6,702 research outputs found
Learning-to-Learn Stochastic Gradient Descent with Biased Regularization
We study the problem of learning-to-learn: inferring a learning algorithm
that works well on tasks sampled from an unknown distribution. As class of
algorithms we consider Stochastic Gradient Descent on the true risk regularized
by the square euclidean distance to a bias vector. We present an average excess
risk bound for such a learning algorithm. This result quantifies the potential
benefit of using a bias vector with respect to the unbiased case. We then
address the problem of estimating the bias from a sequence of tasks. We propose
a meta-algorithm which incrementally updates the bias, as new tasks are
observed. The low space and time complexity of this approach makes it appealing
in practice. We provide guarantees on the learning ability of the
meta-algorithm. A key feature of our results is that, when the number of tasks
grows and their variance is relatively small, our learning-to-learn approach
has a significant advantage over learning each task in isolation by Stochastic
Gradient Descent without a bias term. We report on numerical experiments which
demonstrate the effectiveness of our approach.Comment: 37 pages, 8 figure
Learning-to-Learn Stochastic Gradient Descent with Biased Regularization
We study the problem of learning-to-learn: inferring a learning algorithm that works well on tasks sampled from an unknown distribution. As class of algorithms we consider Stochastic Gradient Descent on the true risk regularized by the square euclidean distance to a bias vector. We present an average excess risk bound for such a learning algorithm. This result quantifies the potential benefit of using a bias vector with respect to the unbiased case. We then address the problem of estimating the bias from a sequence of tasks. We propose a meta-algorithm which incrementally updates the bias, as new tasks are observed. The low space and time complexity of this approach makes it appealing in practice. We provide guarantees on the learning ability of the meta-algorithm. A key feature of our results is that, when the number of tasks grows and their variance is relatively small, our learning-to-learn approach has a significant advantage over learning each task in isolation by Stochastic Gradient Descent without a bias term. We report on numerical experiments which demonstrate the effectiveness of our approach
Practical recommendations for gradient-based training of deep architectures
Learning algorithms related to artificial neural networks and in particular
for Deep Learning may seem to involve many bells and whistles, called
hyper-parameters. This chapter is meant as a practical guide with
recommendations for some of the most commonly used hyper-parameters, in
particular in the context of learning algorithms based on back-propagated
gradient and gradient-based optimization. It also discusses how to deal with
the fact that more interesting results can be obtained when allowing one to
adjust many hyper-parameters. Overall, it describes elements of the practice
used to successfully and efficiently train and debug large-scale and often deep
multi-layer neural networks. It closes with open questions about the training
difficulties observed with deeper architectures
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