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Register a new userTaming neural networks with TUSLA: Non-convex learning via adaptive stochastic gradient Langevin algorithms
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Added by
Sotirios Sabanis
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Artificial neural networks (ANNs) are typically highly nonlinear systems which are finely tuned via the optimization of their associated, non-convex loss functions. Typically, the gradient of any such loss function fails to be dissipative making the use of widely-accepted (stochastic) gradient descent methods problematic. We offer a new learning algorithm based on an appropriately constructed variant of the popular stochastic gradient Langevin dynamics (SGLD), which is called tamed unadjusted stochastic Langevin algorithm (TUSLA). We also provide a nonasymptotic analysis of the new algorithms convergence properties in the context of non-convex learning problems with the use of ANNs. Thus, we provide finite-time guarantees for TUSLA to find approximate minimizers of both empirical and population risks. The roots of the TUSLA algorithm are based on the taming technology for diffusion processes with superlinear coefficients as developed in citet{tamed-euler, SabanisAoAP} and for MCMC algorithms in citet{tula}. Numerical experiments are presented which confirm the theoretical findings and illustrate the need for the use of the new algorithm in comparison to vanilla SGLD within the framework of ANNs.
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We present a new class of adaptive stochastic optimization algorithms, which overcomes many of the known shortcomings of popular adaptive optimizers that are currently used for the fine tuning of artificial neural networks (ANNs). Its underpinning theory relies on advances of Eulers polygonal approximations for stochastic differential equations (SDEs) with monotone coefficients. As a result, it inherits the stability properties of tamed algorithms, while it addresses other known issues, e.g. vanishing gradients in ANNs. In particular, we provide an nonasymptotic analysis and full theoretical guarantees for the convergence properties of an algorithm of this novel class, which we named TH$varepsilon$O POULA (or, simply, TheoPouLa). Finally, several experiments are presented with different types of ANNs, which show the superior performance of TheoPouLa over many popular adaptive optimization algorithms.
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