# Sufficient and approximately sufficient statistics for team decision problems

## Abstract/Contents

- Abstract
- In a decentralized control problem, multiple agents with access to different sets of information choose their actions in order to minimize a common cost. Although decentralized control problems are difficult to solve in general, several special classes of these problems have been found to be tractable. A common theme in these tractable cases is the existence of sufficient statistics, which are compressed versions of the information available to the agents that retain enough information to allow for optimal decisions. Although there is a general theory of sufficient statistics for single-agent decision problems, most of the sufficient statistics known for decentralized decision problems have been obtained through ad hoc analysis. Wu and Lall developed a theory of sufficient statistics for a simple class of decentralized decision problems called team decision problems, and proved that these statistics are sufficient for making optimal decisions, and can be updated efficiently, even when the agents affect how the world changes. This thesis presents a new theory of sufficient statistics for team decision problems. Our new definition is both necessary and sufficient for making optimal decisions in team decision problems, although statistics satisfying this definition can only be updated when the agents do not affect how the world changes. We then generalize our definition to give the first general definition of approximately sufficient statistics for team decision problems. This is an important development because decentralized decision making is such a complex problem that we may need to compress the information given to the agents beyond what is necessary for optimality in order to obtain a problem we can solve in practice. We also propose a practical algorithm for computing approximately sufficient statistics.

## Description

Type of resource | text |
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Form | electronic; electronic resource; remote |

Extent | 1 online resource. |

Publication date | 2017 |

Issuance | monographic |

Language | English |

## Creators/Contributors

Associated with | Lemon, Alexander Downey II |
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Associated with | Stanford University, Department of Electrical Engineering. |

Primary advisor | Lall, Sanjay |

Thesis advisor | Lall, Sanjay |

Thesis advisor | Boyd, Stephen P |

Thesis advisor | Ye, Yinyu |

Advisor | Boyd, Stephen P |

Advisor | Ye, Yinyu |

## Subjects

Genre | Theses |
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## Bibliographic information

Statement of responsibility | Alexander Downey Lemon II. |
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Note | Submitted to the Department of Electrical Engineering. |

Thesis | Thesis (Ph.D.)--Stanford University, 2017. |

Location | electronic resource |

## Access conditions

- Copyright
- © 2017 by Alexander Downey Lemon
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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