arXiv subjects

Xinmeng Huang

Publications and source records attributed to Xinmeng Huang.

24 records · Page 2Linked to original sources

arXiv2022

Collaborative Learning of Discrete Distributions under Heterogeneity and Communication Constraints

In modern machine learning, users often have to collaborate to learn the distribution of the data. Communication can be a significant bottleneck. Prior work has studied homogeneous users -- i.e., whose data follow the same discrete distribution -- and has provided optimal communication-efficient methods for estimating that distribution. However, these methods rely heavily on homogeneity, and are less applicable in the common case when users' discrete distributions are heterogeneous. Here we consider a natural and tractable model of heterogeneity, where users' discrete distributions only vary sparsely, on a small number of entries. We propose a novel two-stage method named SHIFT: First, the users collaborate by communicating with the server to learn a central distribution; relying on methods from robust statistics. Then, the learned central distribution is fine-tuned to estimate their respective individual distribution. We show that SHIFT is minimax optimal in our model of heterogeneity and under communication constraints. Further, we provide experimental results using both synthetic data and $n$-gram frequency estimation in the text domain, which corroborate its efficiency.

stat.ML↗

arXiv2022

Lower Bounds and Nearly Optimal Algorithms in Distributed Learning with Communication Compression

Recent advances in distributed optimization and learning have shown that communication compression is one of the most effective means of reducing communication. While there have been many results on convergence rates under communication compression, a theoretical lower bound is still missing. Analyses of algorithms with communication compression have attributed convergence to two abstract properties: the unbiased property or the contractive property. They can be applied with either unidirectional compression (only messages from workers to server are compressed) or bidirectional compression. In this paper, we consider distributed stochastic algorithms for minimizing smooth and non-convex objective functions under communication compression. We establish a convergence lower bound for algorithms whether using unbiased or contractive compressors in unidirection or bidirection. To close the gap between the lower bound and the existing upper bounds, we further propose an algorithm, NEOLITHIC, which almost reaches our lower bound (up to logarithm factors) under mild conditions. Our results also show that using contractive bidirectional compression can yield iterative methods that converge as fast as those using unbiased unidirectional compression. The experimental results validate our findings.

cs.LG↗

arXiv2022

Removing Data Heterogeneity Influence Enhances Network Topology Dependence of Decentralized SGD

We consider the decentralized stochastic optimization problems, where a network of $n$ nodes, each owning a local cost function, cooperate to find a minimizer of the globally-averaged cost. A widely studied decentralized algorithm for this problem is decentralized SGD (D-SGD), in which each node averages only with its neighbors. D-SGD is efficient in single-iteration communication, but it is very sensitive to the network topology. For smooth objective functions, the transient stage (which measures the number of iterations the algorithm has to experience before achieving the linear speedup stage) of D-SGD is on the order of $Ω(n/(1-β)^2)$ and $Ω(n^3/(1-β)^4)$ for strongly and generally convex cost functions, respectively, where $1-β\in (0,1)$ is a topology-dependent quantity that approaches $0$ for a large and sparse network. Hence, D-SGD suffers from slow convergence for large and sparse networks. In this work, we study the non-asymptotic convergence property of the D$^2$/Exact-diffusion algorithm. By eliminating the influence of data heterogeneity between nodes, D$^2$/Exact-diffusion is shown to have an enhanced transient stage that is on the order of $\tildeΩ(n/(1-β))$ and $Ω(n^3/(1-β)^2)$ for strongly and generally convex cost functions, respectively. Moreover, when D$^2$/Exact-diffusion is implemented with gradient accumulation and multi-round gossip communications, its transient stage can be further improved to $\tildeΩ(1/(1-β)^{\frac{1}{2}})$ and $\tildeΩ(n/(1-β))$ for strongly and generally convex cost functions, respectively. These established results for D$^2$/Exact-Diffusion have the best (i.e., weakest) dependence on network topology to our knowledge compared to existing decentralized algorithms. We also conduct numerical simulations to validate our theories.

math.OC↗

arXiv2021

Improved Analysis and Rates for Variance Reduction under Without-replacement Sampling Orders

When applying a stochastic algorithm, one must choose an order to draw samples. The practical choices are without-replacement sampling orders, which are empirically faster and more cache-friendly than uniform-iid-sampling but often have inferior theoretical guarantees. Without-replacement sampling is well understood only for SGD without variance reduction. In this paper, we will improve the convergence analysis and rates of variance reduction under without-replacement sampling orders for composite finite-sum minimization. Our results are in two-folds. First, we develop a damped variant of Finito called Prox-DFinito and establish its convergence rates with random reshuffling, cyclic sampling, and shuffling-once, under both convex and strongly convex scenarios. These rates match full-batch gradient descent and are state-of-the-art compared to the existing results for without-replacement sampling with variance-reduction. Second, our analysis can gauge how the cyclic order will influence the rate of cyclic sampling and, thus, allows us to derive the optimal fixed ordering. In the highly data-heterogeneous scenario, Prox-DFinito with optimal cyclic sampling can attain a sample-size-independent convergence rate, which, to our knowledge, is the first result that can match with uniform-iid-sampling with variance reduction. We also propose a practical method to discover the optimal cyclic ordering numerically.

cs.LG↗

arXiv2021

DecentLaM: Decentralized Momentum SGD for Large-batch Deep Training

The scale of deep learning nowadays calls for efficient distributed training algorithms. Decentralized momentum SGD (DmSGD), in which each node averages only with its neighbors, is more communication efficient than vanilla Parallel momentum SGD that incurs global average across all computing nodes. On the other hand, the large-batch training has been demonstrated critical to achieve runtime speedup. This motivates us to investigate how DmSGD performs in the large-batch scenario. In this work, we find the momentum term can amplify the inconsistency bias in DmSGD. Such bias becomes more evident as batch-size grows large and hence results in severe performance degradation. We next propose DecentLaM, a novel decentralized large-batch momentum SGD to remove the momentum-incurred bias. The convergence rate for both non-convex and strongly-convex scenarios is established. Our theoretical results justify the superiority of DecentLaM to DmSGD especially in the large-batch scenario. Experimental results on a variety of computer vision tasks and models demonstrate that DecentLaM promises both efficient and high-quality training.

cs.LG↗

arXiv2020

Tight Coefficients of Averaged Operators via Scaled Relative Graph

Many iterative methods in optimization are fixed-point iterations with averaged operators. As such methods converge at an $\mathcal{O}(1/k)$ rate with the constant determined by the averagedness coefficient, establishing small averagedness coefficients for operators is of broad interest. In this paper, we show that the averagedness coefficients of the composition of averaged operators by Ogura and Yamada (Numer Func Anal Opt 32(1--2):113--137, 2002) and the three-operator splitting by Davis and Yin (Set-Valued Var Anal 25(4):829--858, 2017) are tight. The analysis relies on the scaled relative graph, a geometric tool recently proposed by Ryu, Hannah, and Yin (arXiv:1902.09788, 2019).

math.OC↗