The complexity of exact learning of acyclic conditional preference networks from swap examples

Alanazi, Eisa; Mouhoub, Malek; Zilles, Sandra

doi:10.1016/j.artint.2019.103182

Cited by 9 publications

(15 citation statements)

References 42 publications

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“…Instead we want to create a consensus preference ordering (over all socalled swap pairs, i.e., pairs of outcomes that differ only in a single attribute) that best aggregates the given preference orders, under the constraint that this consensus ordering can be represented as a CP-net. Our approach is similar to that of Ali et al (2021), in that we treat preference aggregation as an optimization problem where the input profile and the optimal output are both represented using CP-nets. In contrast to the mCP-nets or PCP-nets approach, this avoids storing all input CP-nets and allows for applying existing CP-net algorithms for reasoning about preferences.…”

Section: Related Workmentioning

confidence: 99%

“…In contrast to the mCP-nets or PCP-nets approach, this avoids storing all input CP-nets and allows for applying existing CP-net algorithms for reasoning about preferences. However, Ali et al (2021) showed that there is no polynomial-time algorithm solving the problem that we focus on. This motivates us to study approximation algorithms for said problem.…”

Section: Related Workmentioning

confidence: 99%

“…In this paper, we always assume implicitly that CP-nets are complete, i.e., any CPT contains the maximum possible number of rules. 2 This assumption can be limiting for algorithmic studies, but is not uncommon in the literature (see, e.g., (Alanazi, Mouhoub, and Zilles 2020;Ali et al 2021)). Note that our study can be generalized to incomplete CP-nets with some additional effort, yet without major conceptual differences.…”

Section: Preliminariesmentioning

confidence: 99%

“…However, feasible solutions to this problem are unlikely to be found, partly because even determining how a given CPnet orders a given outcome pair is NP-hard (Boutilier et al 2004). For this and other reasons, Ali et al (2021) propose to focus on an objective function that counts only swaps that are ordered differently by N and N s . A swap is a pair of outcomes that differ only in the value of a single attribute; deciding how a CP-net orders any given swap can be done in polynomial time (Boutilier et al 2004).…”

Section: Introductionmentioning

confidence: 99%

“…We adopt the objective function proposed by Ali et al (2021). 1 However, they showed that this function cannot be optimized in polynomial time; in particular, sometimes the size of the only optimal solution is exponential in the size of the input.…”

Section: Introductionmentioning

confidence: 99%

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Approximation Algorithms for Preference Aggregation Using CP-Nets

Ali,

Yang,

Zilles

2024

AAAI

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This paper studies the design and analysis of approximation algorithms for aggregating preferences over combinatorial domains, represented using Conditional Preference Networks (CP-nets). Its focus is on aggregating preferences over so-called swaps, for which optimal solutions in general are already known to be of exponential size. We first analyze a trivial 2-approximation algorithm that simply outputs the best of the given input preferences, and establish a structural condition under which the approximation ratio of this algorithm is improved to 4/3. We then propose a polynomial-time approximation algorithm whose outputs are provably no worse than those of the trivial algorithm, but often substantially better. A family of problem instances is presented for which our improved algorithm produces optimal solutions, while, for any ε, the trivial algorithm cannot attain a (2- ε)-approximation. These results may lead to the first polynomial-time approximation algorithm that solves the CP-net aggregation problem for swaps with an approximation ratio substantially better than 2.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approximation Algorithms for Preference Aggregation Using CP-Nets

Ali,

Yang,

Zilles

2024

AAAI

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An Implicit Learning Approach for Solving the Nurse Scheduling Problem

Said

Mohammed

Mouhoub

2021

Lecture Notes in Computer Science

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Solving combinatorial optimization problems involve satisfying a set of hard constraints while optimizing some objectives. In this context, exact or approximate methods can be used. While exact methods guarantee the optimal solution, they often come with an exponential running time as opposed to approximate methods that trade the solution's quality for a better running time. In this context, we tackle the Nurse Scheduling Problem (NSP). The NSP consist in assigning nurses to daily shifts within a planning horizon such that workload constraints are satisfied while hospital's costs and nurses' preferences are optimized. To solve the NSP, we propose implicit and explicit approaches. In the implicit solving approach, we rely on Machine Learning methods using historical data to learn and generate new solutions through the constraints and objectives that may be embedded in the learned patterns. To quantify the quality of using our implicit approach in capturing the embedded constraints and objectives, we rely on the Frobenius Norm, a quality measure used to compute the average error between the generated solutions and historical data. To compensate for the uncertainty related to the implicit approach given that the constraints and objectives may not be concretely visible in the produced solutions, we propose an alternative explicit approach where we first model the NSP using the Constraint Satisfaction Problem (CSP) framework. Then we develop Stochastic Local Search methods and a new Branch and Bound algorithm enhanced with constraint propagation techniques and variables/values ordering heuristics. Since our implicit approach may not guarantee the feasibility or optimality of the generated solution, we propose a data-driven approach to passively learn the NSP as a constraint network. The learned constraint network, formulated as a CSP, will then be solved using the methods we listed earlier.

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