By Frans A. Oliehoek, Christopher Amato
This publication introduces multiagent making plans lower than uncertainty as formalized through decentralized in part observable Markov determination techniques (Dec-POMDPs). The meant viewers is researchers and graduate scholars operating within the fields of synthetic intelligence with regards to sequential determination making: reinforcement studying, decision-theoretic making plans for unmarried brokers, classical multiagent making plans, decentralized keep watch over, and operations examine.
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Extra info for A Concise Introduction to Decentralized POMDPs
Ai,t−1 ) . 3) Notation for joint action histories and sets are analogous to those for observation histories. Finally we note that, clearly, a (joint) AOH consists of a (joint) action and a (joint) observation history: θ¯ t = o¯ t ,¯at . 2 Policies A policy πi for an agent i maps from histories to actions. In the general case, these histories are AOHs, since they contain all information an agent has. The number of AOHs grows exponentially with the horizon of the problem: At time step t, there are (|Ai | · |Oi |)t possible AOHs for agent i.
2 Policies A policy πi for an agent i maps from histories to actions. In the general case, these histories are AOHs, since they contain all information an agent has. The number of AOHs grows exponentially with the horizon of the problem: At time step t, there are (|Ai | · |Oi |)t possible AOHs for agent i. A policy πi assigns an action to each of these histories. As a result, the number of possible policies πi is doubly exponential in the horizon. Under a deterministic policy, only a subset of possible action-observation histories can be reached.
Nondeterministic means that, similarly to NP, solving these problems requires generating a guess about the solution in a nondeterministic way. Exponential time means that verifying whether the guess is a solution takes exponential time. In practice this means that (assuming NEXP = EXP) solving a Dec-POMDP takes doubly exponential time in the worst case. Moreover, Dec-POMDPs cannot be approximated efﬁciently: Rabinovich et al.  showed that even ﬁnding an ‘ε-approximate solution’ is NEXP-complete.