Shiqian Ma

Two papers on bilevel optimization are published in JMLR. “Efficiently Escaping Saddle Points in Bilevel Optimization” and “Riemannian Bilevel Optimization” www.jmlr.org/papers/v26/2... www.jmlr.org/papers/v26/2...

AdaBB: Adaptive Barzilai-Borwein Method for Convex Optimization In this paper, we propose AdaBB, an adaptive gradient method based on the Barzilai-Borwein stepsize. The algorithm is line-search-free and parameter-free, and essentially provides a convergent variant...

Our paper on tuning-free gradient method: “AdaBB: Adaptive Barzilai-Borwein Method for Convex Optimization” is accepted in Math of OR. arxiv.org/abs/2401.08024

Riemannian Proximal Sampler for High-accuracy Sampling on Manifolds We introduce the Riemannian Proximal Sampler, a method for sampling from densities defined on Riemannian manifolds. The performance of this sampler critically depends on two key oracles: the Manifold ...

New work on Riemannian Proximal Sampler, to sample on Riemannian manifolds:

arxiv.org/abs/2502.07265

Comes with high-accuracy (i.e., log(1/eps), where eps is tolerance) guarantees with exact and inexact oracles for Manifold Brownian Increments and Riemannian Heat-kernels

We implement these oracles using heat-kernel truncation & Varadhan's asymptotics, linking our method to entropy-regularized proximal point method on Wasserstein spaces, in the latter case.

Joint work with Yunrui Guan and @shiqianma.bsky.social

Riemannian Bilevel Optimization In this work, we consider the bilevel optimization problem on Riemannian manifolds. We inspect the calculation of the hypergradient of such problems on general manifolds and thus enable the utilizatio...

Our paper Riemannian Bilevel Optimization is accepted in Journal of Machine Learning Research! arxiv.org/abs/2402.02019