  State-level minimum Bayes risk (sMBR) training has become the de facto
standard for sequence-level training of speech recognition acoustic models. It
has an elegant formulation using the expectation semiring, and gives large
improvements in word error rate (WER) over models trained solely using
cross-entropy (CE) or connectionist temporal classification (CTC). sMBR
training optimizes the expected number of frames at which the reference and
hypothesized acoustic states differ. It may be preferable to optimize the
expected WER, but WER does not interact well with the expectation semiring, and
previous approaches based on computing expected WER exactly involve expanding
the lattices used during training. In this paper we show how to perform
optimization of the expected WER by sampling paths from the lattices used
during conventional sMBR training. The gradient of the expected WER is itself
an expectation, and so may be approximated using Monte Carlo sampling. We show
experimentally that optimizing WER during acoustic model training gives 5%
relative improvement in WER over a well-tuned sMBR baseline on a 2-channel
query recognition task (Google Home).
