Solving Relational MDPs with Exogenous Events and Additive Rewards

TL;DR

This paper introduces a new symbolic planning algorithm for relational MDPs with exogenous events, providing performance guarantees and novel evaluation techniques, demonstrated through preliminary experiments.

Contribution

It presents the first algorithm with explicit performance guarantees for relational MDPs with exogenous events, using novel evaluation and reduction methods for decision diagrams.

Findings

Algorithm provides monotonic lower bounds on the optimal value function.

Novel evaluation techniques improve decision diagram handling.

Preliminary experiments validate the approach.

Abstract

We formalize a simple but natural subclass of service domains for relational planning problems with object-centered, independent exogenous events and additive rewards capturing, for example, problems in inventory control. Focusing on this subclass, we present a new symbolic planning algorithm which is the first algorithm that has explicit performance guarantees for relational MDPs with exogenous events. In particular, under some technical conditions, our planning algorithm provides a monotonic lower bound on the optimal value function. To support this algorithm we present novel evaluation and reduction techniques for generalized first order decision diagrams, a knowledge representation for real-valued functions over relational world states. Our planning algorithm uses a set of focus states, which serves as a training set, to simplify and approximate the symbolic solution, and can thus be seen to perform learning for planning. A preliminary experimental evaluation demonstrates the validity of our approach.