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Deep Statistical Solvers
Balthazar Donon · Zhengying Liu · Wenzhuo LIU · Isabelle Guyon · Antoine Marot · Marc Schoenauer

Wed Dec 09 09:00 AM -- 11:00 AM (PST) @ Poster Session 3 #950

This paper introduces Deep Statistical Solvers (DSS), a new class of trainable solvers for optimization problems, arising e.g., from system simulations. The key idea is to learn a solver that generalizes to a given distribution of problem instances. This is achieved by directly using as loss the objective function of the problem, as opposed to most previous Machine Learning based approaches, which mimic the solutions attained by an existing solver. Though both types of approaches outperform classical solvers with respect to speed for a given accuracy, a distinctive advantage of DSS is that they can be trained without a training set of sample solutions. Focusing on use cases of systems of interacting and interchangeable entities (e.g. molecular dynamics, power systems, discretized PDEs), the proposed approach is instantiated within a class of Graph Neural Networks. Under sufficient conditions, we prove that the corresponding set of functions contains approximations to any arbitrary precision of the actual solution of the optimization problem. The proposed approach is experimentally validated on large linear problems, demonstrating super-generalisation properties; And on AC power grid simulations, on which the predictions of the trained model have a correlation higher than 99.99% with the outputs of the classical Newton-Raphson method (known for its accuracy), while being 2 to 3 orders of magnitude faster.

Author Information

Balthazar Donon (RTE R&D / Université Paris-Saclay)
Zhengying Liu (Inria/U. Paris-Saclay)
Wenzhuo LIU (Inria Paris Saclay)
Isabelle Guyon (U. Paris-Saclay & ChaLearn)

Isabelle Guyon recently joined Google Brain as a research scientist. She is also professor of artificial intelligence at Université Paris-Saclay (Orsay). Her areas of expertise include computer vision, bioinformatics, and power systems. She is best known for being a co-inventor of Support Vector Machines. Her recent interests are in automated machine learning, meta-learning, and data-centric AI. She has been a strong promoter of challenges and benchmarks, and is president of ChaLearn, a non-profit dedicated to organizing machine learning challenges. She is community lead of Codalab competitions, a challenge platform used both in academia and industry. She co-organized the “Challenges in Machine Learning Workshop” @ NeurIPS between 2014 and 2019, launched the "NeurIPS challenge track" in 2017 while she was general chair, and pushed the creation of the "NeurIPS datasets and benchmark track" in 2021, as a NeurIPS board member.

Antoine Marot (RTE)
Marc Schoenauer (INRIA / U. Paris-Saclay)

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