Letcher, A;
Balduzzi, D;
Racaniere, S;
Martens, J;
Foerster, J;
Tuyls, K;
Graepel, T;
(2019)
Differentiable Game Mechanics.
Journal of Machine Learning Research
, 20
(84)
pp. 1-40.
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Abstract
Deep learning is built on the foundational guarantee that gradient descent on an objective function converges to local minima. Unfortunately, this guarantee fails in settings, such as generative adversarial nets, that exhibit multiple interacting losses. The behavior of gradient-based methods in games is not well understood and is becoming increasingly important as adversarial and multi-objective architectures proliferate. In this paper, we develop new tools to understand and control the dynamics in n-player differentiable games. The key result is to decompose the game Jacobian into two components. The first, symmetric component, is related to potential games, which reduce to gradient descent on an implicit function. The second, antisymmetric component, 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 differentiable games. Basic experiments show SGA is competitive with recently proposed algorithms for finding stable fixed points in GANs – while at the same time being applicable to, and having guarantees in, much more general cases.
| Type: | Article |
|---|---|
| Title: | Differentiable Game Mechanics |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://jmlr.org/papers/v20/19-008.html |
| Language: | English |
| Additional information: | © The Authors. License: CC-BY 4.0, see (https://creativecommons.org/licenses/by/4.0/). |
| Keywords: | game theory, generative adversarial networks, deep learning, classical mechanics, hamiltonian mechanics, gradient descent, dynamical systems |
| UCL classification: | UCL 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/10076314 |
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