7 papers
On computing Goldstein approximate second-order stationary points of structured nonsmooth nonconvex programs
Jiewen Guan, Anthony Man-Cho So
In this paper, we exhibit a randomized first-order algorithm to compute Goldstein approximate second-order stationary points of -smooth functions, using tools from randomized sm…
On the hardness of deterministic second-order optimization of functions with Lipschitz gradients
Jiewen Guan, Anthony Man-Cho So
We show that no deterministic zero-respecting algorithm (resp., (general) deterministic algorithm) can compute Goldstein approximate second-order stationary points of functions wit…
A Model Can Help Itself: Reward-Free Self-Training for LLM Reasoning
Mengqi Li, Lei Zhao, Anthony Man-Cho So +2
Can language models improve their reasoning performance without external rewards, using only their own sampled responses for training? We show that they can. We propose Self-evolvi…
Learning Graph Topology with Functional Priors via Bilevel Optimization
Chenyue Zhang, Shangyuan Liu, Hoi-To Wai +1
Learning graph topology of complex networks is challenging due to limited data availability and imprecise data models. Different from prior works that focus on structural priors wi…
Testing Approximate Stationarity Concepts for Piecewise Affine Functions
Lai Tian, Anthony Man-Cho So
We study the basic computational problem of detecting approximate stationary points for continuous piecewise affine (PA) functions. Our contributions span multiple aspects, includi…
-norm rank-one symmetric matrix factorization has no spurious second-order stationary points
Jiewen Guan, Anthony Man-Cho So
This paper studies the nonsmooth optimization landscape of the -norm rank-one symmetric matrix factorization problem using tools from second-order variational analysis. Spe…