2 citations · 3 across the 7 of their papers we have counts for
11 papers
Sharper bounds on the thresholds for sensitive and Blackwell optimality
Xavier Allamigeon, Stéphane Gaubert, Julien Grand-Clément +1
In perfect-information two-player stochastic games, the notions of Blackwell and sensitive optimality provide generalizations of the classical mean-payoff optimality and discount o…
Joint Design of Time-of-Use Schedules and Price Levels: a Bilevel Model with Client Participation and Load Flexibility
Abdellah Bulaich Mehamdi, Wim van Ackooij, Luce Brotcorne +2
We study the joint design of a time-of-use (ToU) tariff (the partition of the day into pricing blocks and the price level attached to each block) by a profit-maximizing electricity…
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…
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…
Stationary regimes of piecewise linear dynamical systems with priorities
Xavier Allamigeon, Pascal Capetillo, Stephane Gaubert
Dynamical systems governed by priority rules appear in the modeling of emergency organizations and road traffic. These systems can be modeled by piecewise linear time-delay dynamic…
Directed Metric Structures arising in Large Language Models
Stéphane Gaubert, Yiannis Vlassopoulos
Large Language Models are transformer neural networks which are trained to produce a probability distribution on the possible next words to given texts in a corpus, in such a way t…
Universal Complexity Bounds Based on Value Iteration for Stochastic Mean Payoff Games and Entropy Games
Xavier Allamigeon, Stéphane Gaubert, Ricardo D. Katz +1
We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on a…
Maximal lower bounds in the Löwner order
Nikolas Stott
We show that the set of maximal lower bounds of two symmetric matrices with respect to the Löwner order can be identified to the quotient set . Here, $(p,…