Solving Decision Theory Problems with Probabilistic Answer Set Programming

TL;DR

The paper addresses decision-theoretic problems under uncertainty by encoding them in Probabilistic Answer Set Programming with credal semantics, introducing decision atoms and utilities (DTPASP). It presents a three-layer Algebraic Model Counting (3AMC) approach, implemented via knowledge compilation, to efficiently compute the best lower- and upper-bound strategies, and compares it against enumeration. Across six synthetic datasets, the 3AMC-based method outperforms naive enumeration, demonstrating scalability to nontrivial problem sizes while noting memory considerations. The work advances a unified ASP-based formalism for decision making under uncertainty and provides a scalable inference framework suitable for complex domains with aggregates and constraints.

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).

Figures (6)

• Figure 1: Primal graph of $\mathcal{C}_{run}$ (Example \ref{['ex:running_cnf']}).
• Figure 2: Two tree decomposition of the graph in Figure \ref{['fig:primal_running']}. Each vertex is labeled by the vertices in the corresponding bag.
• Figure 3: Execution times for PASTA and aspmc3 in $t1$ with a fixed number of probabilistic facts and an increasing number of decision atoms.
• Figure 4: Execution times for PASTA and aspmc3 in $t2$ with a fixed number of decision atoms and an increasing number of probabilistic facts.
• Figure 5: Execution times for PASTA and aspmc3 in $t3$, $t4$, $t5$, and $t6$.

Theorems & Definitions (18)

• Example 1
• Example 2
• Example 3
• Example 4
• Definition 1: Definability 10.5555/3060621.3060726
• Example 5
• Definition 2
• Example 6: Running Example.
• Example 7
• Example 8