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Sparse decision trees are one of the most common forms of interpretablemodels. While recent advances have produced algorithms that fully optimizesparse decision trees for prediction, that work does not address policy design,because the algorithms cannot handle weighted data samples. Specifically, theyrely on the discreteness of the loss function, which means that real-valuedweights cannot be directly used. For example, none of the existing techniquesproduce policies that incorporate inverse propensity weighting on individualdata points. We present three algorithms for efficient sparse weighted decisiontree optimization. The first approach directly optimizes the weighted lossfunction; however, it tends to be computationally inefficient for largedatasets. Our second approach, which scales more efficiently, transformsweights to integer values and uses data duplication to transform the weighteddecision tree optimization problem into an unweighted (but larger) counterpart.Our third algorithm, which scales to much larger datasets, uses a randomizedprocedure that samples each data point with a probability proportional to itsweight. We present theoretical bounds on the error of the two fast methods andshow experimentally that these methods can be two orders of magnitude fasterthan the direct optimization of the weighted loss, without losing significantaccuracy.

Fast Optimization of Weighted Sparse Decision Trees for use in Optimal Treatment Regimes and Optimal Policy Design