arXiv research

Paper optimizes portfolio selection with ICX order constraints.

New characterization of second-order stochastic dominance with applications in risk management.

Derives curvature formulas for convex metric sums and conditions for positive average variation.

We consider a square-integrable semimartingale and investigate the convex order relations between its discrete, continuous and predictable quadratic variation. As the main results, we show that if the semimartingale has conditionally independent increments and symmetric jump measure, then its discrete realized variance…

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 first-order methods only guarantee an ergodic convergence rate, that is, the uniform…

Introduces GG-convex risk measures and derives their dual representations.

Paper proposes an efficient algorithm to handle high-order portfolio moments.

SOC-ICNN expands neural network representational capacity by using conic optimization.

Paper compares credit portfolio risks using robust Bernoulli mixture models.

A generalized optimistic method for saddle point problems with improved complexity.

STL-SGD accelerates Local SGD by gradually increasing communication periods.

The paper analyzes SGD with Richardson-Romberg extrapolation for convex optimization problems.

Parallel computing has played an important role in speeding up convex optimization methods for big data analytics and large-scale machine learning (ML). However, the scalability of these optimization methods is inhibited by the cost of communicating and synchronizing processors in a parallel setting. Iterative ML metho…

Recent years have seen increased interest in performance guarantees of gradient descent algorithms for non-convex optimization. A number of works have uncovered that gradient noise plays a critical role in the ability of gradient descent recursions to efficiently escape saddle-points and reach second-order stationary p…

We study a volume/area preserving curvature flow of hypersurfaces that are convex by horospheres in the hyperbolic space, with velocity given by a generic positive, increasing function of the mean curvature, not necessarly homogeneous. For this class of speeds we prove the exponential convergence to a geodesic sphere. …

New algorithm solves complex optimization problems without needing projections.

Hogwild! adapts to distributed data by varying mini-batch sizes.

In this paper, we theoretically prove that gradient descent can find a global minimum of non-convex optimization of all layers for nonlinear deep neural networks of sizes commonly encountered in practice. The theory developed in this paper only requires the practical degrees of over-parameterization unlike previous the…

New geometric proof of convex function differentiability and approximation.

A new optimizer for deep learning improves accuracy and reduces training time.

A new method for nonparametric regression using mesh-based solutions.

In-network distributed estimation of sparse parameter vectors via diffusion LMS strategies has been studied and investigated in recent years. In all the existing works, some convex regularization approach has been used at each node of the network in order to achieve an overall network performance superior to that of th…

Flow deforms locally convex curves to curves of constant k-order width.

Developed a theory of local convexity for second order differential equations on Lie algebroids.

Study convex embeddability in linear and circular orders, applying to knots.

State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization, a polynomial dependence on the approximation guarantee and higher-order smoothn…

Paper analyzes normal approximation for two-timescale stochastic algorithms, revealing interaction between fast and slow timescales.

Study non-standard bi-orders on punctured torus bundles, matching standard ones in key subgroups.

Unified convergence analysis of alpha-SVRG under strong convexity.

Efficient algorithms find optimal monotone transforms for calibration under strictly convex losses.

Sharp comparison for sub-Gaussian random variables in convex order.

Second-order methods improve differential privacy in convex optimization.

Geodesic convexity generalizes the notion of (vector space) convexity to nonlinear metric spaces. But unlike convex optimization, geodesically convex (g-convex) optimization is much less developed. In this paper we contribute to the understanding of g-convex optimization by developing iteration complexity analysis for …

New algorithm reduces regret in stochastic bandit convex optimization.

Study on convex ordering in stochastic control for swing contracts, proving value function convexity.

Study first-order locally convex Lie algebroids in Bastiani calculus.

Strong geodesic convex function and strong monotone vector field of order $m$ on Riemannian manifolds have been established. A characterization of strong geodesic convex function of order $m$ for the continuously differentiable functions has been discussed. The relation between the solution of a new variational inequal…

We study convexity and monotonicity properties for prices of bonds and bond options when the short rate is modeled by a diffusion process. We provide conditions under which convexity of the price in the short rate is guaranteed. Under these conditions the price is decreasing in the drift and increasing in the volatilit…

We consider the adversarial convex bandit problem and we build the first $\mathrm{poly}(T)$-time algorithm with $\mathrm{poly}(n) \sqrt{T}$-regret for this problem. To do so we introduce three new ideas in the derivative-free optimization literature: (i) kernel methods, (ii) a generalization of Bernoulli convolutions, …

Active-set algorithm improves Cox regression for shape-restricted covariates.

First order methods can take extremely long to find global minima of non-convex functions.

Expands learning paradigm to stochastic orders using Choquet-Toland distance and Variational Dominance Criterion.

New algorithms optimize convex functions with high-order derivatives.

In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal stationary points. However, existing results on stochastic non-convex optimizatio…

Optimal algorithms for online convex optimization with random order.

Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing. While NMF is traditionally applied to off-the-shelf time-frequency representations based on the short-time Fourier or Cosine transforms, the ability to learn transforms from raw data attracts increasing attention. However, this adds…

Book covers tools for zeroth-order convex optimisation.

Two flows for convex curves converge to circles smoothly.