arXiv subjects

Matthieu Guillot

Publications and source records attributed to Matthieu Guillot.

3 recordsLinked to original sources

arXiv2023

Golf Strategy Optimization and the "Drive for show, putt for dough" adage

This study explores strategic decision-making in professional golf's Stroke Play format through a computational lens. We develop a Markov Decision Process (MDP) model-specifically, a stochastic shortest path formulation-to optimize a golfer's strategy on any given course, incorporating both course layout and player skill data. While MDPs have been widely used in sports analytics, applying them to golf presents significant scalability challenges due to the curse of dimensionality. Our primary objective is not to predict player performance with high precision, but rather to demonstrate that an exact, data-driven MDP approach is computationally tractable on full scale, real-world instances. We show that, with careful problem structuring, low-level coding, and efficient memory management, it is possible to solve such large-scale models without resorting to heuristics or Q-learning approximations, as used in existing approaches. To illustrate the model's potential, we show how one can use PGA Tour data and aerial course imagery to simulate strategic outcomes and analyze how different skill profiles influence performance. In particular, we assess the relative impact of driving and putting, challenging the popular adage "Drive for show, putt for dough." These results support the value of our methodology as a robust proof of concept and a foundation for future enhancements. All code and analyses (in R and C++) are made available as open-source resources to support reproducibility and further research.

math.OC↗

arXiv2021

Optimal Subgraph on Disturbed Network

During the pandemic of COVID-19, the demand of the transportation systems are drastically changed both qualitatively and quantitatively and the network has become obsolete. In this article, we study the problem of finding an optimal subnetwork that guarantee that (i) the minimal access time from any node of the urban network to the new network is not {\em too large} compared to the original transportation network; (ii) for any itinerary, the delay caused by the deletion of nodes of the transportation network is not {\em too big}; and (iii) the number of nodes of the transportation network has been reduced at least by a known factor. A solution is optimal if it induces a minimal global delay. We model this problem as a Mixed Integer Linear Program before applying the model on a real-case application on the Lyon's buses transportation network.

cs.DM↗

arXiv2017

The Stochastic Shortest Path Problem : A polyhedral combinatorics perspective

In this paper, we give a new framework for the stochastic shortest path problem in finite state and action spaces. Our framework generalizes both the frameworks proposed by Bertsekas and Tsitsikli and by Bertsekas and Yu. We prove that the problem is well-defined and (weakly) polynomial when (i) there is a way to reach the target state from any initial state and (ii) there is no transition cycle of negative costs (a generalization of negative cost cycles). These assumptions generalize the standard assumptions for the deterministic shortest path problem and our framework encapsulates the latter problem (in contrast with prior works). In this new setting, we can show that (a) one can restrict to deterministic and stationary policies, (b) the problem is still (weakly) polynomial through linear programming, (c) Value Iteration and Policy Iteration converge, and (d) we can extend Dijkstra's algorithm.

cs.DM↗