  In Online Learning to Rank (OLTR) the aim is to find an optimal ranking model
by interacting with users. When learning from user behavior, systems must
interact with users while simultaneously learning from those interactions.
Unlike other Learning to Rank (LTR) settings, existing research in this field
has been limited to linear models. This is due to the speed-quality tradeoff
that arises when selecting models: complex models are more expressive and can
find the best rankings but need more user interactions to do so, a requirement
that risks frustrating users during training. Conversely, simpler models can be
optimized on fewer interactions and thus provide a better user experience, but
they will converge towards suboptimal rankings. This tradeoff creates a
deadlock, since novel models will not be able to improve either the user
experience or the final convergence point, without sacrificing the other. Our
contribution is twofold. First, we introduce a fast OLTR model called Sim-MGD
that addresses the speed aspect of the speed-quality tradeoff. Sim-MGD ranks
documents based on similarities with reference documents. It converges rapidly
and, hence, gives a better user experience but it does not converge towards the
optimal rankings. Second, we contribute Cascading Multileave Gradient Descent
(C-MGD) for OLTR that directly addresses the speed-quality tradeoff by using a
cascade that enables combinations of the best of two worlds: fast learning and
high quality final convergence. C-MGD can provide the better user experience of
Sim-MGD while maintaining the same convergence as the state-of-the-art MGD
model. This opens the door for future work to design new models for OLTR
without having to deal with the speed-quality tradeoff.
