Solving Decision Theory Problems with Probabilistic Answer Set Programming

TL;DR

This paper introduces a novel approach to solving decision theory problems using Probabilistic Answer Set Programming with credal semantics, employing a layered algebraic model counting algorithm that outperforms enumeration on synthetic datasets.

Contribution

The paper presents a new encoding method for decision problems in probabilistic answer set programming and a layered algebraic model counting algorithm for efficient solutions.

Findings

The proposed algorithm handles non-trivial instances efficiently.

It outperforms answer set enumeration on synthetic datasets.

Empirical results demonstrate practical feasibility.

Abstract

Solving a decision theory problem usually involves finding the actions, among a set of possible ones, which optimize the expected reward, possibly accounting for the uncertainty of the environment. In this paper, we introduce the possibility to encode decision theory problems with Probabilistic Answer Set Programming under the credal semantics via decision atoms and utility attributes. To solve the task we propose an algorithm based on three layers of Algebraic Model Counting, that we test on several synthetic datasets against an algorithm that adopts answer set enumeration. Empirical results show that our algorithm can manage non trivial instances of programs in a reasonable amount of time. Under consideration in Theory and Practice of Logic Programming (TPLP).