Author

Adrien B. Taylor

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Preprint Aug 2026

Mirror descent algorithms with logarithmic barriers

This work derives convergence guarantees for mirror descent and proximal mirror descent algorithms when a logarithmic barrier is used as a distance-generating function and shows that, in a specific setting, both methods enjoy an O(\log k / k) rate, which is also tight.

A. Marchi, Yura Malitsky, Adrien B. Taylor · 0 citations

Preprint Aug 2026

Mirror Polyak and a Primal-Dual Lifting

This work revisits a variant of the Polyak step-size based on Bregman projections due to Kiwiel (1997), and shows that mirror Polyak enjoys guarantees similar to its Euclidean counterpart, automatically adapting to relative notions of smoothness, Lipschitz continuity, or strong convexity.

Frederik Kunstner, Ryan D'Orazio, V. S. Portella et al. · 1 citation