arXiv subjects

Mingrui Liu

Publications and source records attributed to Mingrui Liu.

At least 55 records · Page 3Linked to original sources

arXiv2023

EPISODE: Episodic Gradient Clipping with Periodic Resampled Corrections for Federated Learning with Heterogeneous Data

Gradient clipping is an important technique for deep neural networks with exploding gradients, such as recurrent neural networks. Recent studies have shown that the loss functions of these networks do not satisfy the conventional smoothness condition, but instead satisfy a relaxed smoothness condition, i.e., the Lipschitz constant of the gradient scales linearly in terms of the gradient norm. Due to this observation, several gradient clipping algorithms have been developed for nonconvex and relaxed-smooth functions. However, the existing algorithms only apply to the single-machine or multiple-machine setting with homogeneous data across machines. It remains unclear how to design provably efficient gradient clipping algorithms in the general Federated Learning (FL) setting with heterogeneous data and limited communication rounds. In this paper, we design EPISODE, the very first algorithm to solve FL problems with heterogeneous data in the nonconvex and relaxed smoothness setting. The key ingredients of the algorithm are two new techniques called \textit{episodic gradient clipping} and \textit{periodic resampled corrections}. At the beginning of each round, EPISODE resamples stochastic gradients from each client and obtains the global averaged gradient, which is used to (1) determine whether to apply gradient clipping for the entire round and (2) construct local gradient corrections for each client. Notably, our algorithm and analysis provide a unified framework for both homogeneous and heterogeneous data under any noise level of the stochastic gradient, and it achieves state-of-the-art complexity results. In particular, we prove that EPISODE can achieve linear speedup in the number of machines, and it requires significantly fewer communication rounds. Experiments on several heterogeneous datasets show the superior performance of EPISODE over several strong baselines in FL.

cs.LG↗

arXiv2022

Multi-Phase Magnetic Fields in the Galaxy NGC 3627

Magnetic fields play an important role in the formation and evolution of a galaxy, but it is challenging to measure them by observation. Here we study the Seyfert galaxy NGC 3627's magnetic field orientations measured from the synchrotron polarization observed with the Very Large Array (VLA) and from the Velocity Gradient Technique (VGT) using spectroscopic data. The latter employs the magnetohydrodynamical (MHD) turbulence's anisotropy to probe the magnetic fields. Being applied to the CO (2-1) and H$α$ emission lines obtained from the PHANGS-ALMA and PHANGS-MUSE surveys, it reveals the magnetic field orientation globally consistent with the polarization. The agreement of the VGT-CO and polarization suggests that the magnetic fields associated with synchrotron emission also percolate through star-forming regions. The VGT-H$α$ measurement reveals the magnetic fields in the warm ionized medium that permeates the disk and disk's vicinity so that it exhibits less agreement with polarization. We find prominent radial fields measured by synchrotron polarization appear in the transition regions from the spiral arms to the galactic bar, while such morphology is less apparent in the VGT-CO and VGT-H$α$ measured magnetic fields. The radial fields suggest that the magnetic torque is important in removing orbiting gas' angular momentum. We notice that magnetic fields inferred from the dust polarization, VGT-CO, and synchrotron polarization are different in the east arm. We interpret this difference as arising from the fact that the three measurements are tracing the magnetic fields associated with pre-collision, the mixture of pre-collision and post-collision, and post-collision flows, respectively.

astro-ph.GA↗

arXiv2022

On Inferring User Socioeconomic Status with Mobility Records

When users move in a physical space (e.g., an urban space), they would have some records called mobility records (e.g., trajectories) generated by devices such as mobile phones and GPS devices. Naturally, mobility records capture essential information of how users work, live and entertain in their daily lives, and therefore, they have been used in a wide range of tasks such as user profile inference, mobility prediction and traffic management. In this paper, we expand this line of research by investigating the problem of inferring user socioeconomic statuses (such as prices of users' living houses as a proxy of users' socioeconomic statuses) based on their mobility records, which can potentially be used in real-life applications such as the car loan business. For this task, we propose a socioeconomic-aware deep model called DeepSEI. The DeepSEI model incorporates two networks called deep network and recurrent network, which extract the features of the mobility records from three aspects, namely spatiality, temporality and activity, one at a coarse level and the other at a detailed level. We conduct extensive experiments on real mobility records data, POI data and house prices data. The results verify that the DeepSEI model achieves superior performance than existing studies. All datasets used in this paper will be made publicly available.

cs.LG↗

arXiv2022

A Communication-Efficient Distributed Gradient Clipping Algorithm for Training Deep Neural Networks

In distributed training of deep neural networks, people usually run Stochastic Gradient Descent (SGD) or its variants on each machine and communicate with other machines periodically. However, SGD might converge slowly in training some deep neural networks (e.g., RNN, LSTM) because of the exploding gradient issue. Gradient clipping is usually employed to address this issue in the single machine setting, but exploring this technique in the distributed setting is still in its infancy: it remains mysterious whether the gradient clipping scheme can take advantage of multiple machines to enjoy parallel speedup. The main technical difficulty lies in dealing with nonconvex loss function, non-Lipschitz continuous gradient, and skipping communication rounds simultaneously. In this paper, we explore a relaxed-smoothness assumption of the loss landscape which LSTM was shown to satisfy in previous works, and design a communication-efficient gradient clipping algorithm. This algorithm can be run on multiple machines, where each machine employs a gradient clipping scheme and communicate with other machines after multiple steps of gradient-based updates. Our algorithm is proved to have $O\left(\frac{1}{Nε^4}\right)$ iteration complexity and $O(\frac{1}{ε^3})$ communication complexity for finding an $ε$-stationary point in the homogeneous data setting, where $N$ is the number of machines. This indicates that our algorithm enjoys linear speedup and reduced communication rounds. Our proof relies on novel analysis techniques of estimating truncated random variables, which we believe are of independent interest. Our experiments on several benchmark datasets and various scenarios demonstrate that our algorithm indeed exhibits fast convergence speed in practice and thus validates our theory.

cs.LG↗

arXiv2022

Fast Composite Optimization and Statistical Recovery in Federated Learning

As a prevalent distributed learning paradigm, Federated Learning (FL) trains a global model on a massive amount of devices with infrequent communication. This paper investigates a class of composite optimization and statistical recovery problems in the FL setting, whose loss function consists of a data-dependent smooth loss and a non-smooth regularizer. Examples include sparse linear regression using Lasso, low-rank matrix recovery using nuclear norm regularization, etc. In the existing literature, federated composite optimization algorithms are designed only from an optimization perspective without any statistical guarantees. In addition, they do not consider commonly used (restricted) strong convexity in statistical recovery problems. We advance the frontiers of this problem from both optimization and statistical perspectives. From optimization upfront, we propose a new algorithm named \textit{Fast Federated Dual Averaging} for strongly convex and smooth loss and establish state-of-the-art iteration and communication complexity in the composite setting. In particular, we prove that it enjoys a fast rate, linear speedup, and reduced communication rounds. From statistical upfront, for restricted strongly convex and smooth loss, we design another algorithm, namely \textit{Multi-stage Federated Dual Averaging}, and prove a high probability complexity bound with linear speedup up to optimal statistical precision. Experiments in both synthetic and real data demonstrate that our methods perform better than other baselines. To the best of our knowledge, this is the first work providing fast optimization algorithms and statistical recovery guarantees for composite problems in FL.

cs.LG↗

arXiv2022

Robustness to Unbounded Smoothness of Generalized SignSGD

Traditional analyses in non-convex optimization typically rely on the smoothness assumption, namely requiring the gradients to be Lipschitz. However, recent evidence shows that this smoothness condition does not capture the properties of some deep learning objective functions, including the ones involving Recurrent Neural Networks and LSTMs. Instead, they satisfy a much more relaxed condition, with potentially unbounded smoothness. Under this relaxed assumption, it has been theoretically and empirically shown that the gradient-clipped SGD has an advantage over the vanilla one. In this paper, we show that clipping is not indispensable for Adam-type algorithms in tackling such scenarios: we theoretically prove that a generalized SignSGD algorithm can obtain similar convergence rates as SGD with clipping but does not need explicit clipping at all. This family of algorithms on one end recovers SignSGD and on the other end closely resembles the popular Adam algorithm. Our analysis underlines the critical role that momentum plays in analyzing SignSGD-type and Adam-type algorithms: it not only reduces the effects of noise, thus removing the need for large mini-batch in previous analyses of SignSGD-type algorithms, but it also substantially reduces the effects of unbounded smoothness and gradient norms. We also compare these algorithms with popular optimizers on a set of deep learning tasks, observing that we can match the performance of Adam while beating the others.

cs.LG↗

arXiv2022

On the Last Iterate Convergence of Momentum Methods

SGD with Momentum (SGDM) is a widely used family of algorithms for large-scale optimization of machine learning problems. Yet, when optimizing generic convex functions, no advantage is known for any SGDM algorithm over plain SGD. Moreover, even the most recent results require changes to the SGDM algorithms, like averaging of the iterates and a projection onto a bounded domain, which are rarely used in practice. In this paper, we focus on the convergence rate of the last iterate of SGDM. For the first time, we prove that for any constant momentum factor, there exists a Lipschitz and convex function for which the last iterate of SGDM suffers from a suboptimal convergence rate of $Ω(\frac{\ln T}{\sqrt{T}})$ after $T$ iterations. Based on this fact, we study a class of (both adaptive and non-adaptive) Follow-The-Regularized-Leader-based SGDM algorithms with increasing momentum and shrinking updates. For these algorithms, we show that the last iterate has optimal convergence $O(\frac{1}{\sqrt{T}})$ for unconstrained convex stochastic optimization problems without projections onto bounded domains nor knowledge of $T$. Further, we show a variety of results for FTRL-based SGDM when used with adaptive stepsizes. Empirical results are shown as well.

cs.LG↗

arXiv2022

Will Bilevel Optimizers Benefit from Loops

Bilevel optimization has arisen as a powerful tool for solving a variety of machine learning problems. Two current popular bilevel optimizers AID-BiO and ITD-BiO naturally involve solving one or two sub-problems, and consequently, whether we solve these problems with loops (that take many iterations) or without loops (that take only a few iterations) can significantly affect the overall computational efficiency. Existing studies in the literature cover only some of those implementation choices, and the complexity bounds available are not refined enough to enable rigorous comparison among different implementations. In this paper, we first establish unified convergence analysis for both AID-BiO and ITD-BiO that are applicable to all implementation choices of loops. We then specialize our results to characterize the computational complexity for all implementations, which enable an explicit comparison among them. Our result indicates that for AID-BiO, the loop for estimating the optimal point of the inner function is beneficial for overall efficiency, although it causes higher complexity for each update step, and the loop for approximating the outer-level Hessian-inverse-vector product reduces the gradient complexity. For ITD-BiO, the two loops always coexist, and our convergence upper and lower bounds show that such loops are necessary to guarantee a vanishing convergence error, whereas the no-loop scheme suffers from an unavoidable non-vanishing convergence error. Our numerical experiments further corroborate our theoretical results.

cs.LG↗

arXiv2022

On the Initialization for Convex-Concave Min-max Problems

Convex-concave min-max problems are ubiquitous in machine learning, and people usually utilize first-order methods (e.g., gradient descent ascent) to find the optimal solution. One feature which separates convex-concave min-max problems from convex minimization problems is that the best known convergence rates for min-max problems have an explicit dependence on the size of the domain, rather than on the distance between initial point and the optimal solution. This means that the convergence speed does not have any improvement even if the algorithm starts from the optimal solution, and hence, is oblivious to the initialization. Here, we show that strict-convexity-strict-concavity is sufficient to get the convergence rate to depend on the initialization. We also show how different algorithms can asymptotically achieve initialization-dependent convergence rates on this class of functions. Furthermore, we show that the so-called "parameter-free" algorithms allow to achieve improved initialization-dependent asymptotic rates without any learning rate to tune. In addition, we utilize this particular parameter-free algorithm as a subroutine to design a new algorithm, which achieves a novel non-asymptotic fast rate for strictly-convex-strictly-concave min-max problems with a growth condition and H{ö}lder continuous solution mapping. Experiments are conducted to verify our theoretical findings and demonstrate the effectiveness of the proposed algorithms.

math.OC↗

arXiv2022

Understanding AdamW through Proximal Methods and Scale-Freeness

Adam has been widely adopted for training deep neural networks due to less hyperparameter tuning and remarkable performance. To improve generalization, Adam is typically used in tandem with a squared $\ell_2$ regularizer (referred to as Adam-$\ell_2$). However, even better performance can be obtained with AdamW, which decouples the gradient of the regularizer from the update rule of Adam-$\ell_2$. Yet, we are still lacking a complete explanation of the advantages of AdamW. In this paper, we tackle this question from both an optimization and an empirical point of view. First, we show how to re-interpret AdamW as an approximation of a proximal gradient method, which takes advantage of the closed-form proximal mapping of the regularizer instead of only utilizing its gradient information as in Adam-$\ell_2$. Next, we consider the property of "scale-freeness" enjoyed by AdamW and by its proximal counterpart: their updates are invariant to component-wise rescaling of the gradients. We provide empirical evidence across a wide range of deep learning experiments showing a correlation between the problems in which AdamW exhibits an advantage over Adam-$\ell_2$ and the degree to which we expect the gradients of the network to exhibit multiple scales, thus motivating the hypothesis that the advantage of AdamW could be due to the scale-free updates.

cs.LG↗

arXiv2021

Velocity Gradients: Magnetic Field Tomography towards the Supernova Remnant W44

As a novel approach for tracing interstellar magnetic fields, the Velocity Gradient Technique (VGT) has been proven to be effective for probing magnetic fields in the diffuse interstellar medium (ISM). In this work, we verify the VGT in a broader context by applying the technique to a molecular cloud interacting with the supernovae remnant (SNR) W44. We probe the magnetic fields with the VGT using CO, $\rm HCO^+$, and H I emission lines and make a comparison with the Planck 353 GHZ dust polarization. We show that the VGT gives an accurate measurement that coheres with the Planck polarization especially in intense molecular gas emission regions. We further study the foreground's contribution to the polarization that results in a misalignment between the VGT and the Planck measurements in low-intensity molecular gas areas. We advance the VGT to achieve magnetic field tomography by decomposing the W44 into various velocity components. We show that W44's velocity component at $v\sim45$ km s$^{-1}$ exhibits the largest coverage and gives the best agreement with Planck polarization in terms of magnetic field orientation.

astro-ph.GA↗

arXiv2021

Loss Landscape Dependent Self-Adjusting Learning Rates in Decentralized Stochastic Gradient Descent

Distributed Deep Learning (DDL) is essential for large-scale Deep Learning (DL) training. Synchronous Stochastic Gradient Descent (SSGD) 1 is the de facto DDL optimization method. Using a sufficiently large batch size is critical to achieving DDL runtime speedup. In a large batch setting, the learning rate must be increased to compensate for the reduced number of parameter updates. However, a large learning rate may harm convergence in SSGD and training could easily diverge. Recently, Decentralized Parallel SGD (DPSGD) has been proposed to improve distributed training speed. In this paper, we find that DPSGD not only has a system-wise run-time benefit but also a significant convergence benefit over SSGD in the large batch setting. Based on a detailed analysis of the DPSGD learning dynamics, we find that DPSGD introduces additional landscape-dependent noise that automatically adjusts the effective learning rate to improve convergence. In addition, we theoretically show that this noise smoothes the loss landscape, hence allowing a larger learning rate. We conduct extensive studies over 18 state-of-the-art DL models/tasks and demonstrate that DPSGD often converges in cases where SSGD diverges for large learning rates in the large batch setting. Our findings are consistent across two different application domains: Computer Vision (CIFAR10 and ImageNet-1K) and Automatic Speech Recognition (SWB300 and SWB2000), and two different types of neural network models: Convolutional Neural Networks and Long Short-Term Memory Recurrent Neural Networks.

cs.LG↗

arXiv2021

Asynchronous Decentralized Distributed Training of Acoustic Models

Large-scale distributed training of deep acoustic models plays an important role in today's high-performance automatic speech recognition (ASR). In this paper we investigate a variety of asynchronous decentralized distributed training strategies based on data parallel stochastic gradient descent (SGD) to show their superior performance over the commonly-used synchronous distributed training via allreduce, especially when dealing with large batch sizes. Specifically, we study three variants of asynchronous decentralized parallel SGD (ADPSGD), namely, fixed and randomized communication patterns on a ring as well as a delay-by-one scheme. We introduce a mathematical model of ADPSGD, give its theoretical convergence rate, and compare the empirical convergence behavior and straggler resilience properties of the three variants. Experiments are carried out on an IBM supercomputer for training deep long short-term memory (LSTM) acoustic models on the 2000-hour Switchboard dataset. Recognition and speedup performance of the proposed strategies are evaluated under various training configurations. We show that ADPSGD with fixed and randomized communication patterns cope well with slow learners. When learners are equally fast, ADPSGD with the delay-by-one strategy has the fastest convergence with large batches. In particular, using the delay-by-one strategy, we can train the acoustic model in less than 2 hours using 128 V100 GPUs with competitive word error rates.

cs.CL↗

arXiv2021

First-order Convergence Theory for Weakly-Convex-Weakly-Concave Min-max Problems

In this paper, we consider first-order convergence theory and algorithms for solving a class of non-convex non-concave min-max saddle-point problems, whose objective function is weakly convex in the variables of minimization and weakly concave in the variables of maximization. It has many important applications in machine learning including training Generative Adversarial Nets (GANs). We propose an algorithmic framework motivated by the inexact proximal point method, where the weakly monotone variational inequality (VI) corresponding to the original min-max problem is solved through approximately solving a sequence of strongly monotone VIs constructed by adding a strongly monotone mapping to the original gradient mapping. We prove first-order convergence to a nearly stationary solution of the original min-max problem of the generic algorithmic framework and establish different rates by employing different algorithms for solving each strongly monotone VI. Experiments verify the convergence theory and also demonstrate the effectiveness of the proposed methods on training GANs.

math.OC↗

arXiv2021

Weakly-Convex Concave Min-Max Optimization: Provable Algorithms and Applications in Machine Learning

Min-max problems have broad applications in machine learning, including learning with non-decomposable loss and learning with robustness to data distribution. Convex-concave min-max problem is an active topic of research with efficient algorithms and sound theoretical foundations developed. However, it remains a challenge to design provably efficient algorithms for non-convex min-max problems with or without smoothness. In this paper, we study a family of non-convex min-max problems, whose objective function is weakly convex in the variables of minimization and is concave in the variables of maximization. We propose a proximally guided stochastic subgradient method and a proximally guided stochastic variance-reduced method for the non-smooth and smooth instances, respectively, in this family of problems. We analyze the time complexities of the proposed methods for finding a nearly stationary point of the outer minimization problem corresponding to the min-max problem.

math.OC↗

arXiv2020

Towards Better Understanding of Adaptive Gradient Algorithms in Generative Adversarial Nets

Adaptive gradient algorithms perform gradient-based updates using the history of gradients and are ubiquitous in training deep neural networks. While adaptive gradient methods theory is well understood for minimization problems, the underlying factors driving their empirical success in min-max problems such as GANs remain unclear. In this paper, we aim at bridging this gap from both theoretical and empirical perspectives. First, we analyze a variant of Optimistic Stochastic Gradient (OSG) proposed in~\citep{daskalakis2017training} for solving a class of non-convex non-concave min-max problem and establish $O(ε^{-4})$ complexity for finding $ε$-first-order stationary point, in which the algorithm only requires invoking one stochastic first-order oracle while enjoying state-of-the-art iteration complexity achieved by stochastic extragradient method by~\citep{iusem2017extragradient}. Then we propose an adaptive variant of OSG named Optimistic Adagrad (OAdagrad) and reveal an \emph{improved} adaptive complexity $O\left(ε^{-\frac{2}{1-α}}\right)$, where $α$ characterizes the growth rate of the cumulative stochastic gradient and $0\leq α\leq 1/2$. To the best of our knowledge, this is the first work for establishing adaptive complexity in non-convex non-concave min-max optimization. Empirically, our experiments show that indeed adaptive gradient algorithms outperform their non-adaptive counterparts in GAN training. Moreover, this observation can be explained by the slow growth rate of the cumulative stochastic gradient, as observed empirically.

math.OC↗

arXiv2020

Improved Schemes for Episodic Memory-based Lifelong Learning

Current deep neural networks can achieve remarkable performance on a single task. However, when the deep neural network is continually trained on a sequence of tasks, it seems to gradually forget the previous learned knowledge. This phenomenon is referred to as \textit{catastrophic forgetting} and motivates the field called lifelong learning. Recently, episodic memory based approaches such as GEM \cite{lopez2017gradient} and A-GEM \cite{chaudhry2018efficient} have shown remarkable performance. In this paper, we provide the first unified view of episodic memory based approaches from an optimization's perspective. This view leads to two improved schemes for episodic memory based lifelong learning, called MEGA-I and MEGA-II. MEGA-I and MEGA-II modulate the balance between old tasks and the new task by integrating the current gradient with the gradient computed on the episodic memory. Notably, we show that GEM and A-GEM are degenerate cases of MEGA-I and MEGA-II which consistently put the same emphasis on the current task, regardless of how the loss changes over time. Our proposed schemes address this issue by using novel loss-balancing updating rules, which drastically improve the performance over GEM and A-GEM. Extensive experimental results show that the proposed schemes significantly advance the state-of-the-art on four commonly used lifelong learning benchmarks, reducing the error by up to 18\%.

cs.LG↗

arXiv2020

Adam$^+$: A Stochastic Method with Adaptive Variance Reduction

Adam is a widely used stochastic optimization method for deep learning applications. While practitioners prefer Adam because it requires less parameter tuning, its use is problematic from a theoretical point of view since it may not converge. Variants of Adam have been proposed with provable convergence guarantee, but they tend not be competitive with Adam on the practical performance. In this paper, we propose a new method named Adam$^+$ (pronounced as Adam-plus). Adam$^+$ retains some of the key components of Adam but it also has several noticeable differences: (i) it does not maintain the moving average of second moment estimate but instead computes the moving average of first moment estimate at extrapolated points; (ii) its adaptive step size is formed not by dividing the square root of second moment estimate but instead by dividing the root of the norm of first moment estimate. As a result, Adam$^+$ requires few parameter tuning, as Adam, but it enjoys a provable convergence guarantee. Our analysis further shows that Adam$^+$ enjoys adaptive variance reduction, i.e., the variance of the stochastic gradient estimator reduces as the algorithm converges, hence enjoying an adaptive convergence. We also propose a more general variant of Adam$^+$ with different adaptive step sizes and establish their fast convergence rate. Our empirical studies on various deep learning tasks, including image classification, language modeling, and automatic speech recognition, demonstrate that Adam$^+$ significantly outperforms Adam and achieves comparable performance with best-tuned SGD and momentum SGD.

cs.LG↗