711 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
Bethe Projections for Non-Local Inference
Many inference problems in structured prediction are naturally solved by
augmenting a tractable dependency structure with complex, non-local auxiliary
objectives. This includes the mean field family of variational inference
algorithms, soft- or hard-constrained inference using Lagrangian relaxation or
linear programming, collective graphical models, and forms of semi-supervised
learning such as posterior regularization. We present a method to
discriminatively learn broad families of inference objectives, capturing
powerful non-local statistics of the latent variables, while maintaining
tractable and provably fast inference using non-Euclidean projected gradient
descent with a distance-generating function given by the Bethe entropy. We
demonstrate the performance and flexibility of our method by (1) extracting
structured citations from research papers by learning soft global constraints,
(2) achieving state-of-the-art results on a widely-used handwriting recognition
task using a novel learned non-convex inference procedure, and (3) providing a
fast and highly scalable algorithm for the challenging problem of inference in
a collective graphical model applied to bird migration.Comment: minor bug fix to appendix. appeared in UAI 201
Target-based Surrogates for Stochastic Optimization
We consider minimizing functions for which it is expensive to compute the
(possibly stochastic) gradient. Such functions are prevalent in reinforcement
learning, imitation learning and adversarial training. Our target optimization
framework uses the (expensive) gradient computation to construct surrogate
functions in a \emph{target space} (e.g. the logits output by a linear model
for classification) that can be minimized efficiently. This allows for multiple
parameter updates to the model, amortizing the cost of gradient computation. In
the full-batch setting, we prove that our surrogate is a global upper-bound on
the loss, and can be (locally) minimized using a black-box optimization
algorithm. We prove that the resulting majorization-minimization algorithm
ensures convergence to a stationary point of the loss. Next, we instantiate our
framework in the stochastic setting and propose the algorithm, which can
be viewed as projected stochastic gradient descent in the target space. This
connection enables us to prove theoretical guarantees for when minimizing
convex functions. Our framework allows the use of standard stochastic
optimization algorithms to construct surrogates which can be minimized by any
deterministic optimization method. To evaluate our framework, we consider a
suite of supervised learning and imitation learning problems. Our experiments
indicate the benefits of target optimization and the effectiveness of
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