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Register a new userMemory Augmented Optimizers for Deep Learning
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Added by
Prasanna Parthasarathi
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Popular approaches for minimizing loss in data-driven learning often involve an abstraction or an explicit retention of the history of gradients for efficient parameter updates. The aggregated history of gradients nudges the parameter updates in the right direction even when the gradients at any given step are not informative. Although the history of gradients summarized in meta-parameters or explicitly stored in memory has been shown effective in theory and practice, the question of whether $all$ or only a subset of the gradients in the history are sufficient in deciding the parameter updates remains unanswered. In this paper, we propose a framework of memory-augmented gradient descent optimizers that retain a limited view of their gradient history in their internal memory. Such optimizers scale well to large real-life datasets, and our experiments show that the memory augmented extensions of standard optimizers enjoy accelerated convergence and improved performance on a majority of computer vision and language tasks that we considered. Additionally, we prove that the proposed class of optimizers with fixed-size memory converge under assumptions of strong convexity, regardless of which gradients are selected or how they are linearly combined to form the update step.
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Learning by integrating multiple heterogeneous data sources is a common requirement in many tasks. Collective Matrix Factorization (CMF) is a technique to learn shared latent representations from arbitrary collections of matrices. It can be used to simultaneously complete one or more matrices, for predicting the unknown entries. Classical CMF methods assume linearity in the interaction of latent factors which can be restrictive and fails to capture complex non-linear interactions. In this paper, we develop the first deep-learning based method, called dCMF, for unsupervised learning of multiple shared representations, that can model such non-linear interactions, from an arbitrary collection of matrices. We address optimization challenges that arise due to dependencies between shared representations through Multi-Task Bayesian Optimization and design an acquisition function adapted for collective learning of hyperparameters. Our experiments show that dCMF significantly outperforms previous CMF algorithms in integrating heterogeneous data for predictive modeling. Further, on two tasks - recommendation and prediction of gene-disease association - dCMF outperforms state-of-the-art matrix completion algorithms that can utilize auxiliary sources of information.
The need for fast and robust optimization algorithms are of critical importance in all areas of machine learning. This paper treats the task of designing optimization algorithms as an optimal control problem. Using regret as a metric for an algorithms performance, we study the existence, uniqueness and consistency of regret-optimal algorithms. By providing first-order optimality conditions for the control problem, we show that regret-optimal algorithms must satisfy a specific structure in their dynamics which we show is equivalent to performing dual-preconditioned gradient descent on the value function generated by its regret. Using these optimal dynamics, we provide bounds on their rates of convergence to solutions of convex optimization problems. Though closed-form optimal dynamics cannot be obtained in general, we present fast numerical methods for approximating them, generating optimization algorithms which directly optimize their long-term regret. Lastly, these are benchmarked against commonly used optimization algorithms to demonstrate their effectiveness.
Episodic memory-based methods can rapidly latch onto past successful strategies by a non-parametric memory and improve sample efficiency of traditional reinforcement learning. However, little effort is put into the continuous domain, where a state is never visited twice, and previous episodic methods fail to efficiently aggregate experience across trajectories. To address this problem, we propose Generalizable Episodic Memory (GEM), which effectively organizes the state-action values of episodic memory in a generalizable manner and supports implicit planning on memorized trajectories. GEM utilizes a double estimator to reduce the overestimation bias induced by value propagation in the planning process. Empirical evaluation shows that our method significantly outperforms existing trajectory-based methods on various MuJoCo continuous control tasks. To further show the general applicability, we evaluate our method on Atari games with discrete action space, which also shows a significant improvement over baseline algorithms.
Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second order statistics of the data, are far less prevalent despite strong theoretical properties, due to their prohibitive computation, memory and communication costs. In an attempt to bridge this gap between theoretical and practical optimization, we present a scalable implementation of a second-order preconditioned method (concretely, a variant of full-matrix Adagrad), that along with several critical algorithmic and numerical improvements, provides significant convergence and wall-clock time improvements compared to conventional first-order methods on state-of-the-art deep models. Our novel design effectively utilizes the prevalent heterogeneous hardware architecture for training deep models, consisting of a multicore CPU coupled with multiple accelerator units. We demonstrate superior performance compared to state-of-the-art on very large learning tasks such as machine translation with Transformers, language modeling with BERT, click-through rate prediction on Criteo, and image classification on ImageNet with ResNet-50.
Implicit deep learning prediction rules generalize the recursive rules of feedforward neural networks. Such rules are based on the solution of a fixed-point equation involving a single vector of hidden features, which is thus only implicitly defined. The implicit framework greatly simplifies the notation of deep learning, and opens up many new possibilities, in terms of novel architectures and algorithms, robustness analysis and design, interpretability, sparsity, and network architecture optimization.
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