Combinatorial optimization assumes that all parameters of the optimization problem, e.g. the weights in the objective function, are fixed. Often, these weights are mere estimates and increasingly machine learning techniques are used to for their estimation. Recently, Smart Predict and Optimize (SPO) has been proposed for problems with a linear objective function over the predictions, more specifically linear programming problems. It takes the regret of the predictions on the linear problem into account, by repeatedly solving it during learning. We investigate the use of SPO to solve more realistic discrete optimization problems. The main challenge is the repeated solving of the optimization problem. To this end, we investigate ways to relax the problem as well as warm-starting the learning and the solving. Our results show that even for discrete problems it often suffices to train by solving the relaxation in the SPO loss. Furthermore, this approach outperforms the state-of-the-art approach of Wilder, Dilkina, and Tambe. We experiment with weighted knapsack problems as well as complex scheduling problems, and show for the first time that a predict-and-optimize approach can successfully be used on large-scale combinatorial optimization problems.
Assessing risk for voluminous legal documents such as request for proposal, contracts is tedious and error prone. We have developed "risk-o-meter", a framework, based on machine learning and natural language processing to review and assess risks of any legal document. Our framework uses Paragraph Vector, an unsupervised model to generate vector representation of text. This enables the framework to learn contextual relations of legal terms and generate sensible context aware embedding. The framework then feeds the vector space into a supervised classification algorithm to predict whether a paragraph belongs to a pre-defined risk category or not. The framework thus extracts risk prone paragraphs. This technique efficiently overcomes the limitations of keyword based search. We have achieved an accuracy of 91% for the risk category having the largest training dataset. This framework will help organizations optimize effort to identify risk from large document base with minimal human intervention and thus will help to have risk mitigated sustainable growth. Its machine learning capability makes it scalable to uncover relevant information from any type of document apart from legal documents, provided the library is pre-populated and rich.
There is an increased interest in solving complex constrained problems where part of the input is not given as facts, but received as raw sensor data such as images or speech. We will use 'visual sudoku' as a prototype problem, where the given cell digits are handwritten and provided as an image thereof. In this case, one first has to train and use a classifier to label the images, so that the labels can be used for solving the problem. In this paper, we explore the hybridisation of classifying the images with the reasoning of a constraint solver. We show that pure constraint reasoning on predictions does not give satisfactory results. Instead, we explore the possibilities of a tighter integration, by exposing the probabilistic estimates of the classifier to the constraint solver. This allows joint inference on these probabilistic estimates, where we use the solver to find the maximum likelihood solution. We explore the tradeoff between the power of the classifier and the power of the constraint reasoning, as well as further integration through the additional use of structural knowledge. Furthermore, we investigate the effect of calibration of the probabilistic estimates on the reasoning. Our results show that such hybrid approaches vastly outperform a separate approach, which encourages a further integration of prediction (probabilities) and constraint solving.
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