Related papers: Theoretical Challenges in Learning for Branch-and-…

A core step of every algorithm for learning regression trees is the selection of the best splitting variable from the available covariates and the corresponding split point. Early tree algorithms (e.g., AID, CART) employed greedy search…

Inferring a decision tree from a given dataset is one of the classic problems in machine learning. This problem consists of buildings, from a labelled dataset, a tree such that each node corresponds to a class and a path between the tree…

This paper presents and evaluates two pruning techniques to reinforce the efficiency of constraint optimization solvers based on multi-valued decision-diagrams (MDD). It adopts the branch-and-bound framework proposed by Bergman et al. in…

Mixed integer linear programs are commonly solved by Branch and Bound algorithms. A key factor of the efficiency of the most successful commercial solvers is their fine-tuned heuristics. In this paper, we leverage patterns in real-world…

While chain-of-thought prompting with Best-of-N (BoN) selection has become popular for mathematical reasoning in large language models (LLMs), its linear structure fails to capture the branching and exploratory nature of complex…

We develop a theoretical framework for the analysis of oblique decision trees, where the splits at each decision node occur at linear combinations of the covariates (as opposed to conventional tree constructions that force axis-aligned…

In line with the growing trend of using machine learning to help solve combinatorial optimisation problems, one promising idea is to improve node selection within a mixed integer programming (MIP) branch-and-bound tree by using a learned…

This paper presents the first generic bi-objective binary linear branch-and-cut algorithm. Studying the impact of valid inequalities in solution and objective spaces, two cutting frameworks are proposed. The multi-point separation problem…

This paper shows that decision trees constructed with Classification and Regression Trees (CART) and C4.5 methodology are consistent for regression and classification tasks, even when the number of predictor variables grows…

A modern radar may be designed to perform multiple functions, such as surveillance, tracking, and fire control. Each function requires the radar to execute a number of transmit-receive tasks. A radar resource management (RRM) module makes…

Neural networks have achieved dramatic improvements in recent years and depict the state-of-the-art methods for many real-world tasks nowadays. One drawback is, however, that many of these models are overparameterized, which makes them both…

Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split:…

Standard planners for sequential decision making (including Monte Carlo planning, tree search, dynamic programming, etc.) are constrained by an implicit sequential planning assumption: The order in which a plan is constructed is the same in…

Branch-and-bound algorithms (B&B) and polynomial-time approximation schemes (PTAS) are two seemingly distant areas of combinatorial optimization. We intend to (partially) bridge the gap between them while expanding the boundary of…

We present an algorithm for learning decision trees using stochastic gradient information as the source of supervision. In contrast to previous approaches to gradient-based tree learning, our method operates in the incremental learning…

Given the remarkable capabilities of large language models (LLMs), there has been a growing interest in evaluating their similarity to the human brain. One approach towards quantifying this similarity is by measuring how well a model…

Standard supervised learning procedures are validated against a test set that is assumed to have come from the same distribution as the training data. However, in many problems, the test data may have come from a different distribution. We…

Long-horizon planning in realistic environments requires the ability to reason over sequential tasks in high-dimensional state spaces with complex dynamics. Classical motion planning algorithms, such as rapidly-exploring random trees, are…

The remarkable progress in deep learning in recent years is largely driven by improvements in scale, where bigger models are trained on larger datasets for longer schedules. To predict the benefit of scale empirically, we argue for a more…

Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch &…