Related papers: Tropical linear-fractional programming and paramet…
We consider both finite-state game graphs and recursive game graphs (or pushdown game graphs), that can model the control flow of sequential programs with recursion, with multi-dimensional mean-payoff objectives. In pushdown games two types…
A probabilistic representation for initial value semilinear parabolic problems based on generalized random trees has been derived. Two different strategies have been proposed, both requiring generating suitable random trees combined with a…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
We examine a new optimization problem formulated in the tropical mathematics setting as a further extension of certain known problems. The problem is to minimize a nonlinear objective function, which is defined on vectors over an idempotent…
The tropical variety of a $d$-dimensional prime ideal in a polynomial ring with complex coefficients is a pure $d$-dimensional polyhedral fan. This fan is shown to be connected in codimension one. We present algorithmic tools for computing…
The Fr\'{e}chet mean is a fundamental notion of central tendency defined as a minimizer of a sum of squared distances in a general metric space. In this paper, we study Fr\'{e}chet means in tropical geometry -- a piecewise linear,…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
Computational equilibrium finding in large zero-sum extensive-form imperfect-information games has led to significant recent AI breakthroughs. The fastest algorithms for the problem are new forms of counterfactual regret minimization [Brown…
Pasque et al. showed that using a tropical symmetric metric as an activation function in the last layer can improve the robustness of convolutional neural networks (CNNs) against state-of-the-art attacks, including the Carlini-Wagner…
Concurrent multi-player mean-payoff games are important models for systems of agents with individual, non-dichotomous preferences. Whilst these games have been extensively studied in terms of their equilibria in non-cooperative settings,…
We show that the asymptotic behavior of the two main competing notions of rank of a linear series on a tropical curve is governed by asymptotic invariants, closely paralleling the theory of volumes in algebraic geometry. We introduce and…
Mean-payoff games (MPGs) are infinite duration two-player zero-sum games played on weighted graphs. Under the hypothesis of perfect information, they admit memoryless optimal strategies for both players and can be solved in…
We continue, in this second article, the study of the the algebraic tools which play a role in tropical algebra. We especially examine here the polynomial algebras over idempotent semi-fields. this work is motivated by the development of…
Optimization problems are considered in the framework of tropical algebra to minimize and maximize a nonlinear objective function defined on vectors over an idempotent semifield, and calculated using multiplicative conjugate transposition.…
We study the numerical approximation of a time-dependent variational mean field game system with local couplings and either periodic or Neumann boundary conditions. Following a variational approach, we employ a finite difference…
We propose a novel algorithm for the solution of mean-payoff games that merges together two seemingly unrelated concepts introduced in the context of parity games, small progress measures and quasi dominions. We show that the integration of…
We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark…
We give a converging semidefinite programming hierarchy of outer approximations for the set of quantum correlations of fixed dimension and derive analytical bounds on the convergence speed of the hierarchy. In particular, we give a…
In this paper, we consider linear quadratic team problems with an arbitrary number of quadratic constraints in both stochastic and deterministic settings. The team consists of players with different measurements about the state of nature.…
The ``losing positions" of certain combinatorial games constitute linear error detecting and correcting codes. We show that a large class of games that can be cast in the form of *annihilation games*, provides a potentially polynomial…