Recursive least squares (RLS) algorithms were once widely used for training small-scale neural networks, due to their fast convergence. However, previous RLS algorithms are unsuitable for training deep neural networks (DNNs), since they have high computational complexity and too many preconditions. In this paper, to overcome these drawbacks, we propose three novel RLS optimization algorithms for training feedforward neural networks, convolutional neural networks and recurrent neural networks (including long short-term memory networks), by using the error backpropagation and our average-approximation RLS method, together with the equivalent gradients of the linear least squares loss function with respect to the linear outputs of hidden layers. Compared with previous RLS optimization algorithms, our algorithms are simple and elegant. They can be viewed as an improved stochastic gradient descent (SGD) algorithm, which uses the inverse autocorrelation matrix of each layer as the adaptive learning rate. Their time and space complexities are only several times those of SGD. They only require the loss function to be the mean squared error and the activation function of the output layer to be invertible. In fact, our algorithms can be also used in combination with other first-order optimization algorithms without requiring these two preconditions. In addition, we present two improved methods for our algorithms. Finally, we demonstrate their effectiveness compared to the Adam algorithm on MNIST, CIFAR-10 and IMDB datasets, and investigate the influences of their hyperparameters experimentally.
In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability. The kernel method is a powerful nonparametric modeling tool for pattern analysis and statistical signal processing. Through a nonlinear mapping, kernel methods transform the data into a set of points in a Reproducing Kernel Hilbert Space. KRLS achieves high accuracy and has fast convergence rate in stationary scenario. However the good performance is obtained …
ORFit: One-Pass Learning via Bridging Orthogonal Gradient Descent and Recursive Least-Squares
Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA 02139, USA（信息与决策系统实验室，麻省理工学院）；Centre for Assured and Connected Autonomy, Cranfield University, Cranfield, Bedfordshire MK43 0AL, UK（保障与连接自主性中心，克兰菲尔德大学）
Trajectory prediction plays a pivotal role in the field of intelligent vehicles. It currently suffers from several challenges,e.g., accumulative error in rollout process and weak adaptability in various scenarios. This paper proposes a parametric-learning recursive least squares (RLS) estimation based on deep neural network for trajectory prediction. We design a flexible plug-in module which can be readily implanted into rollout approaches. Goal points are proposed to capture the long-term prediction stability from the global perspective. We carried experiments out on the NGSIM dataset. The pr…
Stanford University（斯坦福大学）；Worcester Polytechnic Institute（伍斯特理工学院）；University of Illinois at Urbana Champaign（伊利诺伊大学厄巴纳-香槟分校）
We present a new kernel-based algorithm for modeling evenly distributed multidimensional datasets that does not rely on input space sparsification. The presented method reorganizes the typical single-layer kernel-based model into a deep hierarchical structure, such that the weights of a kernel model over each dimension are modeled over its adjacent dimension. We show that modeling weights in the suggested structure leads to significant computational speedup and improved modeling accuracy.
The echo state network (ESN) is a special type of recurrent neural networks for processing the time-series dataset. However, limited by the strong correlation among sequential samples of the agent, ESN-based policy control algorithms are difficult to use the recursive least squares (RLS) algorithm to update the ESN's parameters. To solve this problem, we propose two novel policy control algorithms, ESNRLS-Q and ESNRLS-Sarsa. Firstly, to reduce the correlation of training samples, we use the leaky integrator ESN and the mini-batch learning mode. Secondly, to make RLS suitable for training ESN i…
Southwest Jiaotong University（西南交通大学）；University of York（约克大学）；PUC-Rio（里约热内卢天主教大学）
This work develops a robust diffusion recursive least squares algorithm to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. This algorithm minimizes an exponentially weighted least-squares cost function subject to a time-dependent constraint on the squared norm of the intermediate estimate update at each node. With the help of side information, the constraint is recursively updated in a diffusion strategy. Moreover, a control strategy for resetting the constraint is also proposed to retain good tracking capability when the estimat…
Kernel Recursive Least Squares Dictionary Learning Algorithm
Electrical Engineering Department, Hamedan University of Technology（哈马丹技术大学电子工程系）；Department of Electrical and Computer Engineering, IDE, University of Stavanger（斯塔万格大学电子与计算机工程系）
As an important algorithm in deep reinforcement learning, advantage actor critic (A2C) has been widely succeeded in both discrete and continuous control tasks with raw pixel inputs, but its sample efficiency still needs to improve more. In traditional reinforcement learning, actor-critic algorithms generally use the recursive least squares (RLS) technology to update the parameter of linear function approximators for accelerating their convergence speed. However, A2C algorithms seldom use this technology to train deep neural networks (DNNs) for improving their sample efficiency. In this paper, …
Gordon Center for Medical Imaging（戈登医学影像中心）；Center for Advanced Medical Computing and Analysis（高级医学计算与分析中心）；Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）
Deterministic solutions are becoming more critical for interpretability. Weighted Least-Squares (WLS) has been widely used as a deterministic batch solution with a specific weight design. In the online settings of WLS, exact reweighting is necessary to converge to its batch settings. In order to comply with its necessity, the iteratively reweighted least-squares algorithm is mainly utilized with a linearly growing time complexity which is not attractive for online learning. Due to the high and growing computational costs, an efficient online formulation of reweighted least-squares is desired. …
Convolutional neural networks (CNNs) have succeeded in many practical applications. However, their high computation and storage requirements often make them difficult to deploy on resource-constrained devices. In order to tackle this issue, many pruning algorithms have been proposed for CNNs, but most of them can't prune CNNs to a reasonable level. In this paper, we propose a novel algorithm for training and pruning CNNs based on the recursive least squares (RLS) optimization. After training a CNN for some epochs, our algorithm combines inverse input autocorrelation matrices and weight matrice…
Most of the existing solutions to enterprise threat management are preventive approaches prescribing means to prevent policy violations with varying degrees of success. In this paper we consider the complementary scenario where a number of security violations have already occurred, or security threats, or vulnerabilities have been reported and a security administrator needs to generate optimal response to these security events. We present a principled approach to study and model the human expertise in responding to the emergent threats owing to these security events. A recursive Partial Least …
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Xiamen University（厦门大学）；Fudan University（复旦大学）；Duke University（杜克大学）
In this paper, we propose {\it \underline{R}ecursive} {\it \underline{I}mportance} {\it \underline{S}ketching} algorithm for {\it \underline{R}ank} constrained least squares {\it \underline{O}ptimization} (RISRO). The key step of RISRO is recursive importance sketching, a new sketching framework based on deterministically designed recursive projections, which significantly differs from the randomized sketching in the literature \citep{mahoney2011randomized,woodruff2014sketching}. Several existing algorithms in the literature can be reinterpreted under this new sketching framework and RISRO off…
Matrix factorization learned by implicit alternating least squares (iALS) is a popular baseline in recommender system research publications. iALS is known to be one of the most computationally efficient and scalable collaborative filtering methods. However, recent studies suggest that its prediction quality is not competitive with the current state of the art, in particular autoencoders and other item-based collaborative filtering methods. In this work, we revisit the iALS algorithm and present a bag of tricks that we found useful when applying iALS. We revisit four well-studied benchmarks whe…
Southwest University of Science and Technology（西南科技大学）；Sichuan University（四川大学）；Southwest Jiaotong University（西南交通大学）；University of York（约克大学）；PUC-Rio（里约热内卢天主教大学）
The dichotomous coordinate descent (DCD) algorithm has been successfully used for significant reduction in the complexity of recursive least squares (RLS) algorithms. In this work, we generalize the application of the DCD algorithm to RLS adaptive filtering in impulsive noise scenarios and derive a unified update formula. By employing different robust strategies against impulsive noise, we develop novel computationally efficient DCD-based robust recursive algorithms. Furthermore, to equip the proposed algorithms with the ability to track abrupt changes in unknown systems, a simple variable for…
The recursive least-squares (RLS) algorithm is one of the most well-known algorithms used in adaptive filtering, system identification and adaptive control. Its popularity is mainly due to its fast convergence speed, which is considered to be optimal in practice. In this paper, RLS methods are used to solve reinforcement learning problems, where two new reinforcement learning algorithms using linear value function approximators are proposed and analyzed. The two algorithms are called RLS-TD(lambda) and Fast-AHC (Fast Adaptive Heuristic Critic), respectively. RLS-TD(lambda) can be viewed as the…
