Accelerated Learning with Robustness to Adversarial Regressors
Massachusetts Institute of Technology（麻省理工学院）；Air Force Research Laboratory（空军研究实验室）；Brigham and Women’s Hospital（布莱根妇女医院）；Harvard Medical School（哈佛医学院）
Joseph E. Gaudio, Anuradha M. Annaswamy, José M. Moreu, Michael A. Bolender, Travis E. Gibson
High order momentum-based parameter update algorithms have seen widespread applications in training machine learning models. Recently, connections with variational approaches have led to the derivation of new learning algorithms with accelerated learning guarantees. Such methods however, have only considered the case of static regressors. There is a significant need for parameter update algorithms which can be proven stable in the presence of adversarial time-varying regressors, as is commonplace in control theory. In this paper, we propose a new discrete time algorithm which 1) provides stability and asymptotic convergence guarantees in the presence of adversarial regressors by leveraging insights from adaptive control theory and 2) provides non-asymptotic accelerated learning guarantees leveraging insights from convex optimization. In particular, our algorithm reaches an $ε$ sub-optimal point in at most $\tilde{\mathcal{O}}(1/\sqrtε)$ iterations when regressors are constant - matching lower bounds due to Nesterov of $Ω(1/\sqrtε)$, up to a $\log(1/ε)$ factor and provides guaranteed bounds for stability when regressors are time-varying. We provide numerical experiments for a variant of Nesterov's provably hard convex optimization problem with time-varying regressors, as well as the problem of recovering an image with a time-varying blur and noise using streaming data.
Massachusetts Institute of Technology（麻省理工学院）；Aurora Flight Sciences, a Boeing Company（波音公司旗下极光飞行科学公司）
Gradient-descent based iterative algorithms pervade a variety of problems in estimation, prediction, learning, control, and optimization. Recently iterative algorithms based on higher-order information have been explored in an attempt to lead to accelerated learning. In this paper, we explore a specific a high-order tuner that has been shown to result in stability with time-varying regressors in linearly parametrized systems, and accelerated convergence with constant regressors. We show that this tuner continues to provide bounded parameter estimates even if the gradients are corrupted by nois…
Iterative gradient-based algorithms have been increasingly applied for the training of a broad variety of machine learning models including large neural-nets. In particular, momentum-based methods, with accelerated learning guarantees, have received a lot of attention due to their provable guarantees of fast learning in certain classes of problems and multiple algorithms have been derived. However, properties for these methods hold only for constant regressors. When time-varying regressors occur, which is commonplace in dynamic systems, many of these momentum-based methods cannot guarantee sta…
Accelerated zero-order SGD under high-order smoothness and overparameterized regime
Lomonosov MSU（罗蒙诺索夫莫斯科大学）；ISP RAS（俄罗斯科学院信息问题研究所）；HSE University（高等经济大学）；MIPT（莫斯科物理技术学院）；MSU Institute for Artificial Intelligence（莫斯科大学人工智能研究所）；Innopolis University（因诺波利斯大学）；IITP RAS（俄罗斯科学院信息传输问题研究所）；Skoltech（斯科尔科沃科学技术研究院）
We consider two high-order tuners that have been shown to have accelerated performance, one based on Polyak's heavy ball method and another based on Nesterov's acceleration method. We show that parameter estimates are bounded and converge to the true values exponentially fast when the regressors are persistently exciting. Simulation results corroborate the accelerated performance and accelerated learning properties of these high-order tuners in comparison to algorithms based on normalized gradient descent.
Alternating gradient-descent-ascent (AltGDA) is an optimization algorithm that has been widely used for model training in various machine learning applications, which aims to solve a nonconvex minimax optimization problem. However, the existing studies show that it suffers from a high computation complexity in nonconvex minimax optimization. In this paper, we develop a single-loop and fast AltGDA-type algorithm that leverages proximal gradient updates and momentum acceleration to solve regularized nonconvex minimax optimization problems. By leveraging the momentum acceleration technique, we pr…
University of Pittsburgh（匹兹堡大学）；Simon Fraser University（西蒙弗雷泽大学）
In the paper, we propose a class of accelerated zeroth-order and first-order momentum methods for both nonconvex mini-optimization and minimax-optimization. Specifically, we propose a new accelerated zeroth-order momentum (Acc-ZOM) method for black-box mini-optimization where only function values can be obtained. Moreover, we prove that our Acc-ZOM method achieves a lower query complexity of $\tilde{O}(d^{3/4}ε^{-3})$ for finding an $ε$-stationary point, which improves the best known result by a factor of $O(d^{1/4})$ where $d$ denotes the variable dimension. In particular, our Acc-ZOM does no…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院（KAIST））；Seoul National University College of Medicine, Seoul National University Bundang Hospital（首尔大学医学院，首尔大学盆唐医院）
Recently, deep learning approaches for accelerated MRI have been extensively studied thanks to their high performance reconstruction in spite of significantly reduced runtime complexity. These neural networks are usually trained in a supervised manner, so matched pairs of subsampled and fully sampled k-space data are required. Unfortunately, it is often difficult to acquire matched fully sampled k-space data, since the acquisition of fully sampled k-space data requires long scan time and often leads to the change of the acquisition protocol. Therefore, unpaired deep learning without matched la…
This paper concerns the adaptive control of a class of discrete-time nonlinear systems with all states accessible. Recently, a high-order tuner algorithm was developed for the minimization of convex loss functions with time-varying regressors in the context of an identification problem. Based on Nesterov's algorithm, the high-order tuner was shown to guarantee bounded parameter estimation when regressors vary with time, and to lead to accelerated convergence of the tracking error when regressors are constant. In this paper, we apply the high-order tuner to the adaptive control of a particular …
We investigate the theoretical limits of pipeline parallel learning of deep learning architectures, a distributed setup in which the computation is distributed per layer instead of per example. For smooth convex and non-convex objective functions, we provide matching lower and upper complexity bounds and show that a naive pipeline parallelization of Nesterov's accelerated gradient descent is optimal. For non-smooth convex functions, we provide a novel algorithm coined Pipeline Parallel Random Smoothing (PPRS) that is within a $d^{1/4}$ multiplicative factor of the optimal convergence rate, whe…
Faster Margin Maximization Rates for Generic and Adversarially Robust Optimization Methods
College of Computing, Georgia Institute of Technology（佐治亚理工学院计算学院）；Google Research（谷歌研究院）；School of Electrical and Computer Engineering, Georgia Institute of Technology（佐治亚理工学院电气与计算机工程学院）；School of Industrial and Systems Engineering, Georgia Institute of Technology（佐治亚理工学院工业与系统工程学院）
We introduce a new closed-loop architecture for the online solution of approximate optimal control problems in the context of continuous-time systems. Specifically, we introduce the first algorithm that incorporates dynamic momentum in actor-critic structures to control continuous-time dynamic plants with an affine structure in the input. By incorporating dynamic momentum in our algorithm, we are able to accelerate the convergence properties of the closed-loop system, achieving superior transient performance compared to traditional gradient-descent based techniques. In addition, by leveraging …
University of Washington（华盛顿大学）；Princeton University（普林斯顿大学）；Google Research（谷歌研究院）
This paper considers minimax optimization $\min_x \max_y f(x, y)$ in the challenging setting where $f$ can be both nonconvex in $x$ and nonconcave in $y$. Though such optimization problems arise in many machine learning paradigms including training generative adversarial networks (GANs) and adversarially robust models, many fundamental issues remain in theory, such as the absence of efficiently computable optimality notions, and cyclic or diverging behavior of existing algorithms. Our framework sprouts from the practical consideration that under a computational budget, the max-player can not f…
Improving the Convergence Rate of Ray Search Optimization for Query-Efficient Hard-Label Attacks
Institute of Cyberspace Security, Zhejiang University of Technology（浙江工业大学网络空间安全研究院）；JQ Investments（JQ投资）；Binjiang Institute of Artificial Intelligence, ZJUT（浙江工业大学滨江人工智能研究院）
We study fast algorithms for statistical regression problems under the strong contamination model, where the goal is to approximately optimize a generalized linear model (GLM) given adversarially corrupted samples. Prior works in this line of research were based on the robust gradient descent framework of Prasad et. al., a first-order method using biased gradient queries, or the Sever framework of Diakonikolas et. al., an iterative outlier-removal method calling a stationary point finder. We present nearly-linear time algorithms for robust regression problems with improved runtime or estimatio…
This paper investigates how to accelerate the convergence of distributed optimization algorithms on nonconvex problems with zeroth-order information available only. We propose a zeroth-order (ZO) distributed primal-dual stochastic coordinates algorithm equipped with "powerball" method to accelerate. We prove that the proposed algorithm has a convergence rate of $\mathcal{O}(\sqrt{p}/\sqrt{nT})$ for general nonconvex cost functions. We consider solving the generation of adversarial examples from black-box DNNs problem to compare with the existing state-of-the-art centralized and distributed ZO …
Caltech（加州理工学院）；UC Irvine（加州大学欧文分校）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）
Training neural networks on large datasets can be accelerated by distributing the workload over a network of machines. As datasets grow ever larger, networks of hundreds or thousands of machines become economically viable. The time cost of communicating gradients limits the effectiveness of using such large machine counts, as may the increased chance of network faults. We explore a particularly simple algorithm for robust, communication-efficient learning---signSGD. Workers transmit only the sign of their gradient vector to a server, and the overall update is decided by a majority vote. This a…
Zeroth-order (ZO) optimization is widely used to handle challenging tasks, such as query-based black-box adversarial attacks and reinforcement learning. Various attempts have been made to integrate prior information into the gradient estimation procedure based on finite differences, with promising empirical results. However, their convergence properties are not well understood. This paper makes an attempt to fill up this gap by analyzing the convergence of prior-guided ZO algorithms under a greedy descent framework with various gradient estimators. We provide a convergence guarantee for the pr…
