5,462 research outputs found
Balancing the Communication Load of Asynchronously Parallelized Machine Learning Algorithms
Stochastic Gradient Descent (SGD) is the standard numerical method used to
solve the core optimization problem for the vast majority of machine learning
(ML) algorithms. In the context of large scale learning, as utilized by many
Big Data applications, efficient parallelization of SGD is in the focus of
active research. Recently, we were able to show that the asynchronous
communication paradigm can be applied to achieve a fast and scalable
parallelization of SGD. Asynchronous Stochastic Gradient Descent (ASGD)
outperforms other, mostly MapReduce based, parallel algorithms solving large
scale machine learning problems. In this paper, we investigate the impact of
asynchronous communication frequency and message size on the performance of
ASGD applied to large scale ML on HTC cluster and cloud environments. We
introduce a novel algorithm for the automatic balancing of the asynchronous
communication load, which allows to adapt ASGD to changing network bandwidths
and latencies.Comment: arXiv admin note: substantial text overlap with arXiv:1505.0495
Efficient Optimization of Loops and Limits with Randomized Telescoping Sums
We consider optimization problems in which the objective requires an inner
loop with many steps or is the limit of a sequence of increasingly costly
approximations. Meta-learning, training recurrent neural networks, and
optimization of the solutions to differential equations are all examples of
optimization problems with this character. In such problems, it can be
expensive to compute the objective function value and its gradient, but
truncating the loop or using less accurate approximations can induce biases
that damage the overall solution. We propose randomized telescope (RT) gradient
estimators, which represent the objective as the sum of a telescoping series
and sample linear combinations of terms to provide cheap unbiased gradient
estimates. We identify conditions under which RT estimators achieve
optimization convergence rates independent of the length of the loop or the
required accuracy of the approximation. We also derive a method for tuning RT
estimators online to maximize a lower bound on the expected decrease in loss
per unit of computation. We evaluate our adaptive RT estimators on a range of
applications including meta-optimization of learning rates, variational
inference of ODE parameters, and training an LSTM to model long sequences
Local SGD Converges Fast and Communicates Little
Mini-batch stochastic gradient descent (SGD) is state of the art in large
scale distributed training. The scheme can reach a linear speedup with respect
to the number of workers, but this is rarely seen in practice as the scheme
often suffers from large network delays and bandwidth limits. To overcome this
communication bottleneck recent works propose to reduce the communication
frequency. An algorithm of this type is local SGD that runs SGD independently
in parallel on different workers and averages the sequences only once in a
while.
This scheme shows promising results in practice, but eluded thorough
theoretical analysis. We prove concise convergence rates for local SGD on
convex problems and show that it converges at the same rate as mini-batch SGD
in terms of number of evaluated gradients, that is, the scheme achieves linear
speedup in the number of workers and mini-batch size. The number of
communication rounds can be reduced up to a factor of T^{1/2}---where T denotes
the number of total steps---compared to mini-batch SGD. This also holds for
asynchronous implementations. Local SGD can also be used for large scale
training of deep learning models.
The results shown here aim serving as a guideline to further explore the
theoretical and practical aspects of local SGD in these applications.Comment: to appear at ICLR 2019, 19 page
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