The paper introduces ℓ*-smoothness, a norm-dual generalization of ℓ-smoothness, and proves classical O(1/T), O(1/T²), and Õ(1/√t) rates for mirror descent, accelerated mirror descent, optimistic mirror descent, mirror prox, and stochastic mirror descent.
Proof We prove this lemma by induction
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Mirror Descent Under Generalized Smoothness
The paper introduces ℓ*-smoothness, a norm-dual generalization of ℓ-smoothness, and proves classical O(1/T), O(1/T²), and Õ(1/√t) rates for mirror descent, accelerated mirror descent, optimistic mirror descent, mirror prox, and stochastic mirror descent.