Stochastic Games with Disjunctions of Multiple Objectives

TL;DR

This paper explores stochastic games with disjunctive objectives, providing complexity bounds and a new algorithm for approximating Pareto optimal thresholds, extending the understanding of multi-objective game strategies.

Contribution

It introduces a detailed analysis of disjunctive objectives in stochastic games and proposes a novel value iteration algorithm for Pareto threshold approximation.

Findings

New lower and upper bounds for disjunctive query variants

A novel value iteration algorithm for Pareto threshold approximation

Extended analysis of strategy and computational complexity

Abstract

Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural in situations where several - possibly conflicting - performance criteria like time and energy consumption are relevant. Such conjunctive combinations are the most studied multi-objective setting in the literature. In this paper, we consider the dual disjunctive problem. More concretely, we study turn-based stochastic two-player games on graphs where the winning condition is to guarantee at least one reachability or safety objective from a given set of alternatives. We present a fine-grained overview of strategy and computational complexity of such disjunctive queries (DQs) and provide new lower and upper bounds for several variants of the problem, significantly extending previous works. We also propose a novel value iteration-style algorithm for approximating the set of Pareto optimal thresholds for a given DQ.