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SGA.md

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+# The Mechanics of n-Player Differentiable Games
+David Balduzzi 1 Sebastien Racani´ere` 1 James Martens 1 Jakob Foerster 2 Karl Tuyls 1 Thore Graepel 1
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+## abstract
+The cornerstone underpinning deep learning is the guarantee that gradient descent on an objective converges to local minima. 
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+Unfortunately, this guarantee fails in settings, such as generative adversarial nets, where there are multiple interacting losses. 
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+The behavior of gradient-based methods in games is not well understood – and is becoming increasingly important as adversarial and multiobjective architectures proliferate. 
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+In this paper, we develop new techniques to understand and control the dynamics in general games. 
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+The key result is to decompose the second-order dynamics into two components. 
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+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. 
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+The decomposition motivates Symplectic Gradient Adjustment (SGA), a new algorithm for finding stable fixed points in general games. 
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+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.