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…
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…
A Model Can Help Itself: Reward-Free Self-Training for LLM Reasoning
Mengqi Li, Lei Zhao, Anthony Man-Cho So +2
Can a language model improve reasoning by learning from its own imperfect responses, without rewards or teacher-provided solutions? We present Self-evolving Post-Training (SePT), a…
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…
On subdifferential chain rule of matrix factorization and beyond
Jiewen Guan, Anthony Man-Cho So
In this paper, we study equality-type Clarke subdifferential chain rules of matrix factorization and factorization machine. Specifically, we show for these problems that provided t…