Beyond Backprop: Online Alternating Minimization with Auxiliary Variables

We propose a novel online alternating minimization (AltMin) algorithm for training deep neural networks, provide theoretical convergence guarantees and demonstrate its advantages on several classification tasks as compared both to standard backpropagation with stochastic gradient descent (backprop-SGD) and to offline alternating minimization. The key difference from backpropagation is an explicit optimization over hidden activations, which eliminates gradient chain computation in backprop, and breaks the weight training problem into independent, local optimization subproblems; this allows to avoid vanishing gradient issues, simplify handling non-differentiable nonlinearities, and perform parallel weight updates across the layers. Moreover, parallel local synaptic weight optimization with explicit activation propagation is a step closer to a more biologically plausible learning model than backpropagation, whose biological implausibility has been frequently criticized. Finally, the online nature of our approach allows to handle very large datasets, as well as continual, lifelong learning, which is our key contribution on top of recently proposed offline alternating minimization schemes (e.g., (Carreira-Perpinan andWang 2014), (Taylor et al. 2016)).