Open Loop Execution of Tree-Search Algorithms, extended version

TL;DR

This paper introduces an open loop control method for tree-search stochastic planning that reduces re-planning frequency by analyzing sub-tree statistics, with proven bounds on suboptimal action probability and empirical performance gains.

Contribution

It proposes a novel algorithm for open loop control in tree-search planning, including a decision criterion for re-planning and theoretical bounds on suboptimality.

Findings

Probability of suboptimal action selection converges to zero.

Upper bounds decay logarithmically with tree depth.

Method balances performance loss and computational efficiency.

Abstract

In the context of tree-search stochastic planning algorithms where a generative model is available, we consider on-line planning algorithms building trees in order to recommend an action. We investigate the question of avoiding re-planning in subsequent decision steps by directly using sub-trees as action recommender. Firstly, we propose a method for open loop control via a new algorithm taking the decision of re-planning or not at each time step based on an analysis of the statistics of the sub-tree. Secondly, we show that the probability of selecting a suboptimal action at any depth of the tree can be upper bounded and converges towards zero. Moreover, this upper bound decays in a logarithmic way between subsequent depths. This leads to a distinction between node-wise optimality and state-wise optimality. Finally, we empirically demonstrate that our method achieves a compromise between loss of performance and computational gain.