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We study contextual stochastic optimization problems, where we leverage rich auxiliary observations (e.g., product characteristics) to improve decision making with uncertain variables (e.g., demand). We show how to train forest decision…
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 &…
Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
We consider the problem of collaborative tree exploration posed by Fraigniaud, Gasieniec, Kowalski, and Pelc where a team of $k$ agents is tasked to collectively go through all the edges of an unknown tree as fast as possible. Denoting by…
Contention tree algorithm is initially invented as a solution to improve the stable throughput problem of Slotted ALOHA in multiple access schemes. Even though the throughput is stabilized in tree algorithms, the delay of requests may grow…
In 1971, Knuth gave an $O(n^2)$-time algorithm for the classic problem of finding an optimal binary search tree. Knuth's algorithm works only for search trees based on 3-way comparisons, while most modern computers support only 2-way…
Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamilton-Jacobi approaches, suffer from the curse of…
There has been a lot of recent work on Bayesian methods for reinforcement learning exhibiting near-optimal online performance. The main obstacle facing such methods is that in most problems of interest, the optimal solution involves…
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…
We consider a perimeter defense problem in a rooted full tree graph environment in which a single defending vehicle seeks to defend a set of specified vertices, termed as the perimeter from mobile intruders that enter the environment…
Designing good heuristic functions for graph search requires adequate domain knowledge. It is often easy to design heuristics that perform well and correlate with the underlying true cost-to-go values in certain parts of the search space…
We present an efficient algorithm to reduce the size of nondeterministic tree automata, while retaining their language. It is based on new transition pruning techniques, and quotienting of the state space w.r.t. suitable equivalences. It…
Essential tasks in autonomous driving includes environment perception, detection and tracking, path planning and action control. This paper focus on path planning, which is one of the challenging task as it needs to find optimal path in…
Competition-level code generation tasks pose significant challenges for current state-of-the-art large language models (LLMs). For example, on the LiveCodeBench-Hard dataset, models such as O1-Mini and O1-Preview achieve pass@1 rates of…
The integration of autonomous vehicles into urban and highway environments necessitates the development of robust and adaptable behavior planning systems. This study presents an innovative approach to address this challenge by utilizing a…
Optimal stopping is the problem of deciding when to stop a stochastic system to obtain the greatest reward, arising in numerous application areas such as finance, healthcare and marketing. State-of-the-art methods for high-dimensional…
We present Model Predictive Trees (MPT), a receding horizon tree search algorithm that improves its performance by reusing information efficiently. Whereas existing solvers reuse only the highest-quality trajectory from the previous…
In collective tree exploration, a team of $k$ mobile agents is tasked to go through all edges of an unknown tree as fast as possible. An edge of the tree is revealed to the team when one agent becomes adjacent to that edge. The agents start…
Planning problems are among the most important and well-studied problems in artificial intelligence. They are most typically solved by tree search algorithms that simulate ahead into the future, evaluate future states, and back-up those…