In many computational tasks and dynamical systems, asynchrony and randomization are naturally present and have been considered as ways to increase the speed and reduce the cost of computation while compromising the accuracy and convergence rate. In this work, we show the additional benefits of randomization and asynchrony on the stability of linear dynamical systems. We introduce a natural model for random asynchronous linear time-invariant (LTI) systems which generalizes the standard (synchronous) LTI systems. In this model, each state variable is updated randomly and asynchronously with some probability according to the underlying system dynamics. We examine how the mean-square stability of random asynchronous LTI systems vary with respect to randomization and asynchrony. Surprisingly, we show that the stability of random asynchronous LTI systems does not imply or is not implied by the stability of the synchronous variant of the system and an unstable synchronous system can be stabilized via randomization and/or asynchrony. We further study a special case of the introduced model, namely randomized LTI systems, where each state element is updated randomly with some fixed but unknown probability. We consider the problem of system identification of unknown randomized LTI systems using the precise characterization of mean-square stability via extended Lyapunov equation. For unknown randomized LTI systems, we propose a systematic identification method to recover the underlying dynamics. Given a single input/output trajectory, our method estimates the model parameters that govern the system dynamics, the update probability of state variables, and the noise covariance using the correlation matrices of collected data and the extended Lyapunov equation. Finally, we empirically demonstrate that the proposed method consistently recovers the underlying system dynamics with the optimal rate.
Technion - Israel Institute of Technology（以色列理工学院）；Habana-Labs（哈瓦那实验室）
Background: Recent developments have made it possible to accelerate neural networks training significantly using large batch sizes and data parallelism. Training in an asynchronous fashion, where delay occurs, can make training even more scalable. However, asynchronous training has its pitfalls, mainly a degradation in generalization, even after convergence of the algorithm. This gap remains not well understood, as theoretical analysis so far mainly focused on the convergence rate of asynchronous methods. Contributions: We examine asynchronous training from the perspective of dynamical stabili…
Distributed asynchronous SGD has become widely used for deep learning in large-scale systems, but remains notorious for its instability when increasing the number of workers. In this work, we study the dynamics of distributed asynchronous SGD under the lens of Lagrangian mechanics. Using this description, we introduce the concept of energy to describe the optimization process and derive a sufficient condition ensuring its stability as long as the collective energy induced by the active workers remains below the energy of a target synchronous process. Making use of this criterion, we derive a s…
Courant Institute, NYU（纽约大学柯朗研究所）；Center for Data Science, NYU（纽约大学数据科学中心）；Facebook AI Research（脸书人工智能研究院）
We study the problem of stochastic optimization for deep learning in the parallel computing environment under communication constraints. A new algorithm is proposed in this setting where the communication and coordination of work among concurrent processes (local workers), is based on an elastic force which links the parameters they compute with a center variable stored by the parameter server (master). The algorithm enables the local workers to perform more exploration, i.e. the algorithm allows the local variables to fluctuate further from the center variable by reducing the amount of commun…
Yale University（耶鲁大学）；University of Central Florida（中佛罗里达大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We propose ACProp (Asynchronous-centering-Prop), an adaptive optimizer which combines centering of second momentum and asynchronous update (e.g. for $t$-th update, denominator uses information up to step $t-1$, while numerator uses gradient at $t$-th step). ACProp has both strong theoretical properties and empirical performance. With the example by Reddi et al. (2018), we show that asynchronous optimizers (e.g. AdaShift, ACProp) have weaker convergence condition than synchronous optimizers (e.g. Adam, RMSProp, AdaBelief); within asynchronous optimizers, we show that centering of second momentu…
The performance of fully synchronized distributed systems has faced a bottleneck due to the big data trend, under which asynchronous distributed systems are becoming a major popularity due to their powerful scalability. In this paper, we study the generalization performance of stochastic gradient descent (SGD) on a distributed asynchronous system. The system consists of multiple worker machines that compute stochastic gradients which are further sent to and aggregated on a common parameter server to update the variables, and the communication in the system suffers from possible delays. Under t…
The Ohio State University（俄亥俄州立大学）；Iowa State University（爱荷华州立大学）
To increase the training speed of distributed learning, recent years have witnessed a significant amount of interest in developing both synchronous and asynchronous distributed stochastic variance-reduced optimization methods. However, all existing synchronous and asynchronous distributed training algorithms suffer from various limitations in either convergence speed or implementation complexity. This motivates us to propose an algorithm called STNTHESIS (semi-asynchronous path-integrated stochastic gradient search), which leverages the special structure of the variance-reduction framework to …
Towards Understanding the Generalizability of Delayed Stochastic Gradient Descent
Intelligent Game and Decision Lab（智能游戏与决策实验室）；College of Computer Science and Technology（计算机科学与技术学院）；National University of Defense Technology（国防科技大学）；Sun Yat-sen University（中山大学）；JD Explore Academy（京东探索研究院）
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
Deep reinforcement learning (DRL) algorithms and evolution strategies (ES) have been applied to various tasks, showing excellent performances. These have the opposite properties, with DRL having good sample efficiency and poor stability, while ES being vice versa. Recently, there have been attempts to combine these algorithms, but these methods fully rely on synchronous update scheme, making it not ideal to maximize the benefits of the parallelism in ES. To solve this challenge, asynchronous update scheme was introduced, which is capable of good time-efficiency and diverse policy exploration. …
The University of Hong Kong（香港大学）；Shanghai Jiao Tong University（上海交通大学）；Gradient；University of Southern California（南加州大学）；The Hong Kong Polytechnic University（香港理工大学）
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Deep reinforcement learning (RL) is computationally demanding and requires processing of many data points. Synchronous methods enjoy training stability while having lower data throughput. In contrast, asynchronous methods achieve high throughput but suffer from stability issues and lower sample efficiency due to `stale policies.' To combine the advantages of both methods we propose High-Throughput Synchronous Deep Reinforcement Learning (HTS-RL). In HTS-RL, we perform learning and rollouts concurrently, devise a system design which avoids `stale policies' and ensure that actors interact with e…
In this paper, we investigate the problem of system identification for autonomous Markov jump linear systems (MJS) with complete state observations. We propose switched least squares method for identification of MJS, show that this method is strongly consistent, and derive data-dependent and data-independent rates of convergence. In particular, our data-independent rate of convergence shows that, almost surely, the system identification error is $\mathcal{O}\big(\sqrt{\log(T)/T} \big)$ where $T$ is the time horizon. These results show that switched least squares method for MJS has the same rat…
Recently, Winter and Hahn [1] commented on our work on identifying subtypes of major psychiatry disorders (MPDs) based on neurobiological features using machine learning [2]. They questioned the generalizability of our methods and the statistical significance, stability, and overfitting of the results, and proposed a pipeline for disease subtyping. We appreciate their earnest consideration of our work, however, we need to point out their misconceptions of basic machine-learning concepts and delineate some key issues involved.
This paper proposes methods for identification of large-scale networked systems with guarantees that the resulting model will be contracting -- a strong form of nonlinear stability -- and/or monotone, i.e. order relations between states are preserved. The main challenges that we address are: simultaneously searching for model parameters and a certificate of stability, and scalability to networks with hundreds or thousands of nodes. We propose a model set that admits convex constraints for stability and monotonicity, and has a separable structure that allows distributed identification via the a…
Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamics
RIAS Lab The Italian Institute of Artificial Intelligence for Industry（意大利人工智能工业研究所 RIAS 实验室）；Delft Center for Systems and Control, TU Delft（代尔夫特理工大学代尔夫特系统与控制中心）
