Efficient Memory-Bounded Strategies for Büchi Objectives in Concurrent Stochastic Games

Khái niệm cốt lõi

Max players in concurrent stochastic games with Büchi objectives can achieve near-optimal performance using just a step counter plus 1 bit of public memory.

Tóm tắt

The paper studies 2-player concurrent stochastic games on countable graphs, where the objective is to maximize/minimize the probability of visiting a set of target states infinitely often (Büchi objective).
The key insights are:

Max players have 1-bit Markov strategies that are multiplicatively ε-optimal for the Büchi objective. These strategies use a step counter plus 1 bit of public memory.

This upper bound on the strategy complexity is tight, as neither finite-memory strategies nor Markov strategies are sufficient for Max to be ε-optimal, even in finite-state concurrent Büchi games.

The authors also show that for the combined Büchi and Transience objective, Max has public 1-bit strategies that are uniformly ε-optimal.

For the Transience objective alone, Max has memoryless strategies that are uniformly ε-optimal, though these strategies need to randomize.

The proofs rely on constructing suitable Markov chains and martingales to analyze the strategy complexity. The results generalize prior work on countable Markov decision processes to the more complex setting of concurrent stochastic games.

Thống kê

Max players in concurrent stochastic games with Büchi objectives can achieve near-optimal performance using just a step counter plus 1 bit of public memory.
Neither finite-memory strategies nor Markov strategies are sufficient for Max to be ε-optimal in finite-state concurrent Büchi games.
For the combined Büchi and Transience objective, Max has public 1-bit strategies that are uniformly ε-optimal.
For the Transience objective alone, Max has memoryless strategies that are uniformly ε-optimal, though these strategies need to randomize.

Trích dẫn

"We show that there always exist ε-optimal Max strategies that use just a step counter plus 1 bit of public memory."
"The upper bound is a consequence of a slightly stronger new result: ε-optimal Max strategies for the combined Büchi and Transience objective require just 1 bit of public memory (but cannot be memoryless)."
"We show (Theorem 3.3) that in games with Transience objectives, Max has memoryless strategies that are uniformly ε-optimal."

Thông tin chi tiết chính được chắt lọc từ

Strategy Complexity of Büchi Objectives in Concurrent Stochastic Games

by Stefan Kiefe... lúc arxiv.org 04-25-2024

https://arxiv.org/pdf/2404.15483.pdf

Yêu cầu sâu hơn

How do the strategy complexity results extend to other types of objectives, such as mean-payoff or parity objectives, in concurrent stochastic games

The strategy complexity results presented in the paper for Büchi and Transience objectives in concurrent stochastic games can be extended to other types of objectives, such as mean-payoff or parity objectives. The key idea is to adapt the memory-bounded strategy techniques used in the paper to suit the specific requirements and constraints of these different objectives.
For mean-payoff objectives, where the goal is to optimize the average payoff received during the game, memory-bounded strategies can be designed to ensure that the average payoff meets certain criteria while using limited memory resources. This can involve incorporating the calculation of average payoffs into the strategy selection process, ensuring that the memory constraints are not exceeded while still achieving the desired average payoff values.
Similarly, for parity objectives that involve satisfying specific parity conditions on the states visited during the game, memory-bounded strategies can be developed to meet these conditions while minimizing the memory usage. By carefully selecting actions based on the parity requirements and utilizing memory efficiently, strategies can be constructed to achieve the desired parity objectives within the specified memory limits.
Overall, the strategy complexity results and techniques from the paper can be adapted and extended to address a variety of objectives in concurrent stochastic games, providing a framework for developing memory-bounded strategies tailored to different types of objectives.

Can the techniques used in this paper be applied to develop efficient algorithms for solving concurrent stochastic games with Büchi, Transience, or combined objectives

The techniques used in the paper to analyze strategy complexity in concurrent stochastic games with Büchi, Transience, and combined objectives can be leveraged to develop efficient algorithms for solving these types of games. By understanding the memory requirements for optimal or near-optimal strategies in these games, algorithm designers can create algorithms that are memory-efficient while still achieving good performance in terms of objective satisfaction and gameplay outcomes.
One potential application of these techniques is in the development of algorithmic solutions for model checking and verification of systems with concurrent stochastic behavior. By incorporating the insights from the strategy complexity results, algorithms can be designed to efficiently analyze and verify properties such as reachability, safety, liveness, and fairness in systems with stochastic components.
Furthermore, the memory-bounded strategies identified in the paper can serve as a basis for developing practical algorithms that can be implemented in real-world systems. These algorithms can help in optimizing decision-making processes in multi-agent systems, ensuring that agents make informed choices while respecting memory constraints and achieving desired objectives.
Overall, the techniques and results presented in the paper lay the groundwork for the development of efficient algorithms for solving concurrent stochastic games with various objectives, contributing to advancements in the field of algorithm design and system analysis.

What are the practical implications of these memory-bounded strategies for the design and analysis of real-world multi-agent systems

The memory-bounded strategies identified in the paper have significant practical implications for the design and analysis of real-world multi-agent systems. By demonstrating that memory-efficient strategies can be developed to achieve Büchi, Transience, and combined objectives in concurrent stochastic games, the paper provides valuable insights for system designers and developers.
One practical implication is in the optimization of resource usage in multi-agent systems. Memory-bounded strategies can help in reducing the memory footprint of individual agents, allowing for more efficient utilization of computational resources and improved system performance. This can be particularly beneficial in resource-constrained environments where memory availability is limited.
Additionally, the development of memory-bounded strategies based on the results in the paper can enhance the robustness and reliability of multi-agent systems. By ensuring that agents operate within specified memory constraints while still achieving desired objectives, system designers can create more stable and predictable systems that are less prone to memory-related issues or failures.
Moreover, the techniques for analyzing strategy complexity and designing memory-efficient strategies can be applied to various domains, including autonomous systems, robotics, and artificial intelligence. By incorporating these strategies into the design and implementation of intelligent systems, researchers and practitioners can enhance the performance and scalability of multi-agent systems in real-world applications.
In conclusion, the memory-bounded strategies derived from the paper have practical implications for improving the design, analysis, and performance of real-world multi-agent systems, offering opportunities for more efficient and reliable system operation in diverse application domains.