3 papers
math.OC2026
Near-Optimal Higher-Order Oracle Complexity for Convex--Concave Minimax Optimization
Yanyi Li, Haihan Zhang, Chenheng Zhang +5
For smooth convex--concave minimax optimization, the higher-order lower bound of Chen et al. (2026) applies to a restricted tensor-algorithm class with prescribed regularized Taylo…
math.OC2026
Second-Order Stationarity with Common Random Losses: Matching Tolerance Bounds
Wendao Wu, Haihan Zhang, Chenheng Zhang +5
We establish tight polynomial tolerance bounds for stochastic second-order stationarity when each fresh oracle response is a derivative of one common random scalar loss. For a popu…
math.OC2026
Matching Upper and Lower Bounds for Higher-Order Nonconvex Finite-Sum Optimization
Wendao Wu, Haihan Zhang, Chenheng Zhang +5
We establish tight randomized higher-order oracle complexity for finding first-order stationary points of nonconvex finite sums. Let be the number of components, the init…