This paper extends the minimum Bayes-risk framework to incorporate a loss function specific to the task and the ASR system. The errors are modeled as a noisy channel and the parameters are learned from the data. The resulting loss function is used in the risk criterion for decoding. Experiments on a large vocabulary conversational speech recognition system demonstrate significant gains of about 1% absolute over MAP hypothesis and about 0.6% absolute over untrained loss function. The approach is general enough to be applicable to other sequence recognition problems such as in Optical Character Recognition (OCR) and in analysis of biological sequences.