Periodic Reporting for period 3 - ForM-SMArt (Formal Methods for Stochastic Models: Algorithms and Applications)
Période du rapport: 2024-01-01 au 2025-06-30
• The problem considered in this project is to develop faster algorithmic approaches for formal analysis of stochastic systems.
• Stochastic systems arise in several practical applications, e.g. randomized algorithms, evolutionary dynamics, design of stochastic protocols, systems in uncertain environments, to name a few. Formal analysis of such systems is necessary to develop robust systems with guarantees so that they can be deployed in safety-critical applications. Thus analysis of stochastic systems has deep impact for the society.
• The overall objectives of the project is to develop algorithmic approaches for finite-state and infinite-state stochastic games, stochastic evolutionary dynamics of games, and their applications in different domains.
• Stochastic systems arise in several practical applications, e.g. randomized algorithms, evolutionary dynamics, design of stochastic protocols, systems in uncertain environments, to name a few. Formal analysis of such systems is necessary to develop robust systems with guarantees so that they can be deployed in safety-critical applications. Thus analysis of stochastic systems has deep impact for the society.
• The overall objectives of the project is to develop algorithmic approaches for finite-state and infinite-state stochastic games, stochastic evolutionary dynamics of games, and their applications in different domains.
We have made significant progress since the start of the project. In particular, in each of the four aims we have obtained important results. In the first aim for finite-state stochastic models, we presented the first sub-exponential algorithm that breaks a long-standing barrier for discounted-sum games with unary weights, and presented algorithms for risk-aware sequential-decision making with risk measures from economics theory. For the second aim for infinite-state stochastic models, we presented automated approaches for quantitative bounds on resource usage of probabilistic programs, and present approaches for analysis of relational properties of probabilistic programs. For the third aim on evolutionary games, we presented a framework to analyse the trade-off between resilience and efficiency of cooperation, and resolved the long-standing open problem of existence of amplifiers in spatial games. Finally, in the fourth aim for applications, we showed the effectiveness of our theoretical methods for analysis of problems arising in reinforcement learning and selfish-mining attacks in blockchains.
We achieved several important progress beyond the state of the art. In the first aim we obtain new algorithms that break the long-standing barrier. In the second aim, we present new automated approaches for analysis of fundamental problems for probabilistic programs. In the third aim, we present first networks that promotes cooperation in spatial games, resolving a long-standing open problem. All these results are important developments beyond the state of the art. We have demonstrated the practical applicability of our theoretical approaches in AI (e.g. reinforcement learning), and analysis of blockchains. Overall, in all four aims of the project we achieved significant success. By the end of the project, we will finalize the final research questions we are exploring, e.g. extension of the new algorithm to incorporate stochasticity for Aim 1, applying the approaches for security applications for Aim 2, robustness of amplification related to Aim 3. The answers of these questions will finalize the overall results of the project in the next few months.