Exact Combinatorial Optimization with Graph Convolutional Neural Networks

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose to learn a variable selection policy for branch-and-bound in mixed-integer linear programming, by imitation learning on a diversified variant of the strong branching expert rule. We encode states as bipartite graphs and parameterize the policy as a graph convolutional neural network. Experiments on a series of synthetic problems demonstrate that our approach produces policies that can improve upon expert-designed branching rules on large problems, and generalize to instances significantly larger than seen during training.

Multivariate analysis methods in the search for the Higgs boson produced in association with top pairs at the ATLAS experiment at LHC.

The Large Hadron Collider, located at the CERN laboratories in Geneva, is the largest particle accelerator in the world. One of the main research fields at LHC is the study of the Higgs boson, the latest particle discovered at the ATLAS and CMS experiments. Due to the small production cross section for the Higgs boson, only a substantial statistics can offer the chance to study this particle properties. In order to perform these searches it is desirable to avoid the contamination of the signal signature by the number and variety of the background processes produced in pp collisions at LHC. Much account assumes the study of multivariate methods which, compared to the standard cut-based analysis, can enhance the signal selection of a Higgs boson produced in association with a top quark pair through a dileptonic final state (ttH channel). The statistics collected up to 2012 is not sufficient to supply a significant number of ttH events; however, the methods applied in this thesis will provide a powerful tool for the increasing statistics that will be collected during the next LHC data taking.