Solving Hierarchical Information-Sharing Dec-POMDPs: An Extensive-Form Game Approach
CoRR(2024)
摘要
A recent theory shows that a multi-player decentralized partially observable
Markov decision process can be transformed into an equivalent single-player
game, enabling the application of 's principle of
optimality to solve the single-player game by breaking it down into
single-stage subgames. However, this approach entangles the decision variables
of all players at each single-stage subgame, resulting in backups with a
double-exponential complexity. This paper demonstrates how to disentangle these
decision variables while maintaining optimality under hierarchical information
sharing, a prominent management style in our society. To achieve this, we apply
the principle of optimality to solve any single-stage subgame by breaking it
down further into smaller subgames, enabling us to make single-player decisions
at a time. Our approach reveals that extensive-form games always exist with
solutions to a single-stage subgame, significantly reducing time complexity.
Our experimental results show that the algorithms leveraging these findings can
scale up to much larger multi-player games without compromising optimality.
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