  Online Learning to Rank (OLTR) methods optimize rankers based on user
interactions. State-of-the-art OLTR methods are built specifically for linear
models. Their approaches do not extend well to non-linear models such as neural
networks. We introduce an entirely novel approach to OLTR that constructs a
weighted differentiable pairwise loss after each interaction: Pairwise
Differentiable Gradient Descent (PDGD). PDGD breaks away from the traditional
approach that relies on interleaving or multileaving and extensive sampling of
models to estimate gradients. Instead, its gradient is based on inferring
preferences between document pairs from user clicks and can optimize any
differentiable model. We prove that the gradient of PDGD is unbiased w.r.t.
user document pair preferences. Our experiments on the largest publicly
available Learning to Rank (LTR) datasets show considerable and significant
improvements under all levels of interaction noise. PDGD outperforms existing
OLTR methods both in terms of learning speed as well as final convergence.
Furthermore, unlike previous OLTR methods, PDGD also allows for non-linear
models to be optimized effectively. Our results show that using a neural
network leads to even better performance at convergence than a linear model. In
summary, PDGD is an efficient and unbiased OLTR approach that provides a better
user experience than previously possible.
