Minimax RR-ICM
A minimax variational extension of the RR-ICM that optimizes over the worst case among probability distributions on the sphere. It provides a robust theoretical basis for the polar direction of the Muon optimizer without relying on the average curvature assumption.
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The researchers proposed Minimax RR-ICM, which optimizes over the worst case over probability distributions on the sphere rather than averaging over directions.
In Minimax RR-ICM, every nonzero global minimum point lies on the polar ray of the gradient, and its scale is determined by a one-dimensional convex problem.
The admissible geometry corresponding to Minimax RR-ICM is a positive-semidefinite trace slab, in contrast to the spherical zonotope geometry of RR-ICM.
All Facts (3)
In Minimax RR-ICM, every nonzero global minimum point lies on the polar ray of the gradient, and its scale is determined by a one-dimensional convex problem.
50%UnverifiedThe admissible geometry corresponding to Minimax RR-ICM is a positive-semidefinite trace slab, in contrast to the spherical zonotope geometry of RR-ICM.
50%UnverifiedThe researchers proposed Minimax RR-ICM, which optimizes over the worst case over probability distributions on the sphere rather than averaging over directions.
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