3,414 research outputs found
Stochastic Training of Neural Networks via Successive Convex Approximations
This paper proposes a new family of algorithms for training neural networks
(NNs). These are based on recent developments in the field of non-convex
optimization, going under the general name of successive convex approximation
(SCA) techniques. The basic idea is to iteratively replace the original
(non-convex, highly dimensional) learning problem with a sequence of (strongly
convex) approximations, which are both accurate and simple to optimize.
Differently from similar ideas (e.g., quasi-Newton algorithms), the
approximations can be constructed using only first-order information of the
neural network function, in a stochastic fashion, while exploiting the overall
structure of the learning problem for a faster convergence. We discuss several
use cases, based on different choices for the loss function (e.g., squared loss
and cross-entropy loss), and for the regularization of the NN's weights. We
experiment on several medium-sized benchmark problems, and on a large-scale
dataset involving simulated physical data. The results show how the algorithm
outperforms state-of-the-art techniques, providing faster convergence to a
better minimum. Additionally, we show how the algorithm can be easily
parallelized over multiple computational units without hindering its
performance. In particular, each computational unit can optimize a tailored
surrogate function defined on a randomly assigned subset of the input
variables, whose dimension can be selected depending entirely on the available
computational power.Comment: Preprint submitted to IEEE Transactions on Neural Networks and
Learning System
Optimization Methods for Inverse Problems
Optimization plays an important role in solving many inverse problems.
Indeed, the task of inversion often either involves or is fully cast as a
solution of an optimization problem. In this light, the mere non-linear,
non-convex, and large-scale nature of many of these inversions gives rise to
some very challenging optimization problems. The inverse problem community has
long been developing various techniques for solving such optimization tasks.
However, other, seemingly disjoint communities, such as that of machine
learning, have developed, almost in parallel, interesting alternative methods
which might have stayed under the radar of the inverse problem community. In
this survey, we aim to change that. In doing so, we first discuss current
state-of-the-art optimization methods widely used in inverse problems. We then
survey recent related advances in addressing similar challenges in problems
faced by the machine learning community, and discuss their potential advantages
for solving inverse problems. By highlighting the similarities among the
optimization challenges faced by the inverse problem and the machine learning
communities, we hope that this survey can serve as a bridge in bringing
together these two communities and encourage cross fertilization of ideas.Comment: 13 page
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