Minimizing Regret in Discounted-Sum Games

TL;DR

This paper investigates algorithms for minimizing regret in discounted-sum games on weighted graphs, focusing on computing minimal regret and synthesizing regret-free strategies for the controller in various scenarios.

Contribution

It introduces algorithms for calculating minimal regret and synthesizing regret-free strategies in discounted-sum games, addressing multiple environment strategy variants.

Findings

Algorithms for minimal regret computation

Strategies for regret-free control synthesis

Analysis of different environment strategy scenarios

Abstract

In this paper, we study the problem of minimizing regret in discounted-sum games played on weighted game graphs. We give algorithms for the general problem of computing the minimal regret of the controller (Eve) as well as several variants depending on which strategies the environment (Adam) is permitted to use. We also consider the problem of synthesizing regret-free strategies for Eve in each of these scenarios.