  As automatic speaker verification (ASV) systems are vulnerable to spoofing
attacks, they are typically used in conjunction with spoofing countermeasure
(CM) systems to improve security. For example, the CM can first determine
whether the input is human speech, then the ASV can determine whether this
speech matches the speaker's identity. The performance of such a tandem system
can be measured with a tandem detection cost function (t-DCF). However, ASV and
CM systems are usually trained separately, using different metrics and data,
which does not optimize their combined performance. In this work, we propose to
optimize the tandem system directly by creating a differentiable version of
t-DCF and employing techniques from reinforcement learning. The results
indicate that these approaches offer better outcomes than finetuning, with our
method providing a 20% relative improvement in the t-DCF in the ASVSpoof19
dataset in a constrained setting.
