# DisCo-DSO: Coupling Discrete and Continuous Optimization for Efficient Generative Design in Hybrid Spaces

arXiv: https://arxiv.org/abs/2412.11051 · HTML: https://mlsanity.com/paper/2412.11051/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2024.

## Built on by (most cited first, 3 of 3)

- [DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experience](https://mlsanity.com/paper/2506.04282/) (2025)
- [FePySR: A Neural Feature Extraction Framework for Efficient and Scalable Symbolic Regression](https://mlsanity.com/paper/2605.12704/) (2026)
- [Learning Sparse Decision Trees via Transformer Variational Auto-Encoders](https://mlsanity.com/paper/2609.01430/) (2026)

## Abstract (arXiv)

We consider the challenge of black-box optimization within hybrid discrete-continuous and variable-length spaces, a problem that arises in various applications, such as decision tree learning and symbolic regression. We propose DisCo-DSO (Discrete-Continuous Deep Symbolic Optimization), a novel approach that uses a generative model to learn a joint distribution over discrete and continuous design variables to sample new hybrid designs. In contrast to standard decoupled approaches, in which the discrete and continuous variables are optimized separately, our joint optimization approach uses fewer objective function evaluations, is robust against non-differentiable objectives, and learns from prior samples to guide the search, leading to significant improvement in performance and sample efficiency. Our experiments on a diverse set of optimization tasks demonstrate that the advantages of DisCo-DSO become increasingly evident as the complexity of the problem increases. In particular, we illustrate DisCo-DSO's superiority over the state-of-the-art methods for interpretable reinforcement learning with decision trees.