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Decision rules that explicitly account for non-probabilistic evaluation metrics in machine translation typically require special training, often to estimate parameters in exponential models that govern the search space and the selection of candidate translations. While the traditional Maximum A Posteriori (MAP) decision rule can be optimized as a piecewise linear function in a greedy search of the parameter space, the Minimum Bayes Risk (MBR) decision rule is not well suited to this technique, a condition that makes past results difficult to compare. We present a novel training approach for non-tractable decision rules, allowing us to compare and evaluate these and other decision rules on a large scale translation task, taking advantage of the high dimensional parameter space available to the phrase based Pharaoh decoder. This comparison is timely, and important, as decoders evolve to represent more complex search space decisions and are evaluated against innovative evaluation metrics of translation quality.