Optimistic variant of MWU, and a variant of the Extragradient Method#1
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Optimistic variant of MWU, and a variant of the Extragradient Method#1
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wyz2368
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Dec 7, 2023
| num_iterations = 10 | ||
| num_iterations = 50 | ||
| potential, games = runner(dim) | ||
| games.append([np.array([[2, -1], [-1, 4]]), np.array([[-2, 1], [1, -4]])]) |
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Is the game appended an ordinal potential game?
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No, I appended a zero-sum game in order to point the difference between the vanilla MWU and the two new methods.
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| import numpy as np | |||
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| def FLBR_multiplicative_weights_update(meta_games, num_iterations, step_size, alternate=False): | |||
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Can you add some reference to the implementation of FLBR and Optimistic MWU? Thanks.
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Yes sure, here you go
- Optimistic multiplicative weights update https://arxiv.org/pdf/1807.04252.pdf
- FLBR multiplicative weights update https://arxiv.org/pdf/2106.03579.pdf
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| last_weights = [np.ones(n)/n, np.ones(m)/m] | ||
| weights = [np.ones(n) / n, np.ones(m) / m] | ||
| print(step_size) |
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Please mute all printing used for testing.
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There are two methods. The first one is the Optimistic Multiplicative Weights Update method, and the second one is the Forward Looking Best-Response Multiplicative Weights Update method. Both attain point-wise convergence in the case of 2-player zero-sum games.