Due to the high communication overhead when training machine learning models in a distributed environment, modern algorithms invariably rely on lossy communication compression. However, when untreated, the errors caused by compression propagate, and can lead to severely unstable behavior, including exponential divergence. Almost a decade ago, Seide et al [2014] proposed an error feedback (EF) mechanism, which we refer to as EF14, as an immensely effective heuristic for mitigating this issue. However, despite steady algorithmic and theoretical advances in the EF field in the last decade, our understanding is far from complete. In this work we address one of the most pressing issues. In particular, in the canonical nonconvex setting, all known variants of EF rely on very large batch sizes to converge, which can be prohibitive in practice. We propose a surprisingly simple fix which removes this issue both theoretically, and in practice: the application of Polyak's momentum to the latest incarnation of EF due to Richt\'{a}rik et al. [2021] known as EF21. Our algorithm, for which we coin the name EF21-SGDM, improves the communication and sample complexities of previous error feedback algorithms under standard smoothness and bounded variance assumptions, and does not require any further strong assumptions such as bounded gradient dissimilarity. Moreover, we propose a double momentum version of our method that improves the complexities even further. Our proof seems to be novel even when compression is removed from the method, and as such, our proof technique is of independent interest in the study of nonconvex stochastic optimization enriched with Polyak's momentum.
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Computing a shortest path between two nodes in an undirected unweighted graph is among the most basic algorithmic tasks. Breadth first search solves this problem in linear time, which is clearly also a lower bound in the worst case. However, several works have shown how to solve this problem in sublinear time in expectation when the input graph is drawn from one of several classes of random graphs. In this work, we extend these results by giving sublinear time shortest path (and short path) algorithms for expander graphs. We thus identify a natural deterministic property of a graph (that is satisfied by typical random regular graphs) which suffices for sublinear time shortest paths. The algorithms are very simple, involving only bidirectional breadth first search and short random walks. We also complement our new algorithms by near-matching lower bounds.
Classical statistical theory has been developed under the assumption that the data belongs to a linear space. However, in many applications the intrinsic geometry of the data is more intricate. Neglecting this frequently yields suboptimal or outright unuseable results, i.e., taking the pixel-wise average of images typically results in noise. Incorporating the intrinsic geometry of a dataset into statistical analysis is a highly non-trivial task. In fact different underlying geometries necessitate different approaches, and allow for results of varying strength. Perhaps the most common non-linear geometries appearing in statistical applications are metric spaces of non-positive curvature, such as the manifold of symmetric, positive (semi-)definite matrices. In this paper we introduce a (strong) law of large numbers for independent, but not necessarily identically distributed random variables taking values in complete spaces of non-positive curvature. Using this law of large numbers, we justify a stochastic approximation scheme for the limit of Fr\'echet means on such spaces. Apart from rendering the problem of computing Fr\'echet means computationally more tractable, the structure of this scheme suggests, that averaging operations on Hadamard spaces are more stable than previous results would suggest.
This paper investigates the planning and control problems for multi-robot systems under linear temporal logic (LTL) specifications. In contrast to most of existing literature, which presumes a static and known environment, our study focuses on dynamic environments that can have unknown moving obstacles like humans walking through. Depending on whether local communication is allowed between robots, we consider two different online re-planning approaches. When local communication is allowed, we propose a local trajectory generation algorithm for each robot to resolve conflicts that are detected on-line. In the other case, i.e., no communication is allowed, we develop a model predictive controller to reactively avoid potential collisions. In both cases, task satisfaction is guaranteed whenever it is feasible. In addition, we consider the human-in-the-loop scenario where humans may additionally take control of one or multiple robots. We design a mixed initiative controller for each robot to prevent unsafe human behaviors while guarantee the LTL satisfaction. Using our previous developed ROS software package, several experiments are conducted to demonstrate the effectiveness and the applicability of the proposed strategies.
Building energy prediction and management has become increasingly important in recent decades, driven by the growth of Internet of Things (IoT) devices and the availability of more energy data. However, energy data is often collected from multiple sources and can be incomplete or inconsistent, which can hinder accurate predictions and management of energy systems and limit the usefulness of the data for decision-making and research. To address this issue, past studies have focused on imputing missing gaps in energy data, including random and continuous gaps. One of the main challenges in this area is the lack of validation on a benchmark dataset with various building and meter types, making it difficult to accurately evaluate the performance of different imputation methods. Another challenge is the lack of application of state-of-the-art imputation methods for missing gaps in energy data. Contemporary image-inpainting methods, such as Partial Convolution (PConv), have been widely used in the computer vision domain and have demonstrated their effectiveness in dealing with complex missing patterns. To study whether energy data imputation can benefit from the image-based deep learning method, this study compared PConv, Convolutional neural networks (CNNs), and weekly persistence method using one of the biggest publicly available whole building energy datasets, consisting of 1479 power meters worldwide, as the benchmark. The results show that, compared to the CNN with the raw time series (1D-CNN) and the weekly persistence method, neural network models with reshaped energy data with two dimensions reduced the Mean Squared Error (MSE) by 10% to 30%. The advanced deep learning method, Partial convolution (PConv), has further reduced the MSE by 20-30% than 2D-CNN and stands out among all models.
Recent years have seen many insights on deep learning optimisation being brought forward by finding implicit regularisation effects of commonly used gradient-based optimisers. Understanding implicit regularisation can not only shed light on optimisation dynamics, but it can also be used to improve performance and stability across problem domains, from supervised learning to two-player games such as Generative Adversarial Networks. An avenue for finding such implicit regularisation effects has been quantifying the discretisation errors of discrete optimisers via continuous-time flows constructed by backward error analysis (BEA). The current usage of BEA is not without limitations, since not all the vector fields of continuous-time flows obtained using BEA can be written as a gradient, hindering the construction of modified losses revealing implicit regularisers. In this work, we provide a novel approach to use BEA, and show how our approach can be used to construct continuous-time flows with vector fields that can be written as gradients. We then use this to find previously unknown implicit regularisation effects, such as those induced by multiple stochastic gradient descent steps while accounting for the exact data batches used in the updates, and in generally differentiable two-player games.
Many small to large organizations have adopted the Microservices Architecture (MSA) style to develop and deliver their core businesses. Despite the popularity of MSA in the software industry, there is a limited evidence-based and thorough understanding of the types of issues (e.g., errors, faults, failures, and bugs) that microservices system developers experience, the causes of the issues, and the solutions as potential fixing strategies to address the issues. To ameliorate this gap, we conducted a mixed-methods empirical study that collected data from 2,641 issues from the issue tracking systems of 15 open-source microservices systems on GitHub, 15 interviews, and an online survey completed by 150 practitioners from 42 countries across 6 continents. Our analysis led to comprehensive taxonomies for the issues, causes, and solutions. The findings of this study inform that Technical Debt, Continuous Integration and Delivery, Exception Handling, Service Execution and Communication, and Security are the most dominant issues in microservices systems. Furthermore, General Programming Errors, Missing Features and Artifacts, and Invalid Configuration and Communication are the main causes behind the issues. Finally, we found 177 types of solutions that can be applied to fix the identified issues. Based on our study results, we formulated future research directions that could help researchers and practitioners to engineer emergent and next-generation microservices systems.
Data objects taking value in a general metric space have become increasingly common in modern data analysis. In this paper, we study two important statistical inference problems, namely, two-sample testing and change-point detection, for such non-Euclidean data under temporal dependence. Typical examples of non-Euclidean valued time series include yearly mortality distributions, time-varying networks, and covariance matrix time series. To accommodate unknown temporal dependence, we advance the self-normalization (SN) technique (Shao, 2010) to the inference of non-Euclidean time series, which is substantially different from the existing SN-based inference for functional time series that reside in Hilbert space (Zhang et al., 2011). Theoretically, we propose new regularity conditions that could be easier to check than those in the recent literature, and derive the limiting distributions of the proposed test statistics under both null and local alternatives. For change-point detection problem, we also derive the consistency for the change-point location estimator, and combine our proposed change-point test with wild binary segmentation to perform multiple change-point estimation. Numerical simulations demonstrate the effectiveness and robustness of our proposed tests compared with existing methods in the literature. Finally, we apply our tests to two-sample inference in mortality data and change-point detection in cryptocurrency data.
Training learnable metrics using modern language models has recently emerged as a promising method for the automatic evaluation of machine translation. However, existing human evaluation datasets for text simplification have limited annotations that are based on unitary or outdated models, making them unsuitable for this approach. To address these issues, we introduce the SimpEval corpus that contains: SimpEval_past, comprising 12K human ratings on 2.4K simplifications of 24 past systems, and SimpEval_2022, a challenging simplification benchmark consisting of over 1K human ratings of 360 simplifications including GPT-3.5 generated text. Training on SimpEval, we present LENS, a Learnable Evaluation Metric for Text Simplification. Extensive empirical results show that LENS correlates much better with human judgment than existing metrics, paving the way for future progress in the evaluation of text simplification. We also introduce Rank and Rate, a human evaluation framework that rates simplifications from several models in a list-wise manner using an interactive interface, which ensures both consistency and accuracy in the evaluation process and is used to create the SimpEval datasets.
The theory of mixed finite element methods for solving different types of elliptic partial differential equations in saddle-point formulation is well established since many decades. However, this topic was mostly studied for variational formulations defined upon the same finite-element product spaces of both shape- and test-pairs of primal variable-multiplier. Whenever these two product spaces are different the saddle point problem is asymmetric. It turns out that the conditions to be satisfied by the finite elements product spaces stipulated in the few works on this case may be of limited use in practice. The purpose of this paper is to provide an in-depth analysis of the well-posedness and the uniform stability of asymmetric approximate saddle point problems, based on the theory of continuous linear operators on Hilbert spaces. Our approach leads to necessary and sufficient conditions for such properties to hold, expressed in a readily exploitable form with fine constants. In particular standard interpolation theory suffices to estimate the error of a conforming method.
Positive linear programs (LPs) model many graph and operations research problems. One can solve for a $(1+\epsilon)$-approximation for positive LPs, for any selected $\epsilon$, in polylogarithmic depth and near-linear work via variations of the multiplicative weight update (MWU) method. Despite extensive theoretical work on these algorithms through the decades, their empirical performance is not well understood. In this work, we implement and test an efficient parallel algorithm for solving positive LP relaxations, and apply it to graph problems such as densest subgraph, bipartite matching, vertex cover and dominating set. We accelerate the algorithm via a new step size search heuristic. Our implementation uses sparse linear algebra optimization techniques such as fusion of vector operations and use of sparse format. Furthermore, we devise an implicit representation for graph incidence constraints. We demonstrate the parallel scalability with the use of threading OpenMP and MPI on the Stampede2 supercomputer. We compare this implementation with exact libraries and specialized libraries for the above problems in order to evaluate MWU's practical standing for both accuracy and performance among other methods. Our results show this implementation is faster than general purpose LP solvers (IBM CPLEX, Gurobi) in all of our experiments, and in some instances, outperforms state-of-the-art specialized parallel graph algorithms.
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