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Register a new userOnline Learning Rate Adaptation with Hypergradient Descent
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We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by applying it to stochastic gradient descent, stochastic gradient descent with Nesterov momentum, and Adam, showing that it significantly reduces the need for the manual tuning of the initial learning rate for these commonly used algorithms. Our method works by dynamically updating the learning rate during optimization using the gradient with respect to the learning rate of the update rule itself. Computing this hypergradient needs little additional computation, requires only one extra copy of the original gradient to be stored in memory, and relies upon nothing more than what is provided by reverse-mode automatic differentiation.
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We provide a new adaptive method for online convex optimization, MetaGrad, that is robust to general convex losses but achieves faster rates for a broad class of special functions, including exp-concave and strongly convex functions, but also various types of stochastic and non-stochastic functions without any curvature. We prove this by drawing a connection to the Bernstein condition, which is known to imply fast rates in offline statistical learning. MetaGrad further adapts automatically to the size of the gradients. Its main feature is that it simultaneously considers multiple learning rates, which are weighted directly proportional to their empirical performance on the data using a new meta-algorithm. We provide thr
We propose Banker-OMD, a novel framework generalizing the classical Online Mirror Descent (OMD) technique in online learning algorithm design. Banker-OMD allows algorithms to robustly handle delayed feedback, and offers a general methodology for achieving $tilde{O}(sqrt{T} + sqrt{D})$-style regret bounds in various delayed-feedback online learning tasks, where $T$ is the time horizon length and $D$ is the total feedback delay. We demonstrate the power of Banker-OMD with applications to three important bandit scenarios with delayed feedback, including delayed adversarial Multi-armed bandits (MAB), delayed adversarial linear bandits, and a novel delayed best-of-both-worlds MAB setting. Banker-OMD achieves nearly-optimal performance in all the three settings. In particular, it leads to the first delayed adversarial linear bandit algorithm achieving $tilde{O}(text{poly}(n)(sqrt{T} + sqrt{D}))$ regret.
We study the problem of fitting task-specific learning rate schedules from the perspective of hyperparameter optimization, aiming at good generalization. We describe the structure of the gradient of a validation error w.r.t. the learning rate schedule -- the hypergradient. Based on this, we introduce MARTHE, a novel online algorithm guided by cheap approximations of the hypergradient that uses past information from the optimization trajectory to simulate future behaviour. It interpolates between two recent techniques, RTHO (Franceschi et al., 2017) and HD (Baydin et al. 2018), and is able to produce learning rate schedules that are more stable leading to models that generalize better.
We propose to optimize neural networks with a uniformly-distributed random learning rate. The associated stochastic gradient descent algorithm can be approximated by continuous stochastic equations and analyzed within the Fokker-Planck formalism. In the small learning rate regime, the training process is characterized by an effective temperature which depends on the average learning rate, the mini-batch size and the momentum of the optimization algorithm. By comparing the random learning rate protocol with cyclic and constant protocols, we suggest that the random choice is generically the best strategy in the small learning rate regime, yielding better regularization without extra computational cost. We provide supporting evidence through experiments on both shallow, fully-connected and deep, convolutional neural networks for image classification on the MNIST and CIFAR10 datasets.
In this paper, we address the Online Unsupervised Domain Adaptation (OUDA) problem, where the target data are unlabelled and arriving sequentially. The traditional methods on the OUDA problem mainly focus on transforming each arriving target data to the source domain, and they do not sufficiently consider the temporal coherency and accumulative statistics among the arriving target data. We propose a multi-step framework for the OUDA problem, which institutes a novel method to compute the mean-target subspace inspired by the geometrical interpretation on the Euclidean space. This mean-target subspace contains accumulative temporal information among the arrived target data. Moreover, the transformation matrix computed from the mean-target subspace is applied to the next target data as a preprocessing step, aligning the target data closer to the source domain. Experiments on four datasets demonstrated the contribution of each step in our proposed multi-step OUDA framework and its performance over previous approaches.
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