A Weighted Mini-Bucket Bound Heuristic for Solving Influence Diagrams

Anonymous

Keywords: heuristic, influence diagram, search, planning, graphical model, inference

TL;DR: This paper introduces an elimination based heuristic function for sequential decision making, suitable for guiding AND/OR search algorithms for solving influence diagrams.

Abstract:

Influence diagrams provide a modeling and inference framework for sequential decision problems, representing the probabilistic knowledge by a Bayesian network and the preferences of an agent by utility functions over the random variables and decision variables.
MDPs and POMDPS, widely used for planning under uncertainty can also be represented by influence diagrams.
The time and space complexity of computing the maximum expected utility (MEU) and its maximizing policy is exponential in the induced width of the underlying graphical model, which is often prohibitively large due to the growth of the information set under the sequence of decisions.
In this paper, we develop a weighted mini-bucket approach for bounding the MEU. These bounds can be used as a stand-alone approximation that can be improved as a function of a controlling i-bound parameter.
They can also be used as heuristic functions to guide search, especially for planning
such as MDPs and POMDPs.
We evaluate the scheme empirically against state-of-the-art, thus illustrating its potential.