Below you can see all the talks held at the Proof Mining Seminar in the 2025-2026 season. For forthcoming talks, see the main page.
Wednesday, April 8, 2026
Nicholas Pischke (University of Bath)
Rates of convergence for a stochastic proximal point algorithm in metric spaces of nonpositive curvature
Abstract:
I introduce a stochastic variant of the proximal point algorithm in the general setting of nonlinear (separable) Hadamard spaces for approximating zeros of the mean of a stochastically perturbed monotone vector field and prove its convergence under a suitable strong monotonicity assumption, together with a probabilistic independence assumption and a separability assumption on the tangent spaces. The convergence result is moreover furnished with an explicit rate of convergence for the iteration towards the (unique) solution both in mean and almost surely. While the rates themselves are, in that generality, already novel in the context of Hilbert spaces, the qualitative result itself is novel at least over Hadamard manifolds.
The talk is partially based on joint work with Morenikeji Neri and Thomas Powell.