Sparse tree search optimality guarantees in POMDPs with continuous observation spaces
This provides foundational theoretical guarantees for a widely used technique in real-world decision and control problems, though it is incremental as it formalizes an existing method.
The paper tackles the lack of theoretical justification for observation likelihood weighting in POMDPs with continuous observation spaces, proving that the POWSS algorithm estimates Q-values accurately with high probability and can achieve near-optimal performance by increasing computational resources.
Partially observable Markov decision processes (POMDPs) with continuous state and observation spaces have powerful flexibility for representing real-world decision and control problems but are notoriously difficult to solve. Recent online sampling-based algorithms that use observation likelihood weighting have shown unprecedented effectiveness in domains with continuous observation spaces. However there has been no formal theoretical justification for this technique. This work offers such a justification, proving that a simplified algorithm, partially observable weighted sparse sampling (POWSS), will estimate Q-values accurately with high probability and can be made to perform arbitrarily near the optimal solution by increasing computational power.