  The spoofing countermeasure (CM) systems in automatic speaker verification
(ASV) are not typically used in isolation of each other. These systems can be
combined, for example, into a cascaded system where CM produces first a
decision whether the input is synthetic or bona fide speech. In case the CM
decides it is a bona fide sample, then the ASV system will consider it for
speaker verification. End users of the system are not interested in the
performance of the individual sub-modules, but instead are interested in the
performance of the combined system. Such combination can be evaluated with
tandem detection cost function (t-DCF) measure, yet the individual components
are trained separately from each other using their own performance metrics. In
this work we study training the ASV and CM components together for a better
t-DCF measure by using reinforcement learning. We demonstrate that such
training procedure indeed is able to improve the performance of the combined
system, and does so with more reliable results than with the standard
supervised learning techniques we compare against.
