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 achieves the same rate of convergence as SGD without any additional assumptions for arbitrary compression operators (including the sign operator), indicating that we get gradient compression for free. Our experiments thoroughly substantiate the theory showing the superiority of our algorithm.

COLA: Decentralized Linear Learning

Decentralized machine learning is a promising emerging paradigm in view of global challenges of data ownership and privacy. We consider learning of linear classification and regression models, in the setting where the training data is decentralized over many user devices, and the learning algorithm must run on-device, on an arbitrary communication network, without a central coordinator. We propose COLA, a new decentralized training algorithm with strong theoretical guarantees and superior practical performance. Our framework overcomes many limitations of existing methods, and achieves communication efficiency, scalability, elasticity as well as resilience to changes in data and participating devices.

Don't Use Large Mini-Batches, Use Local SGD

Mini-batch stochastic gradient methods are the current state of the art for large-scale distributed training of neural networks and other machine learning models. However, they fail to adapt to a changing communication vs computation trade-off in a system, in particular when scaling to a large number of workers or devices. More so, the fixed requirement of communication bandwidth for gradient exchange in mini-batch SGD severely limits the scalability to multi-node training e.g. in datacenters, and even more so for training on decentralized networks such as mobile devices. We argue that variants of local SGD, which perform several update steps on a local model before communicating to other nodes, offer significantly improved overall performance and communication efficiency, as well as adaptivity to the underlying system resources. Furthermore, we present a new hierarchical extension of local SGD, and demonstrate that it can efficiently adapt to several levels of computation costs in a heterogeneous distributed system.

Is Wasserstein all you need?

We propose a unified framework for building unsupervised representations of entities and their compositions, by viewing each entity as a histogram (or distribution) over its contexts. This enables us to take advantage of optimal transport and construct representations that effectively harness the geometry of the underlying space containing the contexts. Our method captures uncertainty via modelling the entities as distributions and simultaneously provides interpretability with the optimal transport map, hence giving a novel perspective for building rich and powerful feature representations. As a guiding example, we formulate unsupervised representations for text, and demonstrate it on tasks such as sentence similarity and word entailment detection. Empirical results show strong advantages gained through the proposed framework. This approach can potentially be used for any unsupervised or supervised problem (on text or other modalities) with a co-occurrence structure, such as any sequence data. The key tools at the core of this framework are Wasserstein distances and Wasserstein barycenters, hence raising the question from our title.

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.

CoCoA: A General Framework for Communication-Efficient Distributed Optimization

The scale of modern datasets necessitates the development of efficient distributed optimization methods for machine learning. We present a general-purpose framework for distributed computing environments, CoCoA, that has an efficient communication scheme and is applicable to a wide variety of problems in machine learning and signal processing. We extend the framework to cover general non-strongly-convex regularizers, including L1-regularized problems like lasso, sparse logistic regression, and elastic net regularization, and show how earlier work can be derived as a special case. We provide convergence guarantees for the class of convex regularized loss minimization objectives, leveraging a novel approach in handling non-strongly-convex regularizers and non-smooth loss functions. The resulting framework has markedly improved performance over state-of-the-art methods, as we illustrate with an extensive set of experiments on real distributed datasets.

Sparsified SGD with Memory

Huge scale machine learning problems are nowadays tackled by distributed optimization algorithms, i.e. algorithms that leverage the compute power of many devices for training. The communication overhead is a key bottleneck that hinders perfect scalability. Various recent works proposed to use quantization or sparsification techniques to reduce the amount of data that needs to be communicated, for instance by only sending the most significant entries of the stochastic gradient (top-k sparsification). Whilst such schemes showed very promising performance in practice, they have eluded theoretical analysis so far. In this work we analyze Stochastic Gradient Descent (SGD) with k-sparsification or compression (for instance top-k or random-k) and show that this scheme converges at the same rate as vanilla SGD when equipped with error compensation (keeping track of accumulated errors in memory). That is, communication can be reduced by a factor of the dimension of the problem (sometimes even more) whilst still converging at the same rate. We present numerical experiments to illustrate the theoretical findings and the better scalability for distributed applications.

Simple Unsupervised Keyphrase Extraction using Sentence Embeddings

Keyphrase extraction is the task of automatically selecting a small set of phrases that best describe a given free text document. Supervised keyphrase extraction requires large amounts of labeled training data and generalizes very poorly outside the domain of the training data. At the same time, unsupervised systems have poor accuracy, and often do not generalize well, as they require the input document to belong to a larger corpus also given as input. Addressing these drawbacks, in this paper, we tackle keyphrase extraction from single documents with EmbedRank: a novel unsupervised method, that leverages sentence embeddings. EmbedRank achieves higher F-scores than graph-based state of the art systems on standard datasets and is suitable for real-time processing of large amounts of Web data. With EmbedRank, we also explicitly increase coverage and diversity among the selected keyphrases by introducing an embedding-based maximal marginal relevance (MMR) for new phrases. A user study including over 200 votes showed that, although reducing the phrases' semantic overlap leads to no gains in F-score, our high diversity selection is preferred by humans.

Unsupervised robust nonparametric learning of hidden community properties

We consider learning of fundamental properties of communities in large noisy networks, in the prototypical situation where the nodes or users are split into two classes according to a binary property, e.g., according to their opinions or preferences on a topic. For learning these properties, we propose a nonparametric, unsupervised, and scalable graph scan procedure that is, in addition, robust against a class of powerful adversaries. In our setup, one of the communities can fall under the influence of a knowledgeable adversarial leader, who knows the full network structure, has unlimited computational resources and can completely foresee our planned actions on the network. We prove strong consistency of our results in this setup with minimal assumptions. In particular, the learning procedure estimates the baseline activity of normal users asymptotically correctly with probability 1; the only assumption being the existence of a single implicit community of asymptotically negligible logarithmic size. We provide experiments on real and synthetic data to illustrate the performance of our method, including examples with adversaries.

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.