A Dual Form of Bregman Momentum The dual form of Bregman momentum given in (10) can be obtained by first forming the dual Bregman divergence in terms of the dual variables w (t) and w
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We first provide a proof for Proposition 1. Then, we prove Theorem 3. Proposition 1. Theorem 3. The constrained CMD update (14) coincides with the reparameterized projected gradient update on the composite loss, The rest of the proof follows similarly by solving for (t) and rearranging the terms. Finally, applying the results of Theorem 2 concludes the proof. In this section, we discuss different strategies for discretizing the CMD updates and provide examples for each case. The most straight-forward discretization of the unconstrained CMD update (1) is the forward Euler (i.e.
Neural Information Processing Systems
Jan-24-2025, 22:01:02 GMT
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