Lazy Planning under Uncertainty by Optimizing Decisions on an Ensemble of Incomplete Disturbance Trees

Abstract

This paper addresses the problem of solving discrete-time optimal sequential decision making problems having a disturbance space W composed of a finite number of elements. In this context, the problem of finding from an initial state x ₀ an optimal decision strategy can be stated as an optimization problem which aims at finding an optimal combination of decisions attached to the nodes of a disturbance tree modeling all possible sequences of disturbances w ₀, w ₁, ..., $w_{T-1} \in W^T$ over the optimization horizon T. A significant drawback of this approach is that the resulting optimization problem has a search space which is the Cartesian product of O(|W|^T − 1) decision spaces U, which makes the approach computationally impractical as soon as the optimization horizon grows, even if W has just a handful of elements. To circumvent this difficulty, we propose to exploit an ensemble of randomly generated incomplete disturbance trees of controlled complexity, to solve their induced optimization problems in parallel, and to combine their predictions at time t = 0 to obtain a (near-)optimal first-stage decision. Because this approach postpones the determination of the decisions for subsequent stages until additional information about the realization of the uncertain process becomes available, we call it lazy. Simulations carried out on a robot corridor navigation problem show that even for small incomplete trees, this approach can lead to near-optimal decisions.