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Particle filtering is a popular method for inferring latent states instochastic dynamical systems, whose theoretical properties have been wellstudied in machine learning and statistics communities. In many controlproblems, e.g., partially observed linear dynamical systems (POLDS), oftentimesthe inferred latent state is further used for planning at each step. This paperinitiates a rigorous study on the efficiency of particle filtering forsequential planning, and gives the first particle complexity bounds. Thougherrors in past actions may affect the future, we are able to bound the numberof particles needed so that the long-run reward of the policy based on particlefiltering is close to that based on exact inference. In particular, we showthat, in stable systems, polynomially many particles suffice. Key in our proofis a coupling of the ideal sequence based on the exact planning and thesequence generated by approximate planning based on particle filtering. Webelieve this technique can be useful in other sequential decision-makingproblems.

When is Particle Filtering Efficient for Planning in Partially Observed Linear Dynamical Systems?