Planning in POMDPs Using Multiplicity Automata
This work addresses the problem of efficient planning in structured POMDPs for AI and operations research communities, offering a novel connection to multiplicity automata that could lead to more scalable solutions in specific cases.
The paper tackles the challenge of planning in Partially Observable MDPs (POMDPs) by representing them as multiplicity automata, showing that this representation size equals the rank of the predictive state representation, and provides a planning algorithm that is exponential only in this rank, making it efficient when the rank is logarithmic in the standard representation.
Planning and learning in Partially Observable MDPs (POMDPs) are among the most challenging tasks in both the AI and Operation Research communities. Although solutions to these problems are intractable in general, there might be special cases, such as structured POMDPs, which can be solved efficiently. A natural and possibly efficient way to represent a POMDP is through the predictive state representation (PSR) - a representation which recently has been receiving increasing attention. In this work, we relate POMDPs to multiplicity automata- showing that POMDPs can be represented by multiplicity automata with no increase in the representation size. Furthermore, we show that the size of the multiplicity automaton is equal to the rank of the predictive state representation. Therefore, we relate both the predictive state representation and POMDPs to the well-founded multiplicity automata literature. Based on the multiplicity automata representation, we provide a planning algorithm which is exponential only in the multiplicity automata rank rather than the number of states of the POMDP. As a result, whenever the predictive state representation is logarithmic in the standard POMDP representation, our planning algorithm is efficient.