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Partially Observable Markov Decision Processes (POMDP) is a widely used modelto represent the interaction of an environment and an agent, under stateuncertainty. Since the agent does not observe the environment state, itsuncertainty is typically represented through a probabilistic belief. While theset of possible beliefs is infinite, making exact planning intractable, thebelief space's complexity (and hence planning complexity) is characterized byits covering number. Many POMDP solvers uniformly discretize the belief spaceand give the planning error in terms of the (typically unknown) coveringnumber. We instead propose an adaptive belief discretization scheme, and giveits associated planning error. We furthermore characterize the covering numberwith respect to the POMDP parameters. This allows us to specify the exactmemory requirements on the planner, needed to bound the value function error.We then propose a novel, computationally efficient solver using this scheme. Wedemonstrate that our algorithm is highly competitive with the state of the artin a variety of scenarios.

Adaptive Belief Discretization for POMDP Planning