Decentralized Stochastic Control with Partial History Sharing: A Common Information Approach (1209.1695v1)

Abstract: A general model of decentralized stochastic control called partial history sharing information structure is presented. In this model, at each step the controllers share part of their observation and control history with each other. This general model subsumes several existing models of information sharing as special cases. Based on the information commonly known to all the controllers, the decentralized problem is reformulated as an equivalent centralized problem from the perspective of a coordinator. The coordinator knows the common information and select prescriptions that map each controller's local information to its control actions. The optimal control problem at the coordinator is shown to be a partially observable Markov decision process (POMDP) which is solved using techniques from Markov decision theory. This approach provides (a) structural results for optimal strategies, and (b) a dynamic program for obtaining optimal strategies for all controllers in the original decentralized problem. Thus, this approach unifies the various ad-hoc approaches taken in the literature. In addition, the structural results on optimal control strategies obtained by the proposed approach cannot be obtained by the existing generic approach (the person-by-person approach) for obtaining structural results in decentralized problems; and the dynamic program obtained by the proposed approach is simpler than that obtained by the existing generic approach (the designer's approach) for obtaining dynamic programs in decentralized problems.

• The paper introduces a partial history sharing model and common information approach to unify diverse decentralized control problems into centralized equivalents.
• This common information approach allows a coordinator to view shared data and compute optimal strategies via a partially observable Markov decision process framework.
• The method yields a dynamically programmable solution offering reduced complexity and improved efficiency over existing decentralized control techniques.

Decentralized Stochastic Control with Partial History Sharing: A Common Information Approach

This paper by Nayyar, Mahajan, and Teneketzis presents a novel model for decentralized stochastic control labeled the "partial history sharing information structure." At its core, this model articulates an elegant reformulation of decentralized control problems into centralized ones through a common information approach, using a coordinated system perspective.

In decentralized stochastic control scenarios, conventional methods that assume a centralized decision-maker are inadequate due to the diverse and distributed nature of information accessible to different decision-makers (DMs). The authors consolidate various information-sharing paradigms under one overarching framework where controllers intermittently exchange segments of their observation and control histories through a shared medium.

Key Contributions

The authors' work revolves around three pivotal contributions:

1. Unified Modeling Approach: The paper defines a flexible and general model for decentralized control problems. This model can encapsulate numerous existing decentralization configurations like delayed sharing, periodic sharing, and broadcast information structures, illustrating its versatility.
2. Mapping to Centralized Problems: Central to the paper is the innovative transformation of a decentralized problem into an equivalent centralized problem from a coordinator’s viewpoint, which views the common information. The coordinator computes optimal prescriptions (mappings from local to control actions) using a partially observable Markov decision process (POMDP) framework, leading to structural insights into optimal strategies.
3. Dynamic Programming and Structural Results: The common information approach yields a dynamically programmable solution for determining optimal strategies. Consequentially, it provides not only a streamlined method for achieving optimal strategies but also poses structures irreducible by other generic methods like the person-by-person or designer's approach. The reported dynamic programming decomposition is more efficient compared to traditionally encountered decompositions.

Theoretical and Practical Implications

The theoretical impact of this paper is robust as it refines the understanding of decentralized control problem structures. Particularly, it demonstrates that common information states, derivable through shared memory, are instrumental in consolidating the analysis of disparate decentralized control systems. For practitioners, this facilitates more efficient controller design and strategy optimization in complex, distributed environments such as sensor networks and smart grids.

Numerical Results

An important aspect highlighted by the authors is the simplicity and reduced complexity of their approach compared to existing methods. For instances like control sharing information models, they show how common information states reduce to straightforward forms that closely mimic centralized control scenarios. This reduction is crucial as it significantly cuts down the computational burden typically associated with high-dimensional decentralized problems.

Future Prospects in AI Developments

Moving forward, the methodology elucidated in this paper may impact AI systems where agent collaboration with diverse information endpoints is paramount. These could include cooperative robotics, multi-agent systems in uncertain environments, and adaptive networks where decision-making is distributed yet requires coherence.

Conclusion

The paper’s cohesive approach to recasting decentralized stochastic control problems through common information stands as a significant methodological advance. While the broader implications on AI and control theorems are yet to be fully explored, the established framework sets a promising foundation for integrating decentralized control dynamics more seamlessly across various applications domains. The elucidation and aggregation of disparate perspectives into a centralized, coherent form beckons further exploration and can usher in a sophisticated era of distributed decision-making strategies.