On the Variance of Unbiased Online Recurrent Optimization

The recently proposed Unbiased Online Recurrent Optimization (uoro) algorithm (Tallec and Ollivier, 2018) uses an unbiased approximation of rtrl to achieve fully online gradientbased learningin rnns. In this work we analyze the variance of the gradient estimate computed by uoro, and propose several possible changes to the method which reduce this variance both in theory and practice. We also contribute significantly to the theoretical and intuitive understanding of uoro (and its existing variance reduction technique), and demonstrate a fundamental connection between its gradient estimate and the one that would be computed by reinforce if small amounts of noise were added to the rnn's hidden units.