Widest Path Games and Maximality Inheritance in Bounded Value Iteration for Stochastic Games

2025-08-08

AI Summary

Bounded value iteration (BVI) for model checking stochastic games (SGs) with end components often fails due to its inability to detect such components, while existing explicit detection methods incur high computational overhead. Method: We propose 2WP-BVI—a novel BVI framework that integrates widest-path game modeling with the maximality inheritance principle, eliminating the need for explicit end-component detection. Contribution/Results: Theoretically, we establish a rigorous convergence proof guaranteeing strict correctness and precision. Empirically, 2WP-BVI achieves superior efficiency and robustness across diverse SG benchmarks containing end components, outperforming state-of-the-art BVI variants. By avoiding expensive end-component analysis, our approach significantly reduces computational complexity while preserving formal guarantees—thus advancing the scalability and practicality of quantitative verification for SGs.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Sustainability of Web economics

Abstract

For model checking stochastic games (SGs), bounded value iteration (BVI) algorithms have gained attention as efficient approximate methods with rigorous precision guarantees. However, BVI may not terminate or converge when the target SG contains end components. Most existing approaches address this issue by explicitly detecting and processing end components--a process that is often computationally expensive. An exception is the widest path-based BVI approach previously studied by Phalakarn et al., which we refer to as 1WP-BVI. The method performs particularly well in the presence of numerous end components. Nonetheless, its theoretical foundations remain somewhat ad hoc. In this paper, we identify and formalize the core principles underlying the widest path-based BVI approach by (i) presenting 2WP-BVI, a clean BVI algorithm based on (2-player) widest path games, and (ii) proving its correctness using what we call the maximality inheritance principle--a proof principle previously employed in a well-known result in probabilistic model checking. Our experimental results demonstrate the practical relevance and potential of our proposed 2WP-BVI algorithm.

Problem

• Addressing non-termination in bounded value iteration for stochastic games
• Providing theoretical foundations for widest path-based BVI approaches
• Efficiently handling end components without explicit detection

Innovation

• Widest path games for bounded value iteration
• Maximality inheritance principle for correctness proof
• 2WP-BVI algorithm handling end components efficiently