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In the context of tree-search stochastic planning algorithms where agenerative model is available, we consider on-line planning algorithms buildingtrees in order to recommend an action. We investigate the question of avoidingre-planning in subsequent decision steps by directly using sub-trees as actionrecommender. Firstly, we propose a method for open loop control via a newalgorithm taking the decision of re-planning or not at each time step based onan analysis of the statistics of the sub-tree. Secondly, we show that theprobability of selecting a suboptimal action at any depth of the tree can beupper bounded and converges towards zero. Moreover, this upper bound decays ina logarithmic way between subsequent depths. This leads to a distinctionbetween node-wise optimality and state-wise optimality. Finally, we empiricallydemonstrate that our method achieves a compromise between loss of performanceand computational gain.

Open Loop Execution of Tree-Search Algorithms, extended version