## Abstract

An autoencoder is a neural network for unsupervised learning, which consists of two parts: an encoder and a decoder. The encoder uses data as input, while the decoder uses the encoder output as input. The learning task for the autoencoder is to reconstruct data in the decoder output, despite that dimensionality of the encoder output is smaller than that of the data. In this project, a neural network for classification, i.e, a discriminator, together with an autoencoder, are trained by minimizing the sum of the loss functions of the two networks. We also add the constraints that each parameter of the encoder should equal the corresponding parameter of the discriminator. This corresponds to established semi-supervised methods, which improve classification results when only a fraction of the observations are labeled. In this work, we implement training by employing the Alternating Direction Method of Multipliers (ADMM), which allows the networks to be trained in a distributed manner. Since ADMM mainly has been used in convex distributed optimization, some adjustments are proposed to make it applicable for the non-convex problem of training neural networks. The most important change is that exact minimizations within ADMM are replaced by a number of Stochastic Gradient Descent (SGD) steps, the number of steps increases linearly with the ADMM iterations. The method is experimentally evaluated on two datasets, the so-called two-dimensional interleaving halfmoons and instances from the MNIST database of handwritten digits. The results show that our suggested method can improve classification results, with at least as good results as from unsupervised pretraining.