Voronoi Progressive Widening: Efficient Online Solvers for Continuous Space MDPs and POMDPs with Provably Optimal Components

Markov decision processes (MDPs) and partially observable MDPs (POMDPs) can effectively represent complex real-world decision and control problems. However, continuous space MDPs and POMDPs, i.e. those having continuous state, action and observation spaces, are extremely difficult to solve, and there are few online algorithms with convergence guarantees. This paper introduces Voronoi Progressive Widening (VPW), a general technique to modify tree search algorithms to effectively handle continuous or hybrid action spaces, and proposes and evaluates three continuous space solvers: VOSS, VOWSS, and VOMCPOW. VOSS and VOWSS are theoretical tools based on sparse sampling and Voronoi optimistic optimization designed to justify VPW-based online solvers. While previous algorithms have enjoyed convergence guarantees for problems with continuous state and observation spaces, VOWSS is the first with global convergence guarantees for problems that additionally have continuous action spaces. VOMCPOW is a versatile and efficient VPW-based algorithm that consistently outperforms POMCPOW and BOMCP in several simulation experiments.