This paper presents a novel online relevant set algorithm for a linearly-scored block sequence translation model. The key component is a new procedure to directly optimize the global scoring function used by a statistical machine translation (SMT) decoder. This training procedure treats the decoder as a black-box, and thus can be used to optimize any decoding scheme. The novel algorithm is evaluated using different feature types: 1) commonly used probabilistic features, such as translation, language, or distortion model probabilities, and 2) binary features. In particular, encouraging results on a standard ArabicEnglish translation task are presented for a translation system that uses only binary feature functions. To further demonstrate the effectiveness of the novel training algorithm, a detailed comparison with the widely used minimum-error-rate (MER) training algorithm [2] is presented using the same decoder and feature set. The online algorithm is simplified by introducing so-call...