P-ADMMiRNN: Training RNN with Stable Convergence via An Efficient and Paralleled ADMM Approach

It is hard to train Recurrent Neural Network (RNN) with stable convergence and avoid gradient vanishing and exploding problems, as the weights in the recurrent unit are repeated from iteration to iteration. Moreover, RNN is sensitive to the initialization of weights and bias, which brings difficulties in training. The Alternating Direction Method of Multipliers (ADMM) has become a promising algorithm to train neural networks beyond traditional stochastic gradient algorithms with the gradient-free features and immunity to unsatisfactory conditions. However, ADMM could not be applied to train RNN directly since the state in the recurrent unit is repetitively updated over timesteps. Therefore, this work builds a new framework named ADMMiRNN upon the unfolded form of RNN to address the above challenges simultaneously. We also provide novel update rules and theoretical convergence analysis. We explicitly specify essential update rules in the iterations of ADMMiRNN with constructed approximation techniques and solutions to each sub-problem instead of vanilla ADMM. Numerical experiments are conducted on MNIST, IMDb, and text classification tasks. ADMMiRNN achieves convergent results and outperforms the compared baselines. Furthermore, ADMMiRNN trains RNN more stably without gradient vanishing or exploding than stochastic gradient algorithms. We also provide a distributed paralleled algorithm regarding ADMMiRNN, named P-ADMMiRNN, including Synchronous Parallel ADMMiRNN (SP-ADMMiRNN) and Asynchronous Parallel ADMMiRNN (AP-ADMMiRNN), which is the first to train RNN with ADMM in an asynchronous parallel manner. The source code is publicly available.