Related papers: When is the average number of saddle points typica…
Many problems in machine learning and game theory can be formulated as saddle-point problems, for which various first-order methods have been developed and proven efficient in practice. Under the general convex-concave assumption, most…
We proposed an iterate scheme for solving convex-concave saddle-point problems associated with general convex-concave functions. We demonstrated that when our iterate scheme is applied to a special class of convex-concave functions, which…
Saddle fixed points are the centerpieces of complicated dynamics in a system. The one-dimensional stable and unstable manifolds of these saddle-points are crucial to understanding the dynamics of such systems. While the problem of sketching…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
In this paper, we consider some equilibrium problems (or saddle point problems), in which the domains of the considered mappings are limited at some regions. These restricted regions are defined by some mappings which are called the…
A significant problem with most functional data analyses is that of misaligned curves. Without adjustment, even an analysis as simple as estimation of the mean will fail. One common method to synchronize a set of curves involves equating…
We consider fluctuations in the distribution of critical points - saddle points, minima and maxima - of random gaussian fields. We calculate the asymptotic limits of the two point correlation function for various critical point densities,…
This paper highlights a tension between semiparametric efficiency and bootstrap consistency in the context of a canonical semiparametric estimation problem, namely the problem of estimating the average density. It is shown that although…
We give nearly matching upper and lower bounds on the oracle complexity of finding $\epsilon$-stationary points ($\| \nabla F(x) \| \leq\epsilon$) in stochastic convex optimization. We jointly analyze the oracle complexity in both the local…
When there are infinitely many scenarios, the current studies of two-stage stochastic programming problems rely on the relatively complete recourse assumption. However, such assumption can be unrealistic for many real-world problems. This…
This paper considers smooth strongly convex and strongly concave (SC-SC) stochastic saddle point (SSP) problems. Suppose there is an arbitrary oracle that in expectation returns an $\epsilon$-solution in the sense of certain gaps, which can…
The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of ``functional data analysis,'' it has often been assumed that a sample of random functions is observed…
A sudden change of the Hamiltonian parameter drives a quantum system out of equilibrium. For a finite-size system, expectations of observables start fluctuating in time without converging to a precise limit. A new equilibrium state emerges…
What can we learn about entanglement between individual particles in macroscopic samples by observing only the collective properties of the ensembles? Using only a few experimentally feasible collective properties, we establish an…
We consider random analytic functions given by a Taylor series with independent, centered complex Gaussian coefficients. We give a new sufficient condition for such a function to have bounded mean oscillations. Under a mild regularity…
We show that for a convex function the following, rather modest conditions, are equivalent to monotonicity under local operations and classical communication. The conditions are: 1)invariance under local unitaries, 2) invariance under…
This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…
Quantum entanglement is affected by unitary evolution, which spreads the entanglement through the whole system, and also by measurements, which usually tends to disentangle subsystems from the rest. Their competition has been known to…
In the first part of the paper, we consider a discrete-time stochastic control system. We show that, under certain conditions, the set of random occupational measures generated by the state-control trajectories of the system as well as the…
The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…