On the Convergence of Federated Learning Algorithms without Data Similarity

Data similarity assumptions have traditionally been relied upon to understand the convergence behaviors of federated learning methods. Unfortunately, this approach often demands fine-tuning step sizes based on the level of data similarity. When data similarity is low, these small step sizes result in an unacceptably slow convergence speed for federated methods. In this paper, we present a novel and unified framework for analyzing the convergence of federated learning algorithms without the need for data similarity conditions. Our analysis centers on an inequality that captures the influence of step sizes on algorithmic convergence performance. By applying our theorems to well-known federated algorithms, we derive precise expressions for three widely used step size schedules: fixed, diminishing, and step-decay step sizes, which are independent of data similarity conditions. Finally, we conduct comprehensive evaluations of the performance of these federated learning algorithms, employing the proposed step size strategies to train deep neural network models on benchmark datasets under varying data similarity conditions. Our findings demonstrate significant improvements in convergence speed and overall performance, marking a substantial advancement in federated learning research.

Distributed Momentum Methods Under Biased Gradient Estimations

Distributed stochastic gradient methods are gaining prominence in solving large-scale machine learning problems that involve data distributed across multiple nodes. However, obtaining unbiased stochastic gradients, which have been the focus of most theoretical research, is challenging in many distributed machine learning applications. The gradient estimations easily become biased, for example, when gradients are compressed or clipped, when data is shuffled, and in meta-learning and reinforcement learning. In this work, we establish non-asymptotic convergence bounds on distributed momentum methods under biased gradient estimation on both general non-convex and $\mu$-PL non-convex problems. Our analysis covers general distributed optimization problems, and we work out the implications for special cases where gradient estimates are biased, i.e., in meta-learning and when the gradients are compressed or clipped. Our numerical experiments on training deep neural networks with Top-$K$ sparsification and clipping verify faster convergence performance of momentum methods than traditional biased gradient descent.

SCANIA Component X Dataset: A Real-World Multivariate Time Series Dataset for Predictive Maintenance

This paper presents a description of a real-world, multivariate time series dataset collected from an anonymized engine component (called Component X) of a fleet of trucks from SCANIA, Sweden. This dataset includes diverse variables capturing detailed operational data, repair records, and specifications of trucks while maintaining confidentiality by anonymization. It is well-suited for a range of machine learning applications, such as classification, regression, survival analysis, and anomaly detection, particularly when applied to predictive maintenance scenarios. The large population size and variety of features in the format of histograms and numerical counters, along with the inclusion of temporal information, make this real-world dataset unique in the field. The objective of releasing this dataset is to give a broad range of researchers the possibility of working with real-world data from an internationally well-known company and introduce a standard benchmark to the predictive maintenance field, fostering reproducible research.

Human-Inspired Framework to Accelerate Reinforcement Learning

While deep reinforcement learning (RL) is becoming an integral part of good decision-making in data science, it is still plagued with sample inefficiency. This can be challenging when applying deep-RL in real-world environments where physical interactions are expensive and can risk system safety. To improve the sample efficiency of RL algorithms, this paper proposes a novel human-inspired framework that facilitates fast exploration and learning for difficult RL tasks. The main idea is to first provide the learning agent with simpler but similar tasks that gradually grow in difficulty and progress toward the main task. The proposed method requires no pre-training phase. Specifically, the learning of simpler tasks is only done for one iteration. The generated knowledge could be used by any transfer learning, including value transfer and policy transfer, to reduce the sample complexity while not adding to the computational complexity. So, it can be applied to any goal, environment, and reinforcement learning algorithm - both value-based methods and policy-based methods and both tabular methods and deep-RL methods. We have evaluated our proposed framework on both a simple Random Walk for illustration purposes and on more challenging optimal control problems with constraint. The experiments show the good performance of our proposed framework in improving the sample efficiency of RL-learning algorithms, especially when the main task is difficult.

On the Convergence of Step Decay Step-Size for Stochastic Optimization

The convergence of stochastic gradient descent is highly dependent on the step-size, especially on non-convex problems such as neural network training. Step decay step-size schedules (constant and then cut) are widely used in practice because of their excellent convergence and generalization qualities, but their theoretical properties are not yet well understood. We provide the convergence results for step decay in the non-convex regime, ensuring that the gradient norm vanishes at an $\mathcal{O}(\ln T/\sqrt{T})$ rate. We also provide the convergence guarantees for general (possibly non-smooth) convex problems, ensuring an $\mathcal{O}(\ln T/\sqrt{T})$ convergence rate. Finally, in the strongly convex case, we establish an $\mathcal{O}(\ln T/T)$ rate for smooth problems, which we also prove to be tight, and an $\mathcal{O}(\ln^2 T /T)$ rate without the smoothness assumption. We illustrate the practical efficiency of the step decay step-size in several large scale deep neural network training tasks.

The Internet of Things as a Deep Neural Network

An important task in the Internet of Things (IoT) is field monitoring, where multiple IoT nodes take measurements and communicate them to the base station or the cloud for processing, inference, and analysis. This communication becomes costly when the measurements are high-dimensional (e.g., videos or time-series data). The IoT networks with limited bandwidth and low power devices may not be able to support such frequent transmissions with high data rates. To ensure communication efficiency, this article proposes to model the measurement compression at IoT nodes and the inference at the base station or cloud as a deep neural network (DNN). We propose a new framework where the data to be transmitted from nodes are the intermediate outputs of a layer of the DNN. We show how to learn the model parameters of the DNN and study the trade-off between the communication rate and the inference accuracy. The experimental results show that we can save approximately 96% transmissions with only a degradation of 2.5% in inference accuracy. Our findings have the potentiality to enable many new IoT data analysis applications generating large amount of measurements.

Communication Efficient Sparsification for Large Scale Machine Learning

The increasing scale of distributed learning problems necessitates the development of compression techniques for reducing the information exchange between compute nodes. The level of accuracy in existing compression techniques is typically chosen before training, meaning that they are unlikely to adapt well to the problems that they are solving without extensive hyper-parameter tuning. In this paper, we propose dynamic tuning rules that adapt to the communicated gradients at each iteration. In particular, our rules optimize the communication efficiency at each iteration by maximizing the improvement in the objective function that is achieved per communicated bit. Our theoretical results and experiments indicate that the automatic tuning strategies significantly increase communication efficiency on several state-of-the-art compression schemes.

On Maintaining Linear Convergence of Distributed Learning and Optimization under Limited Communication

In parallel and distributed machine learning multiple nodes or processors coordinate to solve large problems. To do this, nodes need to compress important algorithm information to bits so it can be communicated. The goal of this paper is to explore how we can maintain the convergence of distributed algorithms under such compression. In particular, we consider a general class of linearly convergent parallel/distributed algorithms and illustrate how we can design quantizers compressing the communicated information to few bits while still preserving the linear convergence. We illustrate our results on learning algorithms using different communication structures, such as decentralized algorithms where a single master coordinates information from many workers and fully distributed algorithms where only neighbors in a communication graph can communicate. We also numerically implement our results in distributed learning on smartphones using real-world data.