While the multiple sequence alignment output by an aligner strongly depends on the parameter values used for the alignment scoring function (such as the choice of gap penalties and substitution scores), most users rely on the single default parameter setting provided by the aligner. A different parameter setting, however, might yield a much higher-quality alignment for the specific set of input sequences. The problem of picking a good choice of parameter values for specific input sequences is called parameter advising. A parameter advisor has two ingredients: (i) a set of parameter choices to select from, and (ii) an estimator that provides an estimate of the accuracy of the alignment computed by the aligner using a parameter choice. The parameter advisor picks the parameter choice from the set whose resulting alignment has highest estimated accuracy. We consider for the first time the problem of learning the optimal set of parameter choices for a parameter advisor that uses a given accuracy estimator. The optimal set is one that maximizes the expected true accuracy of the resulting parameter advisor, averaged over a collection of training data. While we prove that learning an optimal set for an advisor is NP-complete, we show there is a natural approximation algorithm for this problem, and prove a tight bound on its approximation ratio. Experiments with an implementation of this approximation algorithm on biological benchmarks, using various accuracy estimators from the literature, show it finds sets for advisors that are surprisingly close to optimal. Furthermore, the resulting parameter advisors are significantly more accurate in practice than simply aligning with a single default parameter choice.