# Convergence Rates for Stochastic Proximal and Projection Estimators

arXiv: https://arxiv.org/abs/2602.06750 · HTML: https://mlsanity.com/paper/2602.06750/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2026.

## Built on by (most cited first, 1 of 1)

- [Proximal basin hopping: global optimization with guarantees](https://mlsanity.com/paper/2605.18364/) (2026)

## Abstract (arXiv)

In this paper, we establish explicit convergence rates for the stochastic smooth approximations of infimal convolutions introduced and developed in citeMR4581306,MR4923371. In particular, we quantify the convergence of the associated barycentric estimators toward proximal mappings and metric projections. We prove a dimension-explicit √δ bound, with explicit constants for the proximal mapping, in the ρ-weakly convex (possibly nonsmooth) setting, and we also obtain a dimension-explicit √δ rate for the metric projection onto an arbitrary convex set with nonempty interior. Under additional regularity, namely C2 smoothness with globally Lipschitz Hessian, we derive an improved linear O(δ) rate with explicit constants, and we obtain refined projection estimates for convex sets with local C2,1 boundary. Examples demonstrate that these rates are optimal.