Combining Stochastic Constraint Optimization and Probabilistic Programming

Latour, Anna L. D.; Babaki, Behrouz; Dries, Anton; Kimmig, Angelika; Broeck, Guy Van den; Nijssen, Siegfried

doi:10.1007/978-3-319-66158-2_32

Cited by 13 publications

(5 citation statements)

References 23 publications

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“…Before we further illustrate this formalism with tasks from the literature, we prove that 2AMC can be solved in polynomial time on X O -first sd-DNNFs. A similar result is already known for DTProbLog (Derkinderen and De Raedt 2020) and SC-ProbLog (Latour et al 2017).…”

Section: Second Level Algebraic Model Countingsupporting

confidence: 86%

“…However, many interesting tasks require two kinds of aggregation, and thus are second level problems that go beyond AMC. Examples include Maximum A Posteriori (MAP) inference in probabilistic programs, which involves maximizing over some variables while summing over others, inference in SLASH and SMProbLog, and optimization tasks in decision-theoretic or constrained probabilistic programming languages such as DTProbLog (Van den Broeck et al 2010;Derkinderen and De Raedt 2020) and SC-ProbLog (Latour et al 2017).…”

Section: Introductionmentioning

confidence: 99%

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Efficient Knowledge Compilation Beyond Weighted Model Counting

Kiesel¹,

Totis²,

Kimmig³

2022

Preprint

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Quantitative extensions of logic programming often require the solution of so called second level inference tasks, i.e., problems that involve a third operation, such as maximization or normalization, on top of addition and multiplication, and thus go beyond the well-known weighted or algebraic model counting setting of probabilistic logic programming under the distribution semantics. We introduce Second Level Algebraic Model Counting (2AMC) as a generic framework for this kind of problems. As 2AMC is to (algebraic) model counting what forall-exists-SAT is to propositional satisfiability, it is notoriously hard to solve. First level techniques based on Knowledge Compilation (KC) have been adapted for specific 2AMC instances by imposing variable order constraints on the resulting circuit. However, those constraints can severely increase the circuit size and thus decrease the efficiency of such approaches. We show that we can exploit the logical structure of a 2AMC problem to omit parts of these constraints, thus limiting the negative effect. Furthermore, we introduce and implement a strategy to generate a sufficient set of constraints statically, with a priori guarantees for the performance of KC. Our empirical evaluation on several benchmarks and tasks confirms that our theoretical results can translate into more efficient solving in practice. Under consideration for acceptance in TPLP. * Full proofs for all technical results are in the technical Appendix A.

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Section: Second Level Algebraic Model Countingsupporting

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Efficient Knowledge Compilation Beyond Weighted Model Counting

Kiesel¹,

Totis²,

Kimmig³

2022

Preprint

Self Cite

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show abstract

“…Alternatively, some authors employ DDs as linearization tools for non-linear expressions Cire 2018, Bergman andLozano 2021) and probabilistic structures (Latour et al 2017, 2019). Thus, a DD network flow formulation is most beneficial when standard procedures lead to poor relaxations and the DD encoding is small.…”

Section: Modelingmentioning

confidence: 99%

Decision Diagrams for Discrete Optimization: A Survey of Recent Advances

Castro¹,

Ciré²,

Beck³

2022

Preprint

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In the last decade, decision diagrams (DDs) have been the basis for a large array of novel approaches for modeling and solving optimization problems. Many techniques now use DDs as a key tool to achieve stateof-the-art performance within other optimization paradigms, such as integer programming and constraint programming. This paper provides a survey of the use of DDs in discrete optimization, particularly focusing on recent developments. We classify these works into two groups based on the type of diagram (i.e., exact or approximate) and present a thorough description of their use. We discuss the main advantages of DDs, point out major challenges, and provide directions for future work.

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“…Another related solution is presented in (Latour et al 2017), where the authors introduce an algorithm to combine Probabilistic (Logic) Programming and Constraint Programming to solve decision-theoretic tasks: as in that paper, we use a compact representation of the probabilistic logic program (they use SDD, we use BDD), and extend an already existing tool (they extend ProbLog, we extend PITA). Differently, they restrict the type of constraints involved (linear constraints over sum of Boolean decision variables) and they do not consider the computation of optimal probability values.…”

Section: Related Workmentioning

confidence: 99%

Optimizing Probabilities in Probabilistic Logic Programs

Azzolini¹,

Riguzzi²

2021

Preprint

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Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions of random variables. Here, we introduce a new class of probabilistic logic programs, namely Probabilistic Optimizable Logic Programs, and we provide an effective algorithm to find the best assignment to probabilities of random variables, such that a set of constraints is satisfied and an objective function is optimized. This paper is under consideration for acceptance in Theory and Practice of Logic Programming.

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Combining Stochastic Constraint Optimization and Probabilistic Programming

Cited by 13 publications

References 23 publications

Efficient Knowledge Compilation Beyond Weighted Model Counting

Efficient Knowledge Compilation Beyond Weighted Model Counting

Decision Diagrams for Discrete Optimization: A Survey of Recent Advances

Optimizing Probabilities in Probabilistic Logic Programs

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