Many real-world problems can be effectively solved by means of combinatorial optimization. However, appropriate models to give to a solver are not always available, and sometimes must be learned from historical data. Although some research has been done in this area, the task of learning (weighted partial) MAX-SAT models has not received much attention thus far, even though such models can be used in many real-world applications. Furthermore, most existing work is limited to learning models from non-contextual data, where instances are labeled as solutions and non-solutions, but without any specification of the contexts in which those labels apply. A recent approach named hassle-sls has addressed these limitations: it can jointly learn hard constraints and weighted soft constraints from labeled contextual examples. However, it is hindered by long runtimes, as evaluating even a single candidate MAX-SAT model requires solving as many models as there are contexts in the training data, which quickly becomes highly expensive when the size of the model increases. In this work, we address these runtime issues. To this end, we make two contributions. First, we propose a faster model evaluation procedure that makes use of knowledge compilation. Second, we propose a genetic algorithm named hassle-gen that decreases the number of evaluations needed to find good models. We experimentally show that both contributions improve on the state of the art by speeding up learning, which in turn allows higher-quality MAX-SAT models to be found within a given learning time budget.

Constraint satisfaction problems (CSPs) are used widely, especially in the field of operations research, to model various real world problems like scheduling or planning. However,modelling a problem as a CSP is not trivial, it is labour intensive and requires both modelling and domain expertise. The emerging field of constraint learning deals with this problem by automatically learning constraints from a given dataset. While there are several interesting approaches for constraint learning, these works are hard to access for a non-expert user. Furthermore, different approaches have different underlying formalism and require different setups before they can be used. This demo paper combines these researches and brings it to non-expert users in the form of an interactive Excel plugin. To do this, we translate different formalism for specifying CSPs into a common language, which allows multiple constraint learners to coexist, making this plugin more powerful than individual constraint learners. Moreover, we integrate learning of CSPs from data with solving them, making it a self sufficient plugin. For the developers of different constraint learners, we provide an API that can be used to integrate their work with this plugin by implementing a handful of functions.

Real world decision making problems often involve both discrete and continuous variables and require a combination of probabilistic and deterministic knowledge. Stimulated by recent advances in automated reasoning technology, hybrid (discrete+continuous) probabilistic reasoning with constraints has emerged as a lively and fast growing research field. In this paper we provide a survey of existing techniques for hybrid probabilistic inference with logic and algebraic constraints. We leverage weighted model integration as a unifying formalism and discuss the different paradigms that have been used as well as the expressivity-efficiency trade-offs that have been investigated. We conclude the survey with a comparative overview of existing implementations and a critical discussion of open challenges and promising research directions.

Combinatorial optimization problems are ubiquitous in artificial intelligence. Designing the underlying models, however, requires substantial expertise, which is a limiting factor in practice. The models typically consist of hard and soft constraints, or combine hard constraints with a preference function. We introduce a novel setting for learning combinatorial optimisation problems from contextual examples. These positive and negative examples show – in a particular context – whether the solutions are good enough or not. We develop our framework using the MAX-SAT formalism. We provide learnability results within the realizable and agnostic settings, as well as hassle, an implementation based on syntax-guided synthesis and showcase its promise on recovering synthetic and benchmark instances from examples.

Weighted model integration (WMI) is a framework for probabilistic inference over distributions with discrete and continuous variables and structured supports. Despite the growing popularity of WMI, existing density estimators ignore the problem of learning a structured support, and thus fail to handle unfeasible configurations and piecewise-linear relations between continuous variables. We propose lariat, a novel method to tackle this challenging problem. In a first step, our approach induces an SMT(ℒℛA) formula representing the support of the structured distribution. Next, it combines the latter with a density learned using a state-of-the-art estimation method. The overall model automatically accounts for the discontinuous nature of the underlying structured distribution. Our experimental results with synthetic and real-world data highlight the promise of the approach.

State-of-the-art probabilistic inference algorithms, such as variable elimination and search-based approaches, rely heavily on the order in which variables are marginalized. Finding the optimal ordering is an NP-complete problem. This computational hardness has led to heuristics to find adequate variable orderings. However, these heuristics have mostly been targeting discrete random variables. We show how variable ordering heuristics from the discrete domain can be ported to the discrete-continuous domain. We equip the state-of-the-art F-XSDD(BR) solver for discrete-continuous problems with such heuristics. Additionally, we propose a novel heuristic called bottom-up min-fill (BU-MiF), yielding a solver capable of determining good variable orderings without having to rely on the user to provide such an ordering. We empirically demonstrate its performance on a set of benchmark problems.

Linear Programming lies at the core of mathematical modelling and optimization. Designing linear programs (LPs) is a difficult and expensive process, as it requires both mathematical programming and domain expertise, and it involves both designing an objective function and feasibility constraints. To support this design process, we propose INCALP, an algorithm for inducing linear programs from examples. Since the objective can often be learned with standard techniques (e.g. regression), INCALP learns the hard constraints only. It does so by encoding constraint learning as a mixed integer linear program. INCALP achieves significant efficiency gains by considering gradually larger subsets of examples, and terminating as soon as a suitable program is found. In addition, INCALP encourages both compactness and sparsity of the learned program. Our empirical analysis on synthetic data and textbook problems highlights the promise of the approach.

Weighted Model Integration (WMI) is a popular technique for probabilistic inference that extends Weighted Model Counting (WMC) -- the standard inference technique for inference in discrete domains -- to domains with both discrete and continuous variables. However, existing WMI solvers each have different interfaces and use different formats for representing WMI problems. Therefore, we introduce pywmi (http://pywmi.org), an open source framework and toolbox for probabilistic inference using WMI, to address these shortcomings. Crucially, pywmi fixes a common internal format for WMI problems and introduces a common interface for WMI solvers. To assist users in modeling WMI problems, pywmi introduces modeling languages based on SMT-LIB.v2 or MiniZinc and parsers for both. To assist users in comparing WMI solvers, pywmi includes implementations of several state-of-the-art solvers, a fast approximate WMI solver, and a command-line interface to solve WMI problems. Finally, to assist developers in implementing new solvers, pywmi provides Python implementations of commonly used subroutines.

Weighted model integration (WMI) extends weighted model counting (WMC) to the integration of functions over mixed discrete-continuous probability spaces. It has shown tremendous promise for solving inference problems in graphical models and probabilistic programs. Yet, state-of-the-art tools for WMI are generally limited either by the range of amenable theories, or in terms of performance. To address both limitations, we propose the use of extended algebraic decision diagrams (XADDs) as a compilation language for WMI. Aside from tackling typical WMI problems, XADDs also enable partial WMI yielding parametrized solutions. To overcome the main roadblock of XADDs -- the computational cost of integration -- we formulate a novel and powerful exact symbolic dynamic programming (SDP) algorithm that seamlessly handles Boolean, integer-valued and real variables, and is able to effectively cache partial computations, unlike its predecessor. Our empirical results demonstrate that these contributions can lead to a significant computational reduction over existing probabilistic inference algorithms.

We introduce the problem of learning SMT(LRA) constraints from data. SMT(LRA) extends propositional logic with (in)equalities between numerical variables. Many relevant formal verification problems can be cast as SMT(LRA) instances and SMT(LRA) has supported recent developments in optimization and counting for hybrid Boolean and numerical domains. We introduce SMT(LRA) learning, the task of learning SMT(LRA) formulas from examples of feasible and infeasible instances, and we contribute INCAL, an exact non-greedy algorithm for this setting. Our approach encodes the learning task itself as an SMT(LRA) satisfiability problem that can be solved directly by SMT solvers. INCAL is an incremental algorithm that achieves exact learning by looking only at a small subset of the data, leading to significant speed-ups. We empirically evaluate our approach on both synthetic instances and benchmark problems taken from the SMT-LIB benchmarks repository.

Spreadsheet data is widely used today by many different people and across industries. However, writing, maintaining and identifying good formulae for spreadsheets can be time consuming and error-prone. To address this issue we have introduced the TaCLe system (Tabular Constraint Learner). The system tackles an inverse learning problem: given a plain comma separated file, it reconstructs the spreadsheet formulae that hold in the tables. Two important considerations are the number of cells and constraints to check, and how to deal with multiple formulae for the same cell. Our system reasons over entire rows and columns and has an intuitive user interface for interacting with the learned constraints and data. It can be seen as an intelligent assistance tool for discovering formulae from data. As a result, the user obtains a spreadsheet that can automatically recompute dependent cells when updating or adding data.