Learning Binary Decision Trees by Argmin Differentiation
This method improves tree learning for machine learning applications by enabling integration into deep networks, though it is incremental as it builds on existing optimization techniques.
The authors tackled the problem of learning binary decision trees for downstream tasks by simultaneously optimizing discrete and continuous parameters using argmin differentiation, resulting in trees competitive with existing methods in supervised and unsupervised settings and faster training than non-greedy baselines.
We address the problem of learning binary decision trees that partition data for some downstream task. We propose to learn discrete parameters (i.e., for tree traversals and node pruning) and continuous parameters (i.e., for tree split functions and prediction functions) simultaneously using argmin differentiation. We do so by sparsely relaxing a mixed-integer program for the discrete parameters, to allow gradients to pass through the program to continuous parameters. We derive customized algorithms to efficiently compute the forward and backward passes. This means that our tree learning procedure can be used as an (implicit) layer in arbitrary deep networks, and can be optimized with arbitrary loss functions. We demonstrate that our approach produces binary trees that are competitive with existing single tree and ensemble approaches, in both supervised and unsupervised settings. Further, apart from greedy approaches (which do not have competitive accuracies), our method is faster to train than all other tree-learning baselines we compare with. The code for reproducing the results is available at https://github.com/vzantedeschi/LatentTrees.