319 papers
This paper establishes a new on-average stability analysis for multipass Preconditioned SGD to derive generalization bounds dependent on effective dimension, revealing how mismatches between population risk curvature and gradient noise geometry can lead to suboptimal performance if preconditioning is improperly chosen.
This paper introduces a maximum-entropy random walk framework for directed hypergraphs that models both broadcasting and merging interaction mechanisms through a Kullback-Leibler divergence projection, utilizing Sinkhorn-Schrödinger iterations to infer transition kernels while analyzing ergodicity and demonstrating effectiveness on synthetic and real-world datasets.
This paper provides the first exact equilibrium characterization for finite-player continuous-time LQG games with endogenous signals by collapsing the infinite hierarchy of beliefs into a deterministic fixed point, thereby deriving an explicit information wedge that quantifies the strategic value of manipulating opponents' forecasts.
This paper establishes the asymptotic convergence and iteration complexity of block majorization-minimization algorithms for smooth nonconvex optimization problems with block constraints on Riemannian manifolds, demonstrating their broad applicability and superior performance over standard Euclidean approaches.
This paper proposes a learned proximal alternating minimization (LPAM) algorithm and its corresponding interpretable network (LPAM-net) for solving two-block nonconvex and nonsmooth optimization problems, proving their convergence to Clarke stationary points and demonstrating superior performance in joint multi-modal MRI reconstruction.
This paper establishes the theoretical framework for solving axial symmetric Navier-Stokes equations in a cylindrical topology by constructing a complete basis of harmonic 1-forms comprising Beltrami, anti-Beltrami, and closed components, thereby reducing the problem to a hierarchy of quadratic relations suitable for future optimization via Physics-Informed Neural Networks.
This paper proposes a co-design framework that jointly optimizes communication topology and differential privacy levels in multi-agent formation control to balance privacy protection, network connectivity, and steady-state performance.
This paper introduces and analyzes the Generalized Multiplicative Gradient (GMG) method for solving convex optimization problems over symmetric cones with non-Lipschitz gradients, establishing an convergence rate through novel theoretical results and demonstrating its superior computational complexity compared to other first-order methods across several key applications.
This paper introduces a distributionally robust framework for the single airport ground holding problem under Wasserstein ambiguity sets, featuring a novel hybrid algorithm that combines Kelly's cutting plane method with the integer L-shaped method to achieve significant computational speedups while enhancing decision-making resilience against capacity distribution shifts.
This paper employs an inverse optimization framework on NFL play-by-play data to demonstrate that coaches' historically conservative fourth-down decisions are consistent with optimizing low quantiles of future value, revealing that their risk preferences have become more tolerant over time and vary based on field position.
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.