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In the context of tree-search stochastic planning algorithms where a generative model is available, we consider on-line planning algorithms building trees in order to recommend an action. We investigate the question of avoiding re-planning…

In recent years, significant progress has been made on algorithms for learning optimal decision trees, primarily in the context of binary features. Extending these methods to continuous features remains substantially more challenging due to…

Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…

Many real-world problems require making sequences of decisions where the outcomes of each decision are probabilistic and uncertain, and the availability of different actions is constrained by the outcomes of previous actions. There is a…

Decision trees, owing to their interpretability, are attractive as control policies for (dynamical) systems. Unfortunately, constructing, or synthesising, such policies is a challenging task. Previous approaches do so by imitating a…

We analyze a tree search problem with an underlying Markov decision process, in which the goal is to identify the best action at the root that achieves the highest cumulative reward. We present a new tree policy that optimally allocates a…

A default assumption in the design of reinforcement-learning algorithms is that a decision-making agent always explores to learn optimal behavior. In sufficiently complex environments that approach the vastness and scale of the real world,…

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…

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.…

Many potential applications of reinforcement learning (RL) are stymied by the large numbers of samples required to learn an effective policy. This is especially true when applying RL to real-world control tasks, e.g. in the sciences or…

Decision tree learning has long been a central topic in theoretical computer science, driven by its practical importance. A fundamental and widely used method for decision tree construction is the top-down greedy heuristic, which…

The note studies the problem of selecting a good enough subset out of a finite number of alternatives under a fixed simulation budget. Our work aims to maximize the posterior probability of correctly selecting a good subset. We formulate…

In natural perception, different items (objects) in a scene are rarely equally relevant to the observer. The brain improves performance by directing attention to the most relevant items, for example the ones most likely to be probed. For a…

When facing many options, we narrow down our focus to very few of them. Although behaviors like this can be a sign of heuristics, they can actually be optimal under limited cognitive resources. Here we study the problem of how to optimally…

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…

While agent evaluation has shifted toward long-horizon tasks, most benchmarks still emphasize local, step-level reasoning rather than the global constrained optimization (e.g., time and financial budgets) that demands genuine planning…

Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time.…

Systems of decision rules and decision trees are widely used as a means for knowledge representation, as classifiers, and as algorithms. They are among the most interpretable models for classifying and representing knowledge. The study of…

Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy…

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 &…