization with Momentum-Based Variance Reduction

Bilevel Optimization has witnessed notable progress recently with new emerging efficient algorithms and has been applied to many machine learning tasks such as data cleaning, few-shot learning, and neural architecture search. However, little attention has been paid to solve the bilevel problems under distributed setting. Federated learning (FL) is an emerging paradigm which solves machine learning tasks over distributed-located data. FL problems are challenging to solve due to the heterogeneity and communication bottleneck. However, it is unclear how these challenges will affect the convergence of Bilevel Optimization algorithms. In this paper, we study Federated Bilevel Optimization problems. Specifically, we first propose the FedBiO, a deterministic gradient-based algorithm and we show it requires $O(ε^{-2})$ number of iterations to reach an $ε$-stationary point. Then we propose FedBiOAcc to accelerate FedBiO with the momentum-based variance-reduction technique under the stochastic scenario. We show FedBiOAcc has complexity of $O(ε^{-1.5})$. Finally, we validate our proposed algorithms via the important Fair Federated Learning task. More specifically, we define a bilevel-based group fair FL objective. Our algorithms show superior performances compared to other baselines in numerical experiments.

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arXiv2022

Bregman Gradient Policy Optimization

In the paper, we design a novel Bregman gradient policy optimization framework for reinforcement learning based on Bregman divergences and momentum techniques. Specifically, we propose a Bregman gradient policy optimization (BGPO) algorithm based on the basic momentum technique and mirror descent iteration. Meanwhile, we further propose an accelerated Bregman gradient policy optimization (VR-BGPO) algorithm based on the variance reduced technique. Moreover, we provide a convergence analysis framework for our Bregman gradient policy optimization under the nonconvex setting. We prove that our BGPO achieves a sample complexity of $O(ε^{-4})$ for finding $ε$-stationary policy only requiring one trajectory at each iteration, and our VR-BGPO reaches the best known sample complexity of $O(ε^{-3})$, which also only requires one trajectory at each iteration. In particular, by using different Bregman divergences, our BGPO framework unifies many existing policy optimization algorithms such as the existing (variance reduced) policy gradient algorithms such as natural policy gradient algorithm. Extensive experimental results on multiple reinforcement learning tasks demonstrate the efficiency of our new algorithms.

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arXiv2022

Accelerated Zeroth-Order and First-Order Momentum Methods from Mini to Minimax Optimization

In the paper, we propose a class of accelerated zeroth-order and first-order momentum methods for both nonconvex mini-optimization and minimax-optimization. Specifically, we propose a new accelerated zeroth-order momentum (Acc-ZOM) method for black-box mini-optimization where only function values can be obtained. Moreover, we prove that our Acc-ZOM method achieves a lower query complexity of $\tilde{O}(d^{3/4}ε^{-3})$ for finding an $ε$-stationary point, which improves the best known result by a factor of $O(d^{1/4})$ where $d$ denotes the variable dimension. In particular, our Acc-ZOM does not need large batches required in the existing zeroth-order stochastic algorithms. Meanwhile, we propose an accelerated zeroth-order momentum descent ascent (Acc-ZOMDA) method for black-box minimax optimization, where only function values can be obtained. Our Acc-ZOMDA obtains a low query complexity of $\tilde{O}((d_1+d_2)^{3/4}κ_y^{4.5}ε^{-3})$ without requiring large batches for finding an $ε$-stationary point, where $d_1$ and $d_2$ denote variable dimensions and $κ_y$ is condition number. Moreover, we propose an accelerated first-order momentum descent ascent (Acc-MDA) method for minimax optimization, whose explicit gradients are accessible. Our Acc-MDA achieves a low gradient complexity of $\tilde{O}(κ_y^{4.5}ε^{-3})$ without requiring large batches for finding an $ε$-stationary point. In particular, our Acc-MDA can obtain a lower gradient complexity of $\tilde{O}(κ_y^{2.5}ε^{-3})$ with a batch size $O(κ_y^4)$, which improves the best known result by a factor of $O(κ_y^{1/2})$. Extensive experimental results on black-box adversarial attack to deep neural networks and poisoning attack to logistic regression demonstrate efficiency of our algorithms.

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arXiv2021

Faster Stochastic Quasi-Newton Methods

Stochastic optimization methods have become a class of popular optimization tools in machine learning. Especially, stochastic gradient descent (SGD) has been widely used for machine learning problems such as training neural networks due to low per-iteration computational complexity. In fact, the Newton or quasi-newton methods leveraging second-order information are able to achieve a better solution than the first-order methods. Thus, stochastic quasi-Newton (SQN) methods have been developed to achieve the better solution efficiently than the stochastic first-order methods by utilizing approximate second-order information. However, the existing SQN methods still do not reach the best known stochastic first-order oracle (SFO) complexity. To fill this gap, we propose a novel faster stochastic quasi-Newton method (SpiderSQN) based on the variance reduced technique of SIPDER. We prove that our SpiderSQN method reaches the best known SFO complexity of $\mathcal{O}(n+n^{1/2}ε^{-2})$ in the finite-sum setting to obtain an $ε$-first-order stationary point. To further improve its practical performance, we incorporate SpiderSQN with different momentum schemes. Moreover, the proposed algorithms are generalized to the online setting, and the corresponding SFO complexity of $\mathcal{O}(ε^{-3})$ is developed, which also matches the existing best result. Extensive experiments on benchmark datasets demonstrate that our new algorithms outperform state-of-the-art approaches for nonconvex optimization.

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arXiv2021

A New Framework for Variance-Reduced Hamiltonian Monte Carlo

We propose a new framework of variance-reduced Hamiltonian Monte Carlo (HMC) methods for sampling from an $L$-smooth and $m$-strongly log-concave distribution, based on a unified formulation of biased and unbiased variance reduction methods. We study the convergence properties for HMC with gradient estimators which satisfy the Mean-Squared-Error-Bias (MSEB) property. We show that the unbiased gradient estimators, including SAGA and SVRG, based HMC methods achieve highest gradient efficiency with small batch size under high precision regime, and require $\tilde{O}(N + κ^2 d^{\frac{1}{2}} \varepsilon^{-1} + N^{\frac{2}{3}} κ^{\frac{4}{3}} d^{\frac{1}{3}} \varepsilon^{-\frac{2}{3}} )$ gradient complexity to achieve $ε$-accuracy in 2-Wasserstein distance. Moreover, our HMC methods with biased gradient estimators, such as SARAH and SARGE, require $\tilde{O}(N+\sqrt{N} κ^2 d^{\frac{1}{2}} \varepsilon^{-1})$ gradient complexity, which has the same dependency on condition number $κ$ and dimension $d$ as full gradient method, but improves the dependency of sample size $N$ for a factor of $N^\frac{1}{2}$. Experimental results on both synthetic and real-world benchmark data show that our new framework significantly outperforms the full gradient and stochastic gradient HMC approaches. The earliest version of this paper was submitted to ICML 2020 with three weak accept but was not finally accepted.

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arXiv2020

Accelerated Stochastic Gradient-free and Projection-free Methods

In the paper, we propose a class of accelerated stochastic gradient-free and projection-free (a.k.a., zeroth-order Frank-Wolfe) methods to solve the constrained stochastic and finite-sum nonconvex optimization. Specifically, we propose an accelerated stochastic zeroth-order Frank-Wolfe (Acc-SZOFW) method based on the variance reduced technique of SPIDER/SpiderBoost and a novel momentum accelerated technique. Moreover, under some mild conditions, we prove that the Acc-SZOFW has the function query complexity of $O(d\sqrt{n}ε^{-2})$ for finding an $ε$-stationary point in the finite-sum problem, which improves the exiting best result by a factor of $O(\sqrt{n}ε^{-2})$, and has the function query complexity of $O(dε^{-3})$ in the stochastic problem, which improves the exiting best result by a factor of $O(ε^{-1})$. To relax the large batches required in the Acc-SZOFW, we further propose a novel accelerated stochastic zeroth-order Frank-Wolfe (Acc-SZOFW*) based on a new variance reduced technique of STORM, which still reaches the function query complexity of $O(dε^{-3})$ in the stochastic problem without relying on any large batches. In particular, we present an accelerated framework of the Frank-Wolfe methods based on the proposed momentum accelerated technique. The extensive experimental results on black-box adversarial attack and robust black-box classification demonstrate the efficiency of our algorithms.

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arXiv2020

Faster Stochastic Alternating Direction Method of Multipliers for Nonconvex Optimization

In this paper, we propose a faster stochastic alternating direction method of multipliers (ADMM) for nonconvex optimization by using a new stochastic path-integrated differential estimator (SPIDER), called as SPIDER-ADMM. Moreover, we prove that the SPIDER-ADMM achieves a record-breaking incremental first-order oracle (IFO) complexity of $\mathcal{O}(n+n^{1/2}ε^{-1})$ for finding an $ε$-approximate stationary point, which improves the deterministic ADMM by a factor $\mathcal{O}(n^{1/2})$, where $n$ denotes the sample size. As one of major contribution of this paper, we provide a new theoretical analysis framework for nonconvex stochastic ADMM methods with providing the optimal IFO complexity. Based on this new analysis framework, we study the unsolved optimal IFO complexity of the existing non-convex SVRG-ADMM and SAGA-ADMM methods, and prove they have the optimal IFO complexity of $\mathcal{O}(n+n^{2/3}ε^{-1})$. Thus, the SPIDER-ADMM improves the existing stochastic ADMM methods by a factor of $\mathcal{O}(n^{1/6})$. Moreover, we extend SPIDER-ADMM to the online setting, and propose a faster online SPIDER-ADMM. Our theoretical analysis shows that the online SPIDER-ADMM has the IFO complexity of $\mathcal{O}(ε^{-\frac{3}{2}})$, which improves the existing best results by a factor of $\mathcal{O}(ε^{-\frac{1}{2}})$. Finally, the experimental results on benchmark datasets validate that the proposed algorithms have faster convergence rate than the existing ADMM algorithms for nonconvex optimization.

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arXiv2020

Momentum-Based Policy Gradient Methods

In the paper, we propose a class of efficient momentum-based policy gradient methods for the model-free reinforcement learning, which use adaptive learning rates and do not require any large batches. Specifically, we propose a fast important-sampling momentum-based policy gradient (IS-MBPG) method based on a new momentum-based variance reduced technique and the importance sampling technique. We also propose a fast Hessian-aided momentum-based policy gradient (HA-MBPG) method based on the momentum-based variance reduced technique and the Hessian-aided technique. Moreover, we prove that both the IS-MBPG and HA-MBPG methods reach the best known sample complexity of $O(ε^{-3})$ for finding an $ε$-stationary point of the non-concave performance function, which only require one trajectory at each iteration. In particular, we present a non-adaptive version of IS-MBPG method, i.e., IS-MBPG*, which also reaches the best known sample complexity of $O(ε^{-3})$ without any large batches. In the experiments, we apply four benchmark tasks to demonstrate the effectiveness of our algorithms.

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