Solving Limited Memory Influence Diagrams

TL;DR

This paper introduces a new exact algorithm for solving influence diagrams with limited memory, handling complex decision scenarios without traditional assumptions, and demonstrates its superior performance and theoretical properties.

Contribution

The paper presents a novel algorithm for influence diagrams that relaxes common assumptions, enabling solutions for problems with simultaneous decisions and limited information.

Findings

Outperforms existing algorithms on large, complex problems

Proves NP-hardness even with small treewidth and bounded states

Provides a fully polynomial time approximation scheme for certain cases

Abstract

We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions and limited information. The algorithm is empirically shown to outperform a state-of-the-art algorithm on randomly generated problems of up to 150 variables and $10^{64}$ solutions. We show that the problem is NP-hard even if the underlying graph structure of the problem has small treewidth and the variables take on a bounded number of states, but that a fully polynomial time approximation scheme exists for these cases. Moreover, we show that the bound on the number of states is a necessary condition for any efficient approximation scheme.