Related papers: Tropical linear-fractional programming and paramet…

We show that, by using multiplicative weights in a game-theoretic thought experiment (and an important convexity result on the composition of multiplicative weights with the relative entropy function), a symmetric bimatrix game (that is, a…

We introduce new discrete best approximation problems, formulated and solved in the framework of tropical algebra, which deals with semirings and semifields with idempotent addition. Given a set of samples, each consisting of the input and…

In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…

For a tropical univariate polynomial $f$ we define its tropical Hilbert function as the dimension of a tropical linear prevariety of solutions of the tropical Macauley matrix of the polynomial up to a (growing) degree. We show that the…

We consider the problem of designing a linear program that has diverse solutions as the right-hand side varies. This problem arises in video game settings where designers aim to have players use different "weapons" or "tactics" as they…

In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…

We introduce $p$-adic manifold learning, propose an algorithm to solve it, and propose benchmark tasks from impartial games.

We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…

Game-theoretical approach to the analysis of parallel algorithms is proposed. The approach is based on presentation of the parallel computing as a congestion game. In the game processes compete for resources such as core of a central…

The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to…

Fractals are self-similar recursive structures that have been used in modeling several real world processes. In this work we study how "fractal-like" processes arise in a prediction game where an adversary is generating a sequence of bits…

In this note, we propose a novel technique to reduce the algorithmic complexity of neural network training by using matrices of tropical real numbers instead of matrices of real numbers. Since the tropical arithmetics replaces…

We introduce the concept of a \emph{cycle pattern} for directed graphs as functions from the set of cycles to the set $\{-,0,+\}$. The key example for such a pattern is derived from a weight function, giving rise to the sign of the total…

We present a general framework for solving a large class of learning problems with non-linear functions of classification rates. This includes problems where one wishes to optimize a non-decomposable performance metric such as the F-measure…

In this paper, we address the inverse problem for linear-quadratic differential non-cooperative games with output-feedback. Given players' stabilizing feedback laws, the goal is to find cost function parameters that lead to a game for which…

We translate the usual class of partial/primitive recursive functions to a pointer recursion framework, accessing actual input values via a pointer reading unit-cost function. These pointer recursive functions classes are proven equivalent…

Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…

In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always…

This paper proves the existence and uniqueness results (in the sense of maximally defined regularity) as well as the stability analysis for the solutions to a class of nonlocal fully-nonlinear parabolic systems, where the nonlocality stems…

We introduce a "high probability" framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high…