329 papers
This paper proposes two novel single-loop zeroth-order primal-dual algorithms, ZO-PDAPG and ZO-RMPDPG, that achieve state-of-the-art iteration complexity guarantees for solving nonconvex-(strongly) concave minimax problems with coupled linear constraints under both deterministic and stochastic settings.
This paper introduces Orthonormal Data Collaboration (ODC), a method that enforces orthonormal bases to transform the alignment challenge into a closed-form Orthogonal Procrustes problem, thereby achieving orthogonal concordance, significantly reducing computational complexity, and improving accuracy without compromising privacy or communication efficiency.
This paper extends Control Lyapunov Value Functions to disturbed nonlinear systems by defining the Robust CLVF (R-CLVF) to identify the smallest robust control invariant set and guarantee exponential stabilization, while addressing computational challenges through warmstart and system decomposition techniques.
This paper proposes and analyzes stochastic greedy algorithms (MRG, DRG, and Random-WSSA) to efficiently solve budget- and performance-constrained weak submodular sensor selection problems with robustness guarantees, demonstrating their effectiveness in Earth-observing satellite constellation applications.
This paper proposes a novel multi-task subset selection framework that achieves localized distributional robustness by introducing a relative-entropy regularization term, which is proven equivalent to maximizing a monotone composition of submodular functions and can be efficiently solved via greedy algorithms, as validated by experiments on satellite sensor selection and image summarization.
This paper establishes that the value function of infinite-dimensional singular stochastic control problems in Hilbert spaces is a -viscosity solution to a variational inequality and satisfies a second-order smooth-fit principle in the controlled direction under specific spectral conditions, by leveraging connections to optimal stopping and techniques from convex and viscosity theory.
This paper proposes an asymptotically optimal online learning and optimization algorithm for minimizing irreversible facility openings under a coverage target, demonstrating that a policy balancing initial limited exploration with subsequent rapid exploitation achieves sub-linear regret that converges exponentially fast to its infinite-horizon limit.
This paper establishes necessary and sufficient conditions for the input-to-state stability (ISS) of impulsive switched systems with both stable and unstable modes by introducing time-varying ISS-Lyapunov functions under relaxed mode-dependent average dwell and leave time constraints, while also providing methods to construct decreasing Lyapunov functions and guarantee ISS even with unknown switching signals.
This paper establishes the convergence properties and rates of projected subgradient methods for paraconvex optimization under various step-size rules and error bound conditions, demonstrating their effectiveness through numerical experiments on diverse robust low-rank matrix recovery problems.
This paper demonstrates that training shallow neural networks with Lipschitz continuous activation functions to approximate smooth target functions suffers from the curse of dimensionality, as the population risk decays at a rate bounded by a power of time that depends inversely on the input dimension, regardless of whether the optimization is analyzed via empirical or population risk or through 2-Wasserstein gradient flow dynamics.
This paper introduces Clip21-SGD2M, a novel federated learning algorithm that combines clipping, heavy-ball momentum, and error feedback to achieve both optimal convergence rates for non-convex problems with heterogeneous data and near-optimal differential privacy guarantees without restrictive assumptions.
This paper compares various recently proposed notions of non-rigidity for horizontal vectors in Carnot groups, which are motivated by the study of monotone sets and Whitney extension properties.
This paper proposes a kernel-based maximum causal entropy inverse reinforcement learning framework for infinite-horizon stationary mean-field games that models unknown rewards in a reproducing kernel Hilbert space to capture nonlinear structures, proves the algorithm's theoretical consistency via Fréchet differentiability, and demonstrates superior policy recovery performance over linear baselines in traffic routing scenarios while extending the approach to finite-horizon non-stationary settings.
This paper proposes an inertial accelerated primal-dual algorithm derived from a time-scaled second-order differential system to solve non-smooth convex optimization problems with linear equality constraints, establishing fast convergence rates for the primal-dual gap, feasibility violation, and objective residual, and validating its performance through numerical experiments.
This paper proposes a proximal stochastic gradient algorithm with adaptive step size and variance reduction for convex composite optimization, establishing its strong convergence, gradient error convergence, and an convergence rate under Lipschitz continuity, while validating its effectiveness through numerical experiments on Logistic and Lasso regression.
This paper introduces a novel matrix-based framework for deriving upper and lower bounds for the Permutation Flowshop Scheduling Problem, demonstrating significant improvements on standard benchmarks and providing new theoretical insights into makespan value estimates and asymptotic approximation ratios.
This paper proposes a novel communication-efficient decentralized symmetric ADMM algorithm that utilizes multiple communication rounds per iteration to achieve linear convergence and reduce total communication costs compared to existing methods.
The paper proposes Deep FlexQP, a deep unfolding-based solver that accelerates nonlinear programming by learning dimension-agnostic parameters for a robust, always-feasible convex QP relaxation, thereby significantly improving the speed and success rates of SQP and safety filter applications while providing rigorous performance guarantees.
This paper proposes D-APDB, a distributed accelerated primal-dual algorithm with backtracking that achieves optimal convergence for decentralized constrained optimization over undirected networks without requiring prior knowledge of Lipschitz constants, making it the first method of its kind to handle private nonlinear constraints efficiently.
This paper establishes sharper convergence guarantees for the Muon optimizer by providing a direct, simplified analysis that achieves faster convergence rates under broader problem settings than existing restrictive theoretical frameworks.