  This paper introduces a novel backup strategy for Monte-Carlo Tree Search
(MCTS) designed for highly stochastic and partially observable Markov decision
processes. We adopt a probabilistic approach, modeling both value and
action-value nodes as Gaussian distributions. We introduce a novel backup
operator that computes value nodes as the Wasserstein barycenter of their
action-value children nodes; thus, propagating the uncertainty of the estimate
across the tree to the root node. We study our novel backup operator when using
a novel combination of $L^1$-Wasserstein barycenter with $\alpha$-divergence,
by drawing a notable connection to the generalized mean backup operator. We
complement our probabilistic backup operator with two sampling strategies,
based on optimistic selection and Thompson sampling, obtaining our Wasserstein
MCTS algorithm. We provide theoretical guarantees of asymptotic convergence to
the optimal policy, and an empirical evaluation on several stochastic and
partially observable environments, where our approach outperforms well-known
related baselines.
