Decision trees are among the most widely used models in machine learning, largely due to their transparent decision logic, making them well-suited for high-stakes decision-making contexts. However, most existing learning algorithms focus on predictive performance, overlooking the joint optimization of other desirable properties, such as structural sparsity. In this work we propose TREVIS, an approach for learning decision trees with respect to complex objectives, based on the exploration of the latent space of a Tree Transformer Variational Auto-Encoder (TTVAE). By mapping decision trees onto