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Test-time compute methods can significantly improve the reasoning capabilities and problem-solving accuracy of large language models (LLMs). However, these approaches require substantially more computational resources, with most compute…
Neural-network-based dynamics models learned from observational data have shown strong predictive capabilities for scene dynamics in robotic manipulation tasks. However, their inherent non-linearity presents significant challenges for…
Branch and bound algorithms have been developed for reliability analysis of coherent systems. They exhibit a set of advantages; in particular, they can find a computationally efficient representation of a system failure or survival event,…
We study exact sparse linear regression with an $\ell_0-\ell_2$ penalty and develop a branch-and-bound (BnB) algorithm explicitly designed for GPU execution. Starting from a perspective reformulation, we derive an interval relaxation that…
Decision trees are powerful tools for classification and regression that attract many researchers working in the burgeoning area of machine learning. One advantage of decision trees over other methods is their interpretability, which is…
We consider the resolution of learning problems involving $\ell_0$-regularization via Branch-and-Bound (BnB) algorithms. These methods explore regions of the feasible space of the problem and check whether they do not contain solutions…
The Maximum s-Bundle Problem (MBP) addresses the task of identifying a maximum s-bundle in a given graph. A graph G=(V, E) is called an s-bundle if its vertex connectivity is at least |V|-s, where the vertex connectivity equals the minimum…
On the occasion of the 20th Mixed Integer Program Workshop's computational competition, this work introduces a new approach for learning to solve MIPs online. Influence branching, a new graph-oriented variable selection strategy, is applied…
Choosing appropriate hyperparameters plays a crucial role in the success of neural networks as hyper-parameters directly control the behavior and performance of the training algorithms. To obtain efficient tuning, Bayesian optimization…
Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. During the past decades, enormous algorithmic progress has been made in solving…
This paper proposes a Mixed-Integer Linear Programming approach for the Soft Graph Clustering Problem. This is the first method that simultaneously allocates membership proportion for vertices that lie in multiple clusters, and that…
Neural networks offer a computationally efficient approximation of model predictive control, but they lack guarantees on the resulting controlled system's properties. Formal certification of neural networks is crucial for ensuring safety,…
Combinatorial optimisation problems framed as mixed integer linear programmes (MILPs) are ubiquitous across a range of real-world applications. The canonical branch-and-bound algorithm seeks to exactly solve MILPs by constructing a search…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
This paper studies graph-based active learning, where the goal is to reconstruct a binary signal defined on the nodes of a weighted graph, by sampling it on a small subset of the nodes. A new sampling algorithm is proposed, which…
In branching simulation, a novel approach to simulation presented in this paper, a multiplicity of plausible scenarios are concurrently developed and implemented. In conventional simulations of complex systems, there arise from time to time…
Branching Time Active Inference (Champion et al., 2021b,a) is a framework proposing to look at planning as a form of Bayesian model expansion. Its root can be found in Active Inference (Friston et al., 2016; Da Costa et al., 2020; Champion…
Neural networks achieve strong empirical performance, but robustness concerns still hinder deployment in safety-critical applications. Formal verification provides robustness guarantees, but current methods face a scalability-completeness…
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…
Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…