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Motivated by neural network training in low-bit floating and fixed-pointenvironments, this work studies the convergence of variants of SGD usingadaptive step sizes with computational error. Considering a general stochasticLipschitz continuous loss function, an asymptotic convergence result to aClarke stationary point is proven as well as the non-asymptotic convergence toan approximate stationary point. It is assumed that only an approximation ofthe loss function's stochastic gradient can be computed in addition to error incomputing the SGD step itself. Different variants of SGD are tested empiricallyin a variety of low-precision arithmetic environments, where improved test setaccuracy is observed compared to SGD for two image recognition tasks.

Variants of SGD for Lipschitz Continuous Loss Functions in Low-Precision Environments