Mirror Descent Beyond Euclidean Stability: An Exponential Separation in Initialization Sensitivity
Mirror Descent (MD) extends Gradient Descent (GD) beyond Euclidean geometry and has recently reappeared as a lens for KL-regularized policy optimization in reinforcement learning and LLM post-training. This raises a basic robustness question, crucial to reproducibility and reliability: how sensitive are MD dynamics to their inputs? We focus on initialization, often itself a pretrained or previously aligned model. Quadratic-regularized MD, including GD and Mahalanobis geometries, is well-known to be stable for convex smooth objectives. We show a sharp contrast: once the regularizer is non-quadratic, MD can be exponentially more sensitive to initialization than GD, even with a well-conditio...
| Authors | Shira Vansover-Hager, Matan Schliserman, Ofir Schlisselberg et al. |
|---|---|
| Primary category | cs.LG |
| Published | 9 June 2026 |
| Last updated at source | 9 June 2026 |
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