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The interplay between Machine Learning (ML) and Constrained Optimization (CO) has recently been the subject of increasing interest, leading to a new and prolific research area covering (e.g.) Decision Focused Learning and Constrained Reinforcement Learning. Such approaches strive to tackle complex decision problems under uncertainty over multiple stages, involving both explicit (cost function, constraints) and implicit knowledge (from data), and possibly subject to execution time restrictions. While a good degree of success has been achieved, the existing methods still have limitations in terms of both applicability and effectiveness. For problems in this class, we propose UNIFY, a unified framework to design a solution policy for complex decision-making problems. Our approach relies on a clever decomposition of the policy in two stages, namely an unconstrained ML model and a CO problem, to take advantage of the strength of each approach while compensating for its weaknesses. With a little design effort, UNIFY can generalize several existing approaches, thus extending their applicability. We demonstrate the method effectiveness on two practical problems, namely an Energy Management System and the Set Multi-cover with stochastic coverage requirements. Finally, we highlight some current challenges of our method and future research directions that can benefit from the cross-fertilization of the two fields.

The advent of the coronavirus pandemic has sparked the interest in predictive models capable of forecasting virus-spreading, especially for boosting and supporting decision-making processes. In this paper, we will outline the main Deep Learning approaches aimed at predicting the spreading of a disease in space and time. The aim is to show the emerging trends in this area of research and provide a general perspective on the possible strategies to approach this problem. In doing so, we will mainly focus on two macro-categories: classical Deep Learning approaches and Hybrid models. Finally, we will discuss the main advantages and disadvantages of different models, and underline the most promising development directions to improve these approaches.

Regularization-based approaches for injecting constraints in Machine Learning (ML) were introduced to improve a predictive model via expert knowledge. We tackle the issue of finding the right balance between the loss (the accuracy of the learner) and the regularization term (the degree of constraint satisfaction). The key results of this paper is the formal demonstration that this type of approach cannot guarantee to find all optimal solutions. In particular, in the non-convex case there might be optima for the constrained problem that do not correspond to any multiplier value.

Deep Learning (DL) models proved themselves to perform extremely well on a wide variety of learning tasks, as they can learn useful patterns from large data sets. However, purely data-driven models might struggle when very difficult functions need to be learned or when there is not enough available training data. Fortunately, in many domains prior information can be retrieved and used to boost the performance of DL models. This paper presents a first survey of the approaches devised to integrate domain knowledge, expressed in the form of constraints, in DL learning models to improve their performance, in particular targeting deep neural networks. We identify five (non-mutually exclusive) categories that encompass the main approaches to inject domain knowledge: 1) acting on the features space, 2) modifications to the hypothesis space, 3) data augmentation, 4) regularization schemes, 5) constrained learning.

Adding constraint support in Machine Learning has the potential to address outstanding issues in data-driven AI systems, such as safety and fairness. Existing approaches typically apply constrained optimization techniques to ML training, enforce constraint satisfaction by adjusting the model design, or use constraints to correct the output. Here, we investigate a different, complementary, strategy based on "teaching" constraint satisfaction to a supervised ML method via the direct use of a state-of-the-art constraint solver: this enables taking advantage of decades of research on constrained optimization with limited effort. In practice, we use a decomposition scheme alternating master steps (in charge of enforcing the constraints) and learner steps (where any supervised ML model and training algorithm can be employed). The process leads to approximate constraint satisfaction in general, and convergence properties are difficult to establish; despite this fact, we found empirically that even a na\"ive setup of our approach performs well on ML tasks with fairness constraints, and on classical datasets with synthetic constraints.

Given enough data, Deep Neural Networks (DNNs) are capable of learning complex input-output relations with high accuracy. In several domains, however, data is scarce or expensive to retrieve, while a substantial amount of expert knowledge is available. It seems reasonable that if we can inject this additional information in the DNN, we could ease the learning process. One such case is that of Constraint Problems, for which declarative approaches exists and pure ML solutions have obtained mixed success. Using a classical constrained problem as a case study, we perform controlled experiments to probe the impact of progressively adding domain and empirical knowledge in the DNN. Our results are very encouraging, showing that (at least in our setup) embedding domain knowledge at training time can have a considerable effect and that a small amount of empirical knowledge is sufficient to obtain practically useful results.

The growing demands of the worldwide IT infrastructure stress the need for reduced power consumption, which is addressed in so-called transprecision computing by improving energy efficiency at the expense of precision. For example, reducing the number of bits for some floating-point operations leads to higher efficiency, but also to a non-linear decrease of the computation accuracy. Depending on the application, small errors can be tolerated, thus allowing to fine-tune the precision of the computation. Finding the optimal precision for all variables in respect of an error bound is a complex task, which is tackled in the literature via heuristics. In this paper, we report on a first attempt to address the problem by combining a Mathematical Programming (MP) model and a Machine Learning (ML) model, following the Empirical Model Learning methodology. The ML model learns the relation between variables precision and the output error; this information is then embedded in the MP focused on minimizing the number of bits. An additional refinement phase is then added to improve the quality of the solution. The experimental results demonstrate an average speedup of 6.5\% and a 3\% increase in solution quality compared to the state-of-the-art. In addition, experiments on a hardware platform capable of mixed-precision arithmetic (PULPissimo) show the benefits of the proposed approach, with energy savings of around 40\% compared to fixed-precision.

Machine Learning (ML) models are very effective in many learning tasks, due to the capability to extract meaningful information from large data sets. Nevertheless, there are learning problems that cannot be easily solved relying on pure data, e.g. scarce data or very complex functions to be approximated. Fortunately, in many contexts domain knowledge is explicitly available and can be used to train better ML models. This paper studies the improvements that can be obtained by integrating prior knowledge when dealing with a non-trivial learning task, namely precision tuning of transprecision computing applications. The domain information is injected in the ML models in different ways: I) additional features, II) ad-hoc graph-based network topology, III) regularization schemes. The results clearly show that ML models exploiting problem-specific information outperform the purely data-driven ones, with an average accuracy improvement around 38%.

Anomaly detection in supercomputers is a very difficult problem due to the big scale of the systems and the high number of components. The current state of the art for automated anomaly detection employs Machine Learning methods or statistical regression models in a supervised fashion, meaning that the detection tool is trained to distinguish among a fixed set of behaviour classes (healthy and unhealthy states). We propose a novel approach for anomaly detection in High Performance Computing systems based on a Machine (Deep) Learning technique, namely a type of neural network called autoencoder. The key idea is to train a set of autoencoders to learn the normal (healthy) behaviour of the supercomputer nodes and, after training, use them to identify abnormal conditions. This is different from previous approaches which where based on learning the abnormal condition, for which there are much smaller datasets (since it is very hard to identify them to begin with). We test our approach on a real supercomputer equipped with a fine-grained, scalable monitoring infrastructure that can provide large amount of data to characterize the system behaviour. The results are extremely promising: after the training phase to learn the normal system behaviour, our method is capable of detecting anomalies that have never been seen before with a very good accuracy (values ranging between 88% and 96%)., Comment: 9 pages, 3 figures

In the past few years, the area of Machine Learning (ML) has witnessed tremendous advancements, becoming a pervasive technology in a wide range of applications. One area that can significantly benefit from the use of ML is Combinatorial Optimization. The three pillars of constraint satisfaction and optimization problem solving, i.e., modeling, search, and optimization, can exploit ML techniques to boost their accuracy, efficiency and effectiveness. In this survey we focus on the modeling component, whose effectiveness is crucial for solving the problem. The modeling activity has been traditionally shaped by optimization and domain experts, interacting to provide realistic results. Machine Learning techniques can tremendously ease the process, and exploit the available data to either create models or refine expert-designed ones. In this survey we cover approaches that have been recently proposed to enhance the modeling process by learning either single constraints, objective functions, or the whole model. We highlight common themes to multiple approaches and draw connections with related fields of research., Comment: Originally submitted to IJCAI2018

Energy efficiency is of paramount importance for the sustainability of HPC systems. Energy consumption limits the peak performance of supercomputers and accounts for a large share of total cost of ownership. Consequently, system owners and final users have started exploring mechanisms to trade off performance for power consumption, for example through frequency and voltage scaling. However, only a limited number of studies have been devoted to explore the economic viability of performance scaling solutions and to devise pricing mechanisms fostering a more energy-conscious usage of resources, without adversely impacting return-of-investment on the HPC facility. We present a parametrized model to analyze the impact of frequency scaling on energy and to assess the potential total cost benefits for the HPC facility and the user. We evaluate four pricing schemes, considering both facility manager and the user perspectives. We then perform a design space exploration considering current and near-future HPC systems and technologies.

In the policy making process a number of disparate and diverse issues such as economic development, environmental aspects, as well as the social acceptance of the policy, need to be considered. A single person might not have all the required expertises, and decision support systems featuring optimization components can help to assess policies. Leveraging on previous work on Strategic Environmental Assessment, we developed a fully-fledged system that is able to provide optimal plans with respect to a given objective, to perform multi-objective optimization and provide sets of Pareto optimal plans, and to visually compare them. Each plan is environmentally assessed and its footprint is evaluated. The heart of the system is an application developed in a popular Constraint Logic Programming system on the Reals sort. It has been equipped with a web service module that can be queried through standard interfaces, and an intuitive graphic user interface., Comment: Accepted at ICLP2014 Conference as Technical Communication, due to appear in Theory and Practice of Logic Programming (TPLP)

In this paper we present a new approach to solve the satisfiability problem (SAT), based on boolean networks (BN). We define a mapping between a SAT instance and a BN, and we solve SAT problem by simulating the BN dynamics. We prove that BN fixed points correspond to the SAT solutions. The mapping presented allows to develop a new class of algorithms to solve SAT. Moreover, this new approach suggests new ways to combine symbolic and connectionist computation and provides a general framework for local search algorithms., Comment: 12 pages, 6 figures, 2 tables

Strategic Environmental Assessment is a procedure aimed at introducing systematic assessment of the environmental effects of plans and programs. This procedure is based on the so-called coaxial matrices that define dependencies between plan activities (infrastructures, plants, resource extractions, buildings, etc.) and positive and negative environmental impacts, and dependencies between these impacts and environmental receptors. Up to now, this procedure is manually implemented by environmental experts for checking the environmental effects of a given plan or program, but it is never applied during the plan/program construction. A decision support system, based on a clear logic semantics, would be an invaluable tool not only in assessing a single, already defined plan, but also during the planning process in order to produce an optimized, environmentally assessed plan and to study possible alternative scenarios. We propose two logic-based approaches to the problem, one based on Constraint Logic Programming and one on Probabilistic Logic Programming that could be, in the future, conveniently merged to exploit the advantages of both. We test the proposed approaches on a real energy plan and we discuss their limitations and advantages., Comment: 17 pages, 1 figure, 26th Int'l. Conference on Logic Programming (ICLP'10)

In classical CLP(FD) systems, domains of variables are completely known at the beginning of the constraint propagation process. However, in systems interacting with an external environment, acquiring the whole domains of variables before the beginning of constraint propagation may cause waste of computation time, or even obsolescence of the acquired data at the time of use. For such cases, the Interactive Constraint Satisfaction Problem (ICSP) model has been proposed as an extension of the CSP model, to make it possible to start constraint propagation even when domains are not fully known, performing acquisition of domain elements only when necessary, and without the need for restarting the propagation after every acquisition. In this paper, we show how a solver for the two sorted CLP language, defined in previous work, to express ICSPs, has been implemented in the Constraint Handling Rules (CHR) language, a declarative language particularly suitable for high level implementation of constraint solvers., Comment: 22 pages, 2 figures, 1 table To appear in Theory and Practice of Logic Programming (TPLP)

Solution techniques for Constraint Satisfaction and Optimisation Problems often make use of backtrack search methods, exploiting variable and value ordering heuristics. In this paper, we propose and analyse a very simple method to apply in case the value ordering heuristic produces ties: postponing the branching decision. To this end, we group together values in a tie, branch on this sub-domain, and defer the decision among them to lower levels of the search tree. We show theoretically and experimentally that this simple modification can dramatically improve the efficiency of the search strategy. Although in practise similar methods may have been applied already, to our knowledge, no empirical or theoretical study has been proposed in the literature to identify when and to what extent this strategy should be used., Comment: 11 pages, 3 figures