Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower bounds that can be significantly better than classical bounding mechanisms, such as linear relaxations. It is well known that the quality of the bound achieved through this flexible bounding method is highly reliant on the ordering of variables chosen for building the diagram, and finding an ordering that optimizes standard metrics, or even improving one, is an NP-hard problem. In this paper, we propose an innovative and generic approach based on deep reinforcement learning for obtaining an ordering for tightening the bounds obtained with relaxed and restricted DDs. We apply the approach to both the Maximum Independent Set Problem and the Maximum Cut Problem. Experimental results on synthetic instances show that the deep reinforcement learning approach, by achieving tighter objective function bounds, generally outperforms ordering methods commonly used in the literature when the distribution of instances is known. To the best knowledge of the authors, this is the first paper to apply machine learning to directly improve relaxation bounds obtained by general-purpose bounding mechanisms for combinatorial optimization problems. Click to Read Paper
Machine Learning in High Energy Physics Community White Paper
Jul 08, 2018
Kim Albertsson, Piero Altoe, Dustin Anderson, Michael Andrews, Juan Pedro Araque Espinosa, Adam Aurisano, Laurent Basara, Adrian Bevan, Wahid Bhimji, Daniele Bonacorsi, Paolo Calafiura, Mario Campanelli, Louis Capps, Federico Carminati, Stefano Carrazza, Taylor Childers, Elias Coniavitis, Kyle Cranmer, Claire David, Douglas Davis, Javier Duarte, Martin Erdmann, Jonas Eschle, Amir Farbin, Matthew Feickert, Nuno Filipe Castro, Conor Fitzpatrick, Michele Floris, Alessandra Forti, Jordi Garra-Tico, Jochen Gemmler, Maria Girone, Paul Glaysher, Sergei Gleyzer, Vladimir Gligorov, Tobias Golling, Jonas Graw, Lindsey Gray, Dick Greenwood, Thomas Hacker, John Harvey, Benedikt Hegner, Lukas Heinrich, Ben Hooberman, Johannes Junggeburth, Michael Kagan, Meghan Kane, Konstantin Kanishchev, Przemysław Karpiński, Zahari Kassabov, Gaurav Kaul, Dorian Kcira, Thomas Keck, Alexei Klimentov, Jim Kowalkowski, Luke Kreczko, Alexander Kurepin, Rob Kutschke, Valentin Kuznetsov, Nicolas Köhler, Igor Lakomov, Kevin Lannon, Mario Lassnig, Antonio Limosani, Gilles Louppe, Aashrita Mangu, Pere Mato, Narain Meenakshi, Helge Meinhard, Dario Menasce, Lorenzo Moneta, Seth Moortgat, Mark Neubauer, Harvey Newman, Hans Pabst, Michela Paganini, Manfred Paulini, Gabriel Perdue, Uzziel Perez, Attilio Picazio, Jim Pivarski, Harrison Prosper, Fernanda Psihas, Alexander Radovic, Ryan Reece, Aurelius Rinkevicius, Eduardo Rodrigues, Jamal Rorie, David Rousseau, Aaron Sauers, Steven Schramm, Ariel Schwartzman, Horst Severini, Paul Seyfert, Filip Siroky, Konstantin Skazytkin, Mike Sokoloff, Graeme Stewart, Bob Stienen, Ian Stockdale, Giles Strong, Savannah Thais, Karen Tomko, Eli Upfal, Emanuele Usai, Andrey Ustyuzhanin, Martin Vala, Sofia Vallecorsa, Mauro Verzetti, Xavier Vilasís-Cardona, Jean-Roch Vlimant, Ilija Vukotic, Sean-Jiun Wang, Gordon Watts, Michael Williams, Wenjing Wu, Stefan Wunsch, Omar Zapata

Machine learning is an important research area in particle physics, beginning with applications to high-level physics analysis in the 1990s and 2000s, followed by an explosion of applications in particle and event identification and reconstruction in the 2010s. In this document we discuss promising future research and development areas in machine learning in particle physics with a roadmap for their implementation, software and hardware resource requirements, collaborative initiatives with the data science community, academia and industry, and training the particle physics community in data science. The main objective of the document is to connect and motivate these areas of research and development with the physics drivers of the High-Luminosity Large Hadron Collider and future neutrino experiments and identify the resource needs for their implementation. Additionally we identify areas where collaboration with external communities will be of great benefit. Click to Read Paper