arXiv subjects

Sai Praneeth Karimireddy

Publications and source records attributed to Sai Praneeth Karimireddy.

67 records · Page 4Linked to original sources

arXiv2021

The Error-Feedback Framework: Better Rates for SGD with Delayed Gradients and Compressed Communication

We analyze (stochastic) gradient descent (SGD) with delayed updates on smooth quasi-convex and non-convex functions and derive concise, non-asymptotic, convergence rates. We show that the rate of convergence in all cases consists of two terms: (i) a stochastic term which is not affected by the delay, and (ii) a higher order deterministic term which is only linearly slowed down by the delay. Thus, in the presence of noise, the effects of the delay become negligible after a few iterations and the algorithm converges at the same optimal rate as standard SGD. This result extends a line of research that showed similar results in the asymptotic regime or for strongly-convex quadratic functions only. We further show similar results for SGD with more intricate form of delayed gradients -- compressed gradients under error compensation and for local~SGD where multiple workers perform local steps before communicating with each other. In all of these settings, we improve upon the best known rates. These results show that SGD is robust to compressed and/or delayed stochastic gradient updates. This is in particular important for distributed parallel implementations, where asynchronous and communication efficient methods are the key to achieve linear speedups for optimization with multiple devices.

cs.LG↗

arXiv2021

Mime: Mimicking Centralized Stochastic Algorithms in Federated Learning

Federated learning (FL) is a challenging setting for optimization due to the heterogeneity of the data across different clients which gives rise to the client drift phenomenon. In fact, obtaining an algorithm for FL which is uniformly better than simple centralized training has been a major open problem thus far. In this work, we propose a general algorithmic framework, Mime, which i) mitigates client drift and ii) adapts arbitrary centralized optimization algorithms such as momentum and Adam to the cross-device federated learning setting. Mime uses a combination of control-variates and server-level statistics (e.g. momentum) at every client-update step to ensure that each local update mimics that of the centralized method run on iid data. We prove a reduction result showing that Mime can translate the convergence of a generic algorithm in the centralized setting into convergence in the federated setting. Further, we show that when combined with momentum based variance reduction, Mime is provably faster than any centralized method--the first such result. We also perform a thorough experimental exploration of Mime's performance on real world datasets.

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arXiv2021

SCAFFOLD: Stochastic Controlled Averaging for Federated Learning

Federated Averaging (FedAvg) has emerged as the algorithm of choice for federated learning due to its simplicity and low communication cost. However, in spite of recent research efforts, its performance is not fully understood. We obtain tight convergence rates for FedAvg and prove that it suffers from `client-drift' when the data is heterogeneous (non-iid), resulting in unstable and slow convergence. As a solution, we propose a new algorithm (SCAFFOLD) which uses control variates (variance reduction) to correct for the `client-drift' in its local updates. We prove that SCAFFOLD requires significantly fewer communication rounds and is not affected by data heterogeneity or client sampling. Further, we show that (for quadratics) SCAFFOLD can take advantage of similarity in the client's data yielding even faster convergence. The latter is the first result to quantify the usefulness of local-steps in distributed optimization.

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arXiv2020

Why are Adaptive Methods Good for Attention Models?

While stochastic gradient descent (SGD) is still the \emph{de facto} algorithm in deep learning, adaptive methods like Clipped SGD/Adam have been observed to outperform SGD across important tasks, such as attention models. The settings under which SGD performs poorly in comparison to adaptive methods are not well understood yet. In this paper, we provide empirical and theoretical evidence that a heavy-tailed distribution of the noise in stochastic gradients is one cause of SGD's poor performance. We provide the first tight upper and lower convergence bounds for adaptive gradient methods under heavy-tailed noise. Further, we demonstrate how gradient clipping plays a key role in addressing heavy-tailed gradient noise. Subsequently, we show how clipping can be applied in practice by developing an \emph{adaptive} coordinate-wise clipping algorithm (ACClip) and demonstrate its superior performance on BERT pretraining and finetuning tasks.

math.OC↗

arXiv2020

PowerGossip: Practical Low-Rank Communication Compression in Decentralized Deep Learning

Lossy gradient compression has become a practical tool to overcome the communication bottleneck in centrally coordinated distributed training of machine learning models. However, algorithms for decentralized training with compressed communication over arbitrary connected networks have been more complicated, requiring additional memory and hyperparameters. We introduce a simple algorithm that directly compresses the model differences between neighboring workers using low-rank linear compressors applied on model differences. Inspired by the PowerSGD algorithm for centralized deep learning, this algorithm uses power iteration steps to maximize the information transferred per bit. We prove that our method requires no additional hyperparameters, converges faster than prior methods, and is asymptotically independent of both the network and the compression. Out of the box, these compressors perform on par with state-of-the-art tuned compression algorithms in a series of deep learning benchmarks.

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arXiv2020

Secure Byzantine-Robust Machine Learning

Increasingly machine learning systems are being deployed to edge servers and devices (e.g. mobile phones) and trained in a collaborative manner. Such distributed/federated/decentralized training raises a number of concerns about the robustness, privacy, and security of the procedure. While extensive work has been done in tackling with robustness, privacy, or security individually, their combination has rarely been studied. In this paper, we propose a secure two-server protocol that offers both input privacy and Byzantine-robustness. In addition, this protocol is communication-efficient, fault-tolerant and enjoys local differential privacy.

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arXiv2020

Accelerating Gradient Boosting Machine

Gradient Boosting Machine (GBM) is an extremely powerful supervised learning algorithm that is widely used in practice. GBM routinely features as a leading algorithm in machine learning competitions such as Kaggle and the KDDCup. In this work, we propose Accelerated Gradient Boosting Machine (AGBM) by incorporating Nesterov's acceleration techniques into the design of GBM. The difficulty in accelerating GBM lies in the fact that weak (inexact) learners are commonly used, and therefore the errors can accumulate in the momentum term. To overcome it, we design a "corrected pseudo residual" and fit best weak learner to this corrected pseudo residual, in order to perform the z-update. Thus, we are able to derive novel computational guarantees for AGBM. This is the first GBM type of algorithm with theoretically-justified accelerated convergence rate. Finally we demonstrate with a number of numerical experiments the effectiveness of AGBM over conventional GBM in obtaining a model with good training and/or testing data fidelity.

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arXiv2020

PowerSGD: Practical Low-Rank Gradient Compression for Distributed Optimization

We study gradient compression methods to alleviate the communication bottleneck in data-parallel distributed optimization. Despite the significant attention received, current compression schemes either do not scale well or fail to achieve the target test accuracy. We propose a new low-rank gradient compressor based on power iteration that can i) compress gradients rapidly, ii) efficiently aggregate the compressed gradients using all-reduce, and iii) achieve test performance on par with SGD. The proposed algorithm is the only method evaluated that achieves consistent wall-clock speedups when benchmarked against regular SGD with an optimized communication backend. We demonstrate reduced training times for convolutional networks as well as LSTMs on common datasets. Our code is available at https://github.com/epfml/powersgd.

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arXiv2020

Amplifying Rényi Differential Privacy via Shuffling

Differential privacy is a useful tool to build machine learning models which do not release too much information about the training data. We study the Rényi differential privacy of stochastic gradient descent when each training example is sampled without replacement (also known as cyclic SGD). Cyclic SGD is typically faster than traditional SGD and is the algorithm of choice in large-scale implementations. We recover privacy guarantees for cyclic SGD which are competitive with those known for sampling with replacement. Our proof techniques make no assumptions on the model or on the data and are hence widely applicable.

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arXiv2019

On Matching Pursuit and Coordinate Descent

Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers a generalized notion of directions. Exploiting the connection between the two algorithms, we present a unified analysis of both, providing affine invariant sublinear $\mathcal{O}(1/t)$ rates on smooth objectives and linear convergence on strongly convex objectives. As a byproduct of our affine invariant analysis of matching pursuit, our rates for steepest coordinate descent are the tightest known. Furthermore, we show the first accelerated convergence rate $\mathcal{O}(1/t^2)$ for matching pursuit and steepest coordinate descent on convex objectives.

stat.ML↗

arXiv2019

Error Feedback Fixes SignSGD and other Gradient Compression Schemes

Sign-based algorithms (e.g. signSGD) have been proposed as a biased gradient compression technique to alleviate the communication bottleneck in training large neural networks across multiple workers. We show simple convex counter-examples where signSGD does not converge to the optimum. Further, even when it does converge, signSGD may generalize poorly when compared with SGD. These issues arise because of the biased nature of the sign compression operator. We then show that using error-feedback, i.e. incorporating the error made by the compression operator into the next step, overcomes these issues. We prove that our algorithm EF-SGD with arbitrary compression operator achieves the same rate of convergence as SGD without any additional assumptions. Thus EF-SGD achieves gradient compression for free. Our experiments thoroughly substantiate the theory and show that error-feedback improves both convergence and generalization. Code can be found at \url{https://github.com/epfml/error-feedback-SGD}.

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arXiv2018

Efficient Greedy Coordinate Descent for Composite Problems

Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent of the dimension $n$, and requiring upto $n$ times fewer iterations. In this paper, we consider greedy updates that are based on subgradients for a class of non-smooth composite problems, which includes $L1$-regularized problems, SVMs and related applications. For these problems we provide (i) the first linear rates of convergence independent of $n$, and show that our greedy update rule provides speedups similar to those obtained in the smooth case. This was previously conjectured to be true for a stronger greedy coordinate selection strategy. Furthermore, we show that (ii) our new selection rule can be mapped to instances of maximum inner product search, allowing to leverage standard nearest neighbor algorithms to speed up the implementation. We demonstrate the validity of the approach through extensive numerical experiments.

math.OC↗

arXiv2018

Global linear convergence of Newton's method without strong-convexity or Lipschitz gradients

We show that Newton's method converges globally at a linear rate for objective functions whose Hessians are stable. This class of problems includes many functions which are not strongly convex, such as logistic regression. Our linear convergence result is (i) affine-invariant, and holds even if an (ii) approximate Hessian is used, and if the subproblems are (iii) only solved approximately. Thus we theoretically demonstrate the superiority of Newton's method over first-order methods, which would only achieve a sublinear $O(1/t^2)$ rate under similar conditions.

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