A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New quasi-Newton method guarantees global superlinear convergence.
Paper improves a method for fast global and local convergence in optimization.
Study random walks on groups with superlinear divergent geodesics.
New averaging technique speeds up Newton method convergence.
Memory-constrained algorithms need superlinear memory for efficient convex optimization.
We study some qualitative properties of ancient solutions of superlinear heat equations on a Riemannian manifold, with particular interest in positivity and constancy in space.
New methods optimize functions faster with less gradient accuracy needed.
New method achieves superlinear convergence rate with limited memory.
New algorithm TUSLA improves learning of non-convex neural networks.
Paper proposes new Langevin samplers for sampling from log-concave distributions with superlinear gradient growth.
Improved stability for matrix recovery from rank-one measurements.
Paper proposes a new method to efficiently incorporate curvature information in stochastic optimization.
OSGM uses online learning to adapt stepsize for faster convergence.
The paper develops efficient estimators for semi-parametric binary models in distributed computing.
In a continuous-time model with multiple assets described by càdlàg processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices arbitrarily unfavorable for high trading intensity. Such frictions induce a duality bet…
We study an optimal liquidation problem under the ambiguity with respect to price impact parameters. Our main results show that the value function and the optimal trading strategy can be characterized by the solution to a semi-linear PDE with superlinear gradient, monotone generator and singular terminal value. We also…
Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions (which form a nonlinear space), equivalently, on random closed sets. …
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and adaptive control. A new point of view is offered for the constrained optimization prob…
New method improves smoothness of minimizing currents near singular points.
KSS method converges and recovers correct clustering under certain conditions.
NR retraction approximates geodesics on submanifolds efficiently.
State of the art methods in astronomical image reconstruction rely on the resolution of a regularized or constrained optimization problem. Solving this problem can be computationally intensive and usually leads to a quadratic or at least superlinear complexity w.r.t. the number of pixels in the image. We investigate in…
Study shows income inequality increases with city size, affecting only the wealthiest deciles.
New algorithm tames non-linear growth in stochastic optimization.
Let a be the 1-skeleton of a triangulated topological annulus. We establish bounds on the combinatorial modulus of a refinement , formed by attaching new vertices and edges to , that depend only on the refinement and not on the structure of itself. This immediately applies to showing that a disk triangul…
This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do…
The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how to coordinate the accuracy in the gradient and Hessian to yield a superlinear ra…
New algorithm samples superlinearly growing log-gradient distributions.
A new algorithm estimates mean adaptively to covariance, faster and more flexible than existing methods.
Optimal transport with -divergence regularization using generalized Sinkhorn algorithm.
We consider a class of fractional stochastic volatility models (including the so-called rough Bergomi model), where the volatility is a superlinear function of a fractional Gaussian process. We show that the stock price is a true martingale if and only if the correlation between the driving Brownian motions of the …
Study PL bordism theories with quantitative bounds on filling simplices.
New RL method handles large state-action spaces with complex models.
Enhanced VMC methods improve neural wavefunction training.
The techniques and analysis presented in this paper provide new methods to solve optimization problems posed on Riemannian manifolds. A new point of view is offered for the solution of constrained optimization problems. Some classical optimization techniques on Euclidean space are generalized to Riemannian manifolds. S…
We give a group theoretic characterization of geodesics with superlinear divergence in the Cayley graph of a right-angled Artin group A(G) with connected defining graph G. We use this to determine when two points in an asymptotic cone of A(G) are separated by a cut-point. As an application, we show that if G does not d…
New method solves constrained optimization problems efficiently.
New RL algorithms reduce costs for single-agent and federated learning.
New tool for parallel and private stochastic convex optimization reduces query complexity.
This paper studies optimal consumption, investment, and healthcare spending under Epstein-Zin preferences. Given consumption and healthcare spending plans, Epstein-Zin utilities are defined over an agent's random lifetime, partially controllable by the agent as healthcare reduces mortality growth. To the best of our kn…
We generalize the notion of cusp excursion of geodesic rays by introducing for any the excursion in the cusps of a hyperbolic -manifold of finite volume. We show that on one hand, this excursion is at most linear for geodesics that are generic with respect to the hitting measure of a random walk.…
Study on nonlinear elliptic equations with variable exponents, proving existence and multiplicity of solutions.
Deep learning algorithms often require solving a highly non-linear and nonconvex unconstrained optimization problem. Methods for solving optimization problems in large-scale machine learning, such as deep learning and deep reinforcement learning (RL), are generally restricted to the class of first-order algorithms, lik…
State-space models are used in a wide range of time series analysis formulations. Kalman filtering and smoothing are work-horse algorithms in these settings. While classic algorithms assume Gaussian errors to simplify estimation, recent advances use a broader range of optimization formulations to allow outlier-robust e…
Artificial Neural Networks (ANNs) have received increasing attention in recent years with applications that span a wide range of disciplines including vital domains such as medicine, network security and autonomous transportation. However, neural network architectures are becoming increasingly complex and with an incre…
Reinforcement Learning (RL) algorithms allow artificial agents to improve their action selections so as to increase rewarding experiences in their environments. Deep Reinforcement Learning algorithms require solving a nonconvex and nonlinear unconstrained optimization problem. Methods for solving the optimization probl…
Research examines correlations of complex logarithms of lattice points, showing level repulsion and Poissonian behavior.
We are interested in strong approximations of one-dimensional SDEs which have non-Lipschitz coefficients and which take values in a domain. Under a set of general assumptions we derive an implicit scheme that preserves the domain of the SDEs and is strongly convergent with rate one. Moreover, we show that this general …