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Register a new userNG+ : A Multi-Step Matrix-Product Natural Gradient Method for Deep Learning
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Minghan Yang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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In this paper, a novel second-order method called NG+ is proposed. By following the rule ``the shape of the gradient equals the shape of the parameter, we define a generalized fisher information matrix (GFIM) using the products of gradients in the matrix form rather than the traditional vectorization. Then, our generalized natural gradient direction is simply the inverse of the GFIM multiplies the gradient in the matrix form. Moreover, the GFIM and its inverse keeps the same for multiple steps so that the computational cost can be controlled and is comparable with the first-order methods. A global convergence is established under some mild conditions and a regret bound is also given for the online learning setting. Numerical results on image classification with ResNet50, quantum chemistry modeling with Schnet, neural machine translation with Transformer and recommendation system with DLRM illustrate that GN+ is competitive with the state-of-the-art methods.
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In this paper, we develop an efficient sketchy empirical natural gradient method (SENG) for large-scale deep learning problems. The empirical Fisher information matrix is usually low-rank since the sampling is only practical on a small amount of data at each iteration. Although the corresponding natural gradient direction lies in a small subspace, both the computational cost and memory requirement are still not tractable due to the high dimensionality. We design randomized techniques for different neural network structures to resolve these challenges. For layers with a reasonable dimension, sketching can be performed on a regularized least squares subproblem. Otherwise, since the gradient is a vectorization of the product between two matrices, we apply sketching on the low-rank approximations of these matrices to compute the most expensive parts. A distributed version of SENG is also developed for extremely large-scale applications. Global convergence to stationary points is established under some mild assumptions and a fast linear convergence is analyzed under the neural tangent kernel (NTK) case. Extensive experiments on convolutional neural networks show the competitiveness of SENG compared with the state-of-the-art methods. On the task ResNet50 with ImageNet-1k, SENG achieves 75.9% Top-1 testing accuracy within 41 epochs. Experiments on the distributed large-batch training show that the scaling efficiency is quite reasonable.
We propose a new approach to increase inference performance in environments that require a specific sequence of actions in order to be solved. This is for example the case for maze environments where ideally an optimal path is determined. Instead of learning a policy for a single step, we want to learn a policy that can predict n actions in advance. Our proposed method called policy horizon regression (PHR) uses knowledge of the environment sampled by A2C to learn an n dimensional policy vector in a policy distillation setup which yields n sequential actions per observation. We test our method on the MiniGrid and Pong environments and show drastic speedup during inference time by successfully predicting sequences of actions on a single observation.
Time series prediction with neural networks has been the focus of much research in the past few decades. Given the recent deep learning revolution, there has been much attention in using deep learning models for time series prediction, and hence it is important to evaluate their strengths and weaknesses. In this paper, we present an evaluation study that compares the performance of deep learning models for multi-step ahead time series prediction. The deep learning methods comprise simple recurrent neural networks, long short-term memory (LSTM) networks, bidirectional LSTM networks, encoder-decoder LSTM networks, and convolutional neural networks. We provide a further comparison with simple neural networks that use stochastic gradient descent and adaptive moment estimation (Adam) for training. We focus on univariate time series for multi-step-ahead prediction from benchmark time-series datasets and provide a further comparison of the results with related methods from the literature. The results show that the bidirectional and encoder-decoder LSTM network provides the best performance in accuracy for the given time series problems.
Although application examples of multilevel optimization have already been discussed since the 90s, the development of solution methods was almost limited to bilevel cases due to the difficulty of the problem. In recent years, in machine learning, Franceschi et al. have proposed a method for solving bilevel optimization problems by replacing their lower-level problems with the $T$ steepest descent update equations with some prechosen iteration number $T$. In this paper, we have developed a gradient-based algorithm for multilevel optimization with $n$ levels based on their idea and proved that our reformulation with $n T$ variables asymptotically converges to the original multilevel problem. As far as we know, this is one of the first algorithms with some theoretical guarantee for multilevel optimization. Numerical experiments show that a trilevel hyperparameter learning model considering data poisoning produces more stable prediction results than an existing bilevel hyperparameter learning model in noisy data settings.
We study reinforcement learning (RL) in a setting with a network of agents whose states and actions interact in a local manner where the objective is to find localized policies such that the (discounted) global reward is maximized. A fundamental challenge in this setting is that the state-action space size scales exponentially in the number of agents, rendering the problem intractable for large networks. In this paper, we propose a Scalable Actor-Critic (SAC) framework that exploits the network structure and finds a localized policy that is a $O(rho^kappa)$-approximation of a stationary point of the objective for some $rhoin(0,1)$, with complexity that scales with the local state-action space size of the largest $kappa$-hop neighborhood of the network.
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