We present a new algorithm for optimizing min-max loss functions that arise in training GANs. We prove that our algorithm converges to an equilibrium point in time polynomial in the dimension , and smoothness parameters of the loss function. The point our algorithm converges to is stable when the maximizing player can respond using any sequence of steps which increase the loss at each step, and the minimizing player is empowered to simulate the maximizing player 's response for arbitrarily many steps but is restricted to move according to updates sampled from a stochastic gradient oracle. We apply our algorithm to train GANs on Gaussian mixtures, MNIST and CIFAR-10. We observe that our algorithm trains stably and avoids mode collapse, while achieving a training time per iteration and memory requirement similar to gradient descent-ascent.
We present a first-order algorithm for nonconvex-nonconcave min-max optimization problems such as those that arise in training GANs. Our algorithm provably converges in time polynomial in the dimension and smoothness parameters of the loss function. To achieve convergence, we 1) give a novel approximation to the global strategy of the max-player based on first-order algorithms such as gradient ascent, and 2) empower the min-player to look ahead and simulate the max-player 's response for arbitrarily many steps , but restrict the min-player to move according to updates sampled from a stochastic gradient oracle. Our algorithm, when used to train GANs on synthetic and real-world datasets, does not cycle, results in GANs that seem to avoid mode collapse, and achieves a training time per iteration and memory requirement similar to gradient descent-ascent.
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new algorithm for optimizing
first-order algorithm for nonconvex-nonconcave
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loss functions
optimization problems such as those
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We prove that our algorithm converges to an equilibrium point
Our algorithm provably converges
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,
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The point our algorithm converges to is stable when the maximizing player can respond using any sequence of steps which increase the loss at each step, and
To achieve convergence, we 1) give a novel approximation to
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minimizing player is empowered to simulate
global strategy of
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maximizing player
max-player based on first-order algorithms such as gradient ascent, and 2) empower the min-player to look ahead and simulate the max-player
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but is restricted
, but restrict the min-player
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We apply our algorithm
Our algorithm, when used
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Gaussian mixtures, MNIST and CIFAR-10. We observe that our algorithm trains stably and avoids
synthetic and real-world datasets, does not cycle, results in GANs that seem to avoid
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while achieving
and achieves