This paper establishes a direct connection between Approximate Message Passing (AMP) and the Convex Gaussian Min-max Theorem (CGMT) for regularized linear regression and M-estimation.

This paper shows that stochastic nonconvex optimization can be reduced to ordinary static regret minimization in online convex optimization, and establishes convergence rates for smooth and Lipschitz…

The paper establishes conditions for QUBO formulations of combinatorial optimization problems that guarantee valid binary and feasible local minimizers using gradient-based methods.

This paper introduces Curvature-Weighted Gradient Diversity (CWGD), a geometry-aware measure for optimization noise that reduces the asymptotic optimization error floor by up to a factor of two compar…

This paper proves the conjecture that Local SGD outperforms Mini-batch SGD under bounded second-order heterogeneity for general convex objectives, improving the convergence guarantee and lower bounds.

The paper characterizes the minimax optimal excess-risk rate for pure $\varepsilon$-DP stochastic convex optimization with heavy-tailed gradients, providing an algorithm that achieves this rate.

The paper introduces a unified theoretical framework for gradient aggregation in multi-objective optimization, establishing convergence rates and sufficient conditions for achieving Pareto stationarit…

This paper provides the first non-vacuous generalization analysis for the Stochastic Variance Reduced Gradient (SVRG) method by establishing sharp, data-dependent algorithmic stability bounds, thereby…

The paper establishes tight upper and lower bounds on the statistical cost of approximate machine unlearning for smooth strongly convex losses, showing that the optimal unlearning rate depends critica…

The paper analyzes a new class of asynchronous adaptive first-order optimization methods and proves their stochastic convergence rate is O(1/sqrt{t}) for non-convex functions.

This paper constructs an epsilon-cover of the joint value set of m constant-degree polynomials over a convex set H in the linfty-norm, with size n^(O(log(mn)/ε^2)), given that the polynomials have a c…

This paper analyzes Bregman ADMM for nonconvex linearly constrained problems under two-sided relative smoothness, showing convergence to strict saddle points and almost-sure second-order stationarity.

This paper derives the complete theory of covariance regret functional for decision making, providing insights on steepest-descent directions and boundary-optimal solutions.

This paper improves the foundations of neural likelihood approximation for Bayesian inverse problems by making the learning problem strictly convex and showing convergence to the true likelihood.

The paper proposes DiReCT, a novel framework that treats data selection during LLM annealing as a constrained optimization problem based on the spectral geometry of the loss landscape, achieving state…

This paper proposes a data collection strategy using solver iterates to augment datasets for training generative models, improving the efficiency of the data-model-optimization loop in one-sided box-c…