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The Mechanics of n-Player Differentiable Games

Balduzzi, D; Racaniere, S; Martens, J; Foerster, J; Tuyls, K; Graepel, T; (2018) The Mechanics of n-Player Differentiable Games. In: Dy, JG and Krause, A, (eds.) Proceedings of the 35th International Conference on Machine Learning. (pp. pp. 363-372). JMLR.org Green open access

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Abstract

The cornerstone underpinning deep learning is the guarantee that gradient descent on an objective converges to local minima. Unfortunately, this guarantee fails in settings, such as generative adversarial nets, where there are multiple interacting losses. The behavior of gradient-based methods in games is not well understood – and is becoming increasingly important as adversarial and multiobjective architectures proliferate. In this paper, we develop new techniques to understand and control the dynamics in general games. The key result is to decompose the second-order dynamics into two components. The first is related to potential games, which reduce to gradient descent on an implicit function; the second relates to Hamiltonian games, a new class of games that obey a conservation law, akin to conservation laws in classical mechanical systems. The decomposition motivates Symplectic Gradient Adjustment (SGA), a new algorithm for finding stable fixed points in general games. Basic experiments show SGA is competitive with recently proposed algorithms for finding stable fixed points in GANs – whilst at the same time being applicable to – and having guarantees in – much more general games.

Type: Proceedings paper
Title: The Mechanics of n-Player Differentiable Games
Event: International Conference on Machine Learning, 10-15 July 2018, Stockholm, Sweden
Open access status: An open access version is available from UCL Discovery
Publisher version: http://proceedings.mlr.press/v80/
Language: English
Additional information: Copyright 2018 by the author(s). Published under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0).
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10053320
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