arXiv research

Paper addresses quadratic feasibility problems and their sample complexity.

A new algorithm for solving constrained convex optimization problems efficiently.

We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may be present in the feasible set, and the classical l1 approach may be unsuccessfu…

New method trains Boltzmann machines without supervision.

Quadratic memory is essential for optimal convex optimization queries.

Gradient descent is efficient for solving feasibility problems with minimal memory and queries.

New conditions ensure Dantzig-Wolfe relaxation matches rank-constrained optimization problems.

We study the problem of controlling linear time-invariant systems with known noisy dynamics and adversarially chosen quadratic losses. We present the first efficient online learning algorithms in this setting that guarantee $O(\sqrt{T})$ regret under mild assumptions, where $T$ is the time horizon. Our algorithms rely …

Neural network discovers exact solutions to QP with linear constraints.

We present a convergence rate analysis for biased stochastic gradient descent (SGD), where individual gradient updates are corrupted by computation errors. We develop stochastic quadratic constraints to formulate a small linear matrix inequality (LMI) whose feasible points lead to convergence bounds of biased SGD. Base…

New method reduces training time for deep hedging networks.

New method improves feasibility of fitting Gaussian vectors to an ellipsoid.

This work introduces a fixed-point optimization for variational inference.

Model liquidity premia using a risk-sharing economy with quadratic costs.

In this paper we study decomposition methods based on separable approximations for minimizing the augmented Lagrangian. In particular, we study and compare the Diagonal Quadratic Approximation Method (DQAM) of Mulvey and Ruszczyński and the Parallel Coordinate Descent Method (PCDM) of Richtárik and Takáč. We show that …

A new algorithm solves constrained optimization problems with stochastic gradients.

Improved Frank-Wolfe algorithm for constrained convex optimization with nearest extreme point oracle.

We study the implicit bias of AdaGrad on separable linear classification problems. We show that AdaGrad converges to a direction that can be characterized as the solution of a quadratic optimization problem with the same feasible set as the hard SVM problem. We also give a discussion about how different choices of the …

Efficiently solves heterogeneous QPs by reducing variables using instance-specific projections.

HAMD optimizes cubic portfolios without quadratization, achieving better results.

New algorithm tackles stochastic optimization with inequality constraints.

We introduce a variant of (sparse) PCA in which the set of feasible support sets is determined by a graph. In particular, we consider the following setting: given a directed acyclic graph $G$ on $p$ vertices corresponding to variables, the non-zero entries of the extracted principal component must coincide with vertice…

New tensor recovery method uses Riemannian optimization on Segre manifold.

A scalable framework optimizes multi-asset portfolios with constraints.

In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe algorithm that has access to the full gradient of the objective functions. We show t…

Faster algorithms for structured SVMs reduce computation time.

Develops a test to distinguish between standard and rough volatility.

New method solves stochastic optimization problems with random models.

Support vector regression (SVR) is one of the most popular machine learning algorithms aiming to generate the optimal regression curve through maximizing the minimal margin of selected training samples, i.e., support vectors. Recent researchers reveal that maximizing the margin distribution of whole training dataset ra…

Unified theory of ownership concentration, overlap, and dependence.

SGD achieves a $O(ε^{-4})$ bound for minimizing gradient norm of smooth functions.

In this work, we introduce a Monte Carlo method for the dynamic hedging of general European-type contingent claims in a multidimensional Brownian arbitrage-free market. Based on bounded variation martingale approximations for Galtchouk-Kunita-Watanabe decompositions, we propose a feasible and constructive methodology w…

A new penalty-free method optimizes portfolios without quantum annealing penalties.

Paper addresses feasibility of counterfactual explanations in ML models, especially for critical domains.

Proposes a new algorithm for solving optimization problems with stochastic objectives and equality constraints.

New algorithm finds best feasible arm in grouped bandits.

Paper introduces a neural network for consistent estimation of optimal transport maps.

This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + ε_j$, $j=1, \ldots, m$, with independent sub-exponential noise $ε_j$. The goals are to understand the effect of the sparsity of $x$ on the estimation prec…

Bayesian search optimizes exploration of feasible solutions under expensive constraints.

Develops a new framework for integrating satellite allocations in small portfolios.

A new method solves variational inequality problems with multiple constraints without needing optimal Lagrange multipliers.

Simplifies neural network constraints with computationally efficient method.

The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range constraints. Split feasibility generalizes important inverse problems including con…

We introduce a multivariate stochastic volatility model for asset returns that imposes no restrictions to the structure of the volatility matrix and treats all its elements as functions of latent stochastic processes. When the number of assets is prohibitively large, we propose a factor multivariate stochastic volatili…

Enhances OTA FL algorithms by defining inverse feasibility for linear models.

Many engineering problems require identifying feasible domains under implicit constraints. One example is finding acceptable car body styling designs based on constraints like aesthetics and functionality. Current active-learning based methods learn feasible domains for bounded input spaces. However, we usually lack pr…

Paper develops new spot regression estimators using candlesticks for asset pricing.

Study proposes a neural network approach for high inflation investment portfolios with leverage constraints.