Implementation Of Stochastic Gradient Descent Research Articles

Scaling up stochastic gradient descent for non-convex optimisation

Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions and large datasets. We address the bottleneck problem arising when using both shared and distributed memory. Typically, the former is bounded by limited computation resources and bandwidth whereas the latter suffers from communication overheads. We propose a unified distributed and parallel implementation of SGD (named DPSGD) that relies on both asynchronous distribution and lock-free parallelism. By combining two strategies into a unified framework, DPSGD is able to strike a better trade-off between local computation and communication. The convergence properties of DPSGD are studied for non-convex problems such as those arising in statistical modelling and machine learning. Our theoretical analysis shows that DPSGD leads to speed-up with respect to the number of cores and number of workers while guaranteeing an asymptotic convergence rate of O(1/sqrt{T}) given that the number of cores is bounded by T^{1/4} and the number of workers is bounded by T^{1/2} where T is the number of iterations. The potential gains that can be achieved by DPSGD are demonstrated empirically on a stochastic variational inference problem (Latent Dirichlet Allocation) and on a deep reinforcement learning (DRL) problem (advantage actor critic - A2C) resulting in two algorithms: DPSVI and HSA2C. Empirical results validate our theoretical findings. Comparative studies are conducted to show the performance of the proposed DPSGD against the state-of-the-art DRL algorithms.

Train Me If You Can: Decentralized Learning on the Deep Edge

The end of Moore’s Law aligned with data privacy concerns is forcing machine learning (ML) to shift from the cloud to the deep edge. In the next-generation ML systems, the inference and part of the training process will perform at the edge, while the cloud stays responsible for major updates. This new computing paradigm, called federated learning (FL), alleviates the cloud and network infrastructure while increasing data privacy. Recent advances empowered the inference pass of quantized artificial neural networks (ANNs) on Arm Cortex-M and RISC-V microcontroller units (MCUs). Nevertheless, the training remains confined to the cloud, imposing the transaction of high volumes of private data over a network and leading to unpredictable delays when ML applications attempt to adapt to adversarial environments. To fill this gap, we make the first attempt to evaluate the feasibility of ANN training in Arm Cortex-M MCUs. From the available optimization algorithms, stochastic gradient descent (SGD) has the best trade-off between accuracy, memory footprint, and latency. However, its original form and the variants available in the literature still do not fit the stringent requirements of Arm Cortex-M MCUs. We propose L-SGD, a lightweight implementation of SGD optimized for maximum speed and minimal memory footprint in this class of MCUs. We developed a floating-point version and another that operates over quantized weights. For a fully-connected ANN trained on the MNIST dataset, L-SGD (float-32) is 4.20× faster than the SGD while requiring only 2.80% of the memory with negligible accuracy loss. Results also show that quantized training is still unfeasible to train an ANN from the scratch but is a lightweight solution to perform minor model fixes and counteract the fairness problem in typical FL systems.

Model averaging in distributed machine learning: a case study with Apache Spark

The increasing popularity of Apache Spark has attracted many users to put their data into its ecosystem. On the other hand, it has been witnessed in the literature that Spark is slow when it comes to distributed machine learning (ML). One resort is to switch to specialized systems such as parameter servers, which are claimed to have better performance. Nonetheless, users have to undergo the painful procedure of moving data into and out of Spark. In this paper, we investigate performance bottlenecks of MLlib (an official Spark package for ML) in detail, by focusing on analyzing its implementation of stochastic gradient descent (SGD)—the workhorse under the training of many ML models. We show that the performance inferiority of Spark is caused by implementation issues rather than fundamental flaws of the bulk synchronous parallel (BSP) model that governs Spark’s execution: we can significantly improve Spark’s performance by leveraging the well-known “model averaging” (MA) technique in distributed ML. Indeed, model averaging is not limited to SGD, and we further showcase an application of MA to training latent Dirichlet allocation (LDA) models within Spark. Our implementation is not intrusive and requires light development effort. Experimental evaluation results reveal that the MA-based versions of SGD and LDA can be orders of magnitude faster compared to their counterparts without using MA.

Accelerating generalized linear models with MLWeaving

Learning from the data stored in a database is an important function increasingly available in relational engines. Methods using lower precision input data are of special interest given their overall higher efficiency. However, in databases, these methods have a hidden cost: the quantization of the real value into a smaller number is an expensive step. To address this issue, we present ML-Weaving, a data structure and hardware acceleration technique intended to speed up learning of generalized linear models over low precision data. MLWeaving provides a compact in-memory representation that enables the retrieval of data at any level of precision. MLWeaving also provides a highly efficient implementation of stochastic gradient descent on FPGAs and enables the dynamic tuning of precision, instead of using a fixed precision level during learning. Experimental results show that MLWeaving converges up to 16 x faster than low-precision implementations of first-order methods on CPUs.

A parallel and distributed stochastic gradient descent implementation using commodity clusters

Deep Learning is an increasingly important subdomain of artificial intelligence, which benefits from training on Big Data. The size and complexity of the model combined with the size of the training dataset makes the training process very computationally and temporally expensive. Accelerating the training process of Deep Learning using cluster computers faces many challenges ranging from distributed optimizers to the large communication overhead specific to systems with off the shelf networking components. In this paper, we present a novel distributed and parallel implementation of stochastic gradient descent (SGD) on a distributed cluster of commodity computers. We use high-performance computing cluster (HPCC) systems as the underlying cluster environment for the implementation. We overview how the HPCC systems platform provides the environment for distributed and parallel Deep Learning, how it provides a facility to work with third party open source libraries such as TensorFlow, and detail our use of third-party libraries and HPCC functionality for implementation. We provide experimental results that validate our work and show that our implementation can scale with respect to both dataset size and the number of compute nodes in the cluster.

Differentially Private Distributed Constrained Optimization

Many resource allocation problems can be formulated as an optimization problem whose constraints contain sensitive information about participating users. This paper concerns solving this kind of optimization problem in a distributed manner while protecting the privacy of user information. Without privacy considerations, existing distributed algorithms normally consist in a central entity computing and broadcasting certain public coordination signals to participating users. However, the coordination signals often depend on user information, so that an adversary who has access to the coordination signals can potentially decode information on individual users and put user privacy at risk. We present a distributed optimization algorithm that preserves differential privacy, which is a strong notion that guarantees user privacy regardless of any auxiliary information an adversary may have. The algorithm achieves privacy by perturbing the public signals with additive noise, whose magnitude is determined by the sensitivity of the projection operation onto user-specified constraints. By viewing the differentially private algorithm as an implementation of stochastic gradient descent, we are able to derive a bound for the suboptimality of the algorithm. We illustrate the implementation of our algorithm via a case study of electric vehicle charging. Specifically, we derive the sensitivity and present numerical simulations for the algorithm. Through numerical simulations, we are able to investigate various aspects of the algorithm when being used in practice, including the choice of step size, number of iterations, and the trade-off between privacy level and suboptimality.

Ant colony optimization and stochastic gradient descent.

In this article, we study the relationship between the two techniques known as ant colony optimization (ACO) and stochastic gradient descent. More precisely, we show that some empirical ACO algorithms approximate stochastic gradient descent in the space of pheromones, and we propose an implementation of stochastic gradient descent that belongs to the family of ACO algorithms. We then use this insight to explore the mutual contributions of the two techniques.