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arXiv research

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.

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1223 · Sep 202319922001200920172026
39 results for Karush-Kuhn-Tucker

LCBO tackles constrained optimization in high dimensions, offering a polynomial convergence rate.

problem Bayesian optimization for high-dimensional constrained problems.
method LCBO uses local descent and uncertainty-driven exploration, proving polynomial convergence rate.
result LCBO achieves a polynomial convergence rate for KKT residuals in high dimensions.

The paper studies neural networks' convergence near origin and saddle points.

problem Directional convergence of neural networks near small initializations and saddle points.
method Gradient flow dynamics analysis of two-homogeneous neural networks.
result Neural networks' weights approximately converge in direction to KKT points for small initializations.

New insights into how linear classifiers and leaky ReLU networks can overfit without harming generalization.

problem Understanding conditions for benign overfitting in linear classifiers and leaky ReLU networks.
method Utilizing Karush--Kuhn--Tucker (KKT) conditions for margin maximization.
result Satisfaction of KKT conditions leads to benign overfitting in linear classifiers and leaky ReLU networks.

New algorithm reduces regret in both adversarial and stochastic contexts.

problem Contextual combinatorial semi-bandits with adversarial and corrupted stochastic regimes.
method Follow-the-Regularized-Leader (FTRL) framework with Shannon entropy regularizer, accelerated by Karush-Kuhn-Tucker conditions.
result Achieves O~(T)\widetilde{\mathcal{O}}(\sqrt{T}) regret in adversarial and O~(lnT)\widetilde{\mathcal{O}}(\ln T) regret in corrupted stochastic regimes.

GD iterates for non-homogeneous deep nets increase margin and converge in direction.

problem Understanding implicit bias in non-homogeneous deep networks.
method Characterization of GD iterates' properties starting from small empirical risk.
result GD iterates converge in direction despite diverging norms, satisfying KKT conditions.

The paper refines NOTEARS for learning Bayesian networks, improving accuracy and efficiency.

problem Learning Bayesian networks from continuous optimization.
method Generalized algebraic characterizations and Karush-Kuhn-Tucker (KKT) conditions for optimization.
result Local search post-processing improves structural Hamming distance by a factor of 2 or more.

DCCNNs reduce computational overhead and ambiguity in convolutional neural networks.

problem Reducing computational overhead and ambiguity in convolutional neural networks.
method Introducing a primal learning problem and constructing a dual convex training program, using Fenchel conjugates and Karush-Kuhn-Tucker conditions.
result Eliminates ambiguity and reduces computational overhead in constructing a large kernel matrix.

Paper proposes ExsdHawkes to model LOBs, capturing volatility dynamics.

problem Modeling volatility signature plots in LOBs with high-frequency trading dynamics.
method Extended State-Dependent Hawkes Process (ExsdHawkes) with relaxed constraints.
result ExsdHawkes uniquely reproduces volatility signature plots, identifying MLOs as catalysts.

We consider rules for discarding predictors in lasso regression and related problems, for computational efficiency. El Ghaoui et al (2010) propose "SAFE" rules that guarantee that a coefficient will be zero in the solution, based on the inner products of each predictor with the outcome. In this paper we propose strong …

2010-11-09abs ↗pdf ↗

Neural network discovers exact solutions to QP with linear constraints.

problem Discovering exact solutions to Quadratic Programs (QP) with linear constraints using neural networks.
method Proposes a neural network modeling approach that analytically derives model parameters from problem coefficients, ensuring closed-form solutions without training.
result The closed-form NN model produces exact solutions for every critical region of the QP solution function, outperforming DNNs and commercial solvers in terms of optimality and feasibility.

The paper tackles partial inference in structured prediction using a convex optimization approach.

problem Maximizing a score function with unary and pairwise potentials in graph label spaces.
method Generative model approach with two-stage convex optimization for label recovery.
result Conditions for recovering a majority of labels with provable guarantees.

Study KKT conditions for multi-objective optimization on Hadamard manifolds.

problem Optimizing multi-objective interval-valued functions on Hadamard manifolds.
method Developed KKT conditions for Pareto optimal solutions under different ordering and convexity notions.
result Results are more general than on Euclidean spaces.

Early training of deep neural networks leads to small, directionally converging weights.

problem Training dynamics of deep homogeneous neural networks with small initializations.
method Gradient flow analysis and study of KKT points for neural correlation function.
result Weights converge in direction to KKT points during early training stages.

We analyze the necessary and sufficient conditions for exact inference of a latent model. In latent models, each entity is associated with a latent variable following some probability distribution. The challenging question we try to solve is: can we perform exact inference without observing the latent variables, even w…

2019-01-28abs ↗pdf ↗

New single-loop algorithm tackles weakly convex constraints in stochastic optimization.

problem Optimization with weakly convex constraints in machine learning.
method Single-loop penalty-based stochastic algorithm using hinge-based penalty.
result Achieves state-of-the-art complexity for finding approximate KKT solutions.

Gradient ascent method successfully removes specific data points from neural networks without retraining.

problem Addressing privacy and ethical concerns by removing specific data points from trained models.
method Gradient ascent approach to unlearning, leveraging the implicit bias of gradient descent towards margin maximization conditions.
result Gradient ascent method can successfully unlearn specific data points from two-layer ReLU neural networks without retraining.

The paper proves inequalities for isometries in loxodromic Kleinian groups.

problem Discreteness criteria for subgroups of PSL2(C)_2(\mathbb{C}).
method Generalization of discreteness criteria, using trace inequalities and optimization problems.
result Inequalities involving traces and hyperbolic displacements for loxodromic Kleinian groups.

New method tackles non-smooth tensor data for better recovery.

problem Non-smooth changes in tensor data degrade traditional t-SVD methods.
method Learnable tensor nuclear norm, Alternating Proximal Multiplier Method (APMM), multi-objective tensor recovery framework.
result The proposed method effectively recovers tensor data with non-smooth changes.

Machine learning models trained on data from the outside world can be corrupted by data poisoning attacks that inject malicious points into the models' training sets. A common defense against these attacks is data sanitization: first filter out anomalous training points before training the model. In this paper, we deve…

2018-11-02abs ↗pdf ↗

We embed KKT points in neural networks of different sizes.

problem Classifying data using homogeneous neural networks.
method Introducing KKT point embedding principle and proving it for different network types.
result KKT points of a smaller network can be mapped to those of a larger network via linear transformations.

New method solves constrained stochastic optimization problems efficiently.

problem Online statistical inference of constrained stochastic nonlinear optimization problems.
method Stochastic Sequential Quadratic Programming (StoSQP) with iterative sketching solver.
result The rescaled primal-dual sequence converges to a mean-zero Gaussian distribution.

Unified framework for clustering and learning causal graphs across subjects.

problem Bias and obscured subpopulation-specific dependencies in multivariate systems.
method Directed Acyclic Graph-based Dependency Clustering via Alternating Direction Method of Multipliers (DAG-DC-ADMM) integrated with Structural Equation Modeling (SEM).
result Unified framework recovers cluster-specific causal dependency structures with high true positive rate and low false discovery rate.

We present new computations of approximately length-minimizing polygons with fixed thickness. These curves model the centerlines of "tight" knotted tubes with minimal length and fixed circular cross-section. Our curves approximately minimize the ropelength (or quotient of length and thickness) for polygons in their kno…

2010-02-08abs ↗pdf ↗

In this paper, we develop an alternating direction method of multipliers (ADMM) for deep neural networks training with sigmoid-type activation functions (called \textit{sigmoid-ADMM pair}), mainly motivated by the gradient-free nature of ADMM in avoiding the saturation of sigmoid-type activations and the advantages of …

2019-02-06abs ↗pdf ↗

This paper introduces ff-DPO, a generalized approach to Direct Preference Optimization using diverse divergence constraints.

problem Aligning large language models with human preferences while mitigating safety risks.
method Incorporates diverse divergence constraints to simplify the relationship between reward and optimal policy, eliminating the need for estimating the normalizing constant.
result Optimizes LLMs to align with human preferences more efficiently and under a broader set of divergence constraints.

Enhanced PC2^2 improves surrogate modeling for high-dimensional problems.

problem Degrading performance and efficiency of PC2^2 in high-dimensional parameter spaces.
method Integrates SULM solver and D-optimal sampling strategy into PC2^2 framework.
result Enhanced PC2^2 demonstrates better comprehensive capability and efficiency.

AM-PPI uses multiple predictors to reduce label cost in healthcare AI.

problem Reduces label cost in post-deployment monitoring of healthcare AI.
method Combines model predictions with a small labeled sample, routing each instance to a cost-appropriate subset of predictors.
result Produces narrower confidence intervals than single-predictor methods.

Renet improves Elastic Net by dynamically selecting between convex blending and refitting, enhancing prediction accuracy.

problem Elastic Net's shrinkage bias limits its prediction accuracy in high-dimensional settings.
method Adaptive relaxation procedure that dynamically dispatches between convex blending and efficient sub-path refitting.
result Renet consistently outperforms standard Elastic Net and Adaptive Elastic Net in high-dimensional, low signal-to-noise ratio, and high-multicollinearity scenarios.

Boosted Difference of Convex Functions Algorithm solves VaR constrained portfolio optimization.

problem Designing VaR optimal portfolios under financial regulations.
method Boosted Difference of Convex Functions Algorithm (BDCA) with a novel line search framework.
result BDCA linearly converges to a Karush-Kuhn-Tucker point for VaR constrained portfolio problems.