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This paper proves that online gradient descent achieves optimal √T regret for hidden-convex losses under a Hessian compatibility condition, resolving open questions in adversarial online learning. It also extends results to one-point bandit feedback with a T^{3/4} expected regret bound.
This paper proposes a robust subspace-constrained quadratic model for learning low-dimensional structures from high-dimensional data, accommodating heavy-tailed noise. A gradient-based algorithm with backtracking line search is developed, and experiments show improved robustness and reconstruction accuracy.
This paper studies nonconvex stochastic optimization under Blum-Gladyshev noise, where gradient variance grows with distance from initialization. It proves convergence guarantees for normalized SGD with momentum and a variance-reduced STORM method, achieving minimax optimal rates under certain conditions.
This paper introduces SHAPE, a structured adaptive port-Hamiltonian optimizer for fixed-budget nonconvex optimization that uses event-triggered mechanisms to balance descent, exploration, and budget allocation.