Optimal Classification Trees for Continuous Feature Data Using Dynamic Programming with Branch-and-Bound

Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three. Therefore, most methods rely on a coarse binarization of continuous features to maintain scalability. We propose a novel algorithm that optimizes trees directly on the continuous feature data using dynamic programming with branch-and-bound. We develop new pruning techniques that eliminate many sub-optimal splits in the search when similar to previously computed splits and we provide an efficient subroutine for computing optimal depth-two trees. Our experiments demonstrate that these techniques improve runtime by one or more orders of magnitude over state-of-the-art optimal methods and improve test accuracy by 5% over greedy heuristics.

SimuDICE: Offline Policy Optimization Through World Model Updates and DICE Estimation

In offline reinforcement learning, deriving an effective policy from a pre-collected set of experiences is challenging due to the distribution mismatch between the target policy and the behavioral policy used to collect the data, as well as the limited sample size. Model-based reinforcement learning improves sample efficiency by generating simulated experiences using a learned dynamic model of the environment. However, these synthetic experiences often suffer from the same distribution mismatch. To address these challenges, we introduce SimuDICE, a framework that iteratively refines the initial policy derived from offline data using synthetically generated experiences from the world model. SimuDICE enhances the quality of these simulated experiences by adjusting the sampling probabilities of state-action pairs based on stationary DIstribution Correction Estimation (DICE) and the estimated confidence in the model's predictions. This approach guides policy improvement by balancing experiences similar to those frequently encountered with ones that have a distribution mismatch. Our experiments show that SimuDICE achieves performance comparable to existing algorithms while requiring fewer pre-collected experiences and planning steps, and it remains robust across varying data collection policies.