  Partially Observable Markov Decision Processes (POMDPs) are a powerful
framework for planning under uncertainty. They allow to model state uncertainty
as a belief probability distribution. Approximate solvers based on Monte Carlo
sampling show great success to relax the computational demand and perform
online planning. However, scaling to complex realistic domains with many
actions and long planning horizons is still a major challenge, and a key point
to achieve good performance is guiding the action-selection process with
domain-dependent policy heuristics which are tailored for the specific
application domain. We propose to learn high-quality heuristics from POMDP
traces of executions generated by any solver. We convert the belief-action
pairs to a logical semantics, and exploit data- and time-efficient Inductive
Logic Programming (ILP) to generate interpretable belief-based policy
specifications, which are then used as online heuristics. We evaluate
thoroughly our methodology on two notoriously challenging POMDP problems,
involving large action spaces and long planning horizons, namely, rocksample
and pocman. Considering different state-of-the-art online POMDP solvers,
including POMCP, DESPOT and AdaOPS, we show that learned heuristics expressed
in Answer Set Programming (ASP) yield performance superior to neural networks
and similar to optimal handcrafted task-specific heuristics within lower
computational time. Moreover, they well generalize to more challenging
scenarios not experienced in the training phase (e.g., increasing rocks and
grid size in rocksample, incrementing the size of the map and the aggressivity
of ghosts in pocman).
