5 papers
Equality of tropical rank and dimension for semimodules of tropical rational functions, and computational aspects
Omid Amini, Stéphane Gaubert, Lucas Gierczak
The tropical rank of a semimodule of rational functions on a metric graph mirrors the concept of rank in linear algebra. Defined in terms of the maximal number of tropically indepe…
Relu and softplus neural nets as zero-sum turn-based games
Stephane Gaubert, Yiannis Vlassopoulos
We show that the output of a ReLU neural network can be interpreted as the value of a zero-sum, turn-based, stopping game, which we call the ReLU net game. The game runs in the dir…
Duality between polyhedral approximation of value functions and optimal quantization of measures
Abdellah Bulaich Mehamdi, Wim van Ackooij, Luce Brotcorne +2
Approximating a convex function by a polyhedral function that has a limited number of facets is a fundamental problem with applications in various fields, from mitigating the curse…
Thresholds for sensitive optimality and Blackwell optimality in stochastic games
Stéphane Gaubert, Julien Grand-Clément, Ricardo D. Katz
We investigate refinements of the mean-payoff criterion in two-player zero-sum perfect-information stochastic games. A strategy is Blackwell optimal if it is optimal in the discoun…
Computing the Congestion Phases of Dynamical Systems with Priorities and Application to Emergency Departments
Xavier Allamigeon, Pascal Capetillo, Stéphane Gaubert
Medical emergency departments are complex systems in which patients must be treated according to priority rules based on the severity of their condition. We develop a model of emer…