Topmoumoute Online Natural Gradient Algorithm

Guided by the goal of obtaining an optimization algorithm that is both fast and yields good generalization, we study the descent direction maximizing the de- crease in generalization error or the probability of not increasing generalization error. The surprising result is that from both the Bayesian and frequentist perspec- tives this can yield the natural gradient direction. Although that direction can be very expensive to compute we develop an efcient, general, online approximation to the natural gradient descent which is suited to large scale problems. We re- port experimental results showing much faster convergence in computation time and in number of iterations with TONGA (Topmoumoute Online natural Gradient Algorithm) than with stochastic gradient descent, even on very large datasets.