  This paper introduces Voronoi Progressive Widening (VPW), a generalization of
Voronoi optimistic optimization (VOO) and action progressive widening to
partially observable Markov decision processes (POMDPs). Tree search algorithms
can use VPW to effectively handle continuous or hybrid action spaces by
efficiently balancing local and global action searching. This paper proposes
two VPW-based algorithms and analyzes them from theoretical and simulation
perspectives. Voronoi Optimistic Weighted Sparse Sampling (VOWSS) is a
theoretical tool that justifies VPW-based online solvers, and it is the first
algorithm with global convergence guarantees for continuous state, action, and
observation POMDPs. Voronoi Optimistic Monte Carlo Planning with Observation
Weighting (VOMCPOW) is a versatile and efficient algorithm that consistently
outperforms state-of-the-art POMDP algorithms in several simulation
experiments.
