On-device research index

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.

168,657 papers · 148 categories

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48 results for “convex learning”

Learning Convex Optimization Modelscs.LG

Convex optimization models predict outputs from inputs via optimization problems.

problem Predicting outputs from inputs using convex optimization models.

method Proposed a heuristic for learning parameters of convex optimization models from datasets.

result Demonstrated the effectiveness of the proposed method on three model classes.

convex optimization machine learning parameter learning differentiation MAP models

2020-06-07abs ↗pdf ↗

On Convex Clustering Solutionsstat.ML

Convex clustering can only learn convex clusters, with significant gaps between clusters.

problem Understanding the limitations and capabilities of convex clustering.

method Analyzing convex clustering solutions, proving properties, and characterizing clusters.

result Convex clustering can only learn convex clusters with significant gaps between clusters.

convex clustering cluster types optimality disjoint bounding balls consistency

2021-05-18abs ↗pdf ↗

Convex Optimization with an Interpolation-based Projection and its Application to Deep Learningcs.LG

A new projection method for convex optimization reduces computation costs.

problem Efficiently projecting points into convex sets for deep learning.

method Interpolation-based projection for cheaper computation.

result The proposed method converges for linear and convex constraints.

convex optimization projection deep learning reinforcement learning supervised learning

2020-11-13abs ↗pdf ↗

Hyper Input Convex Neural Networks for Shape Constrained Learning and Optimal Transportcs.LG

HyCNNs improve convex function learning and optimal transport.

problem Learning and optimizing convex functions efficiently.

method Combining Maxout networks and ICNNs to create a new neural architecture.

result HyCNNs require fewer parameters and outperform existing methods in convex tasks.

Convex Neural Networks Optimal Transport Shape Constrained Learning Maxout Networks Input Convex Neural Networks

2026-04-29abs ↗pdf ↗

Convex Relaxation Regression: Black-Box Optimization of Smooth Functions by Learning Their Convex Envelopesstat.ML

Finding efficient and provable methods to solve non-convex optimization problems is an outstanding challenge in machine learning and optimization theory. A popular approach used to tackle non-convex problems is to use convex relaxation techniques to find a convex surrogate for the problem. Unfortunately, convex relaxat…

2016-02-05abs ↗pdf ↗

Learning Rate Annealing Can Provably Help Generalization, Even for Convex Problemscs.LG

Learning rate annealing helps even in convex problems, improving generalization.

problem Improving generalization in neural networks, especially convex problems.

method Learning rate annealing schedule (large initial, then small learning rate).

result Gradient descent can reach minima with better generalization using learning rate annealing.

learning rate annealing convex problems generalization neural networks

2020-05-15abs ↗pdf ↗

Localization, Convexity, and Star Aggregationstat.ML

The paper generalizes offset Rademacher complexities to convex and non-convex problems.

problem Improper learning and convexity in statistical learning.

method Generalization of offset Rademacher complexities to convex and non-convex problems.

result The offset complexity provides versatile analytic tools for both convex and non-convex learning.

offset complexity Rademacher complexities convexity non-convex improper learning

2021-05-19abs ↗pdf ↗

A Sample Complexity Separation between Non-Convex and Convex Meta-Learningcs.LG

One popular trend in meta-learning is to learn from many training tasks a common initialization for a gradient-based method that can be used to solve a new task with few samples. The theory of meta-learning is still in its early stages, with several recent learning-theoretic analyses of methods such as Reptile [Nichol …

2020-02-25abs ↗pdf ↗

Faster Algorithms for Learning Convex Functionsstat.ML

Faster algorithms solve convex function learning problems.

problem Approximating arbitrary convex functions in various learning tasks.

method 2-block ADMM method with closed-form block computations.

result Converges with

O(n\sqrt{d}/ε)

for convex Lipschitz regression.

convex function learning ADMM method 2-block ADMM closed-form computation convex regression

2021-11-02abs ↗pdf ↗

Nesterov acceleration in benignly non-convex landscapesmath.OC

Improved optimization guarantees for deep learning models with Nesterov acceleration.

problem Optimization in non-convex deep learning landscapes.

method Analysis of Nesterov acceleration in benignly non-convex landscapes.

result Identical guarantees can be obtained in optimization problems with weak geometric assumptions, especially in overparametrized deep learning.

Nesterov acceleration non-convex optimization deep learning optimization guarantees benign non-convexity

2024-10-10abs ↗pdf ↗

When compressive learning fails: blame the decoder or the sketch?cs.LG

This work explores the non-convex optimization in compressive learning and the performance of heuristics.

problem The challenge of learning from compressed representations in compressive learning.

method Numerical simulations of the non-convex optimization landscape and heuristic performance.

result Properties of the non-convex optimization landscape and heuristic performance are explored.

compressive learning non-convex optimization heuristics sketch mixture model

2020-09-14abs ↗pdf ↗

Unveiling Hidden Convexity in Deep Learning: a Sparse Signal Processing Perspectivecs.LG

Paper reveals hidden convexities in deep learning models using sparse signal processing.

problem Non-convex loss functions in deep learning models complicate optimization and theoretical understanding.

method Developed convex equivalences of ReLU NNs and their connections to sparse signal processing models.

result Recent research has uncovered hidden convexities in certain NN architectures, notably two-layer ReLU networks and other architectures.

Deep Learning Convexity ReLU Networks Sparse Signal Processing Optimization

2026-03-25abs ↗pdf ↗

Randomized Geometric Algebra Methods for Convex Neural Networkscs.LG

Randomized Geometric Algebra for Convex Neural Networks Optimizes Transfer Learning.

problem Training neural networks to global optimality via convex optimization.

method Randomized algorithms in Clifford's Geometric Algebra for hypercomplex vector spaces.

result Convex optimization and geometric algebra improve LLMs' robustness and reliability in transfer learning.

Convex Optimization Geometric Algebra Transfer Learning Randomized Algorithms Neural Networks

2024-06-04abs ↗pdf ↗

Learning Weakly Convex Sets in Metric Spacescs.LG

Paper tackles efficient learning of non-convex hypotheses in metric spaces.

problem Efficiently find consistent hypotheses for non-convex hypotheses composed of possibly several disconnected regions.

method Proposes a general domain-independent algorithm for finding consistent weakly convex hypotheses and proves sufficient conditions for its efficiency.

result Shows that consistent hypothesis finding problem can be solved in polynomial time for a broad class of weakly convex hypotheses over metric spaces.

machine learning consistent hypothesis weakly convex hypotheses metric spaces polynomial time

2021-05-10abs ↗pdf ↗

Disciplined Geodesically Convex Programmingmath.OC

Extends DCP framework to Hadamard manifolds for geodesically convex functions.

problem Verifying convexity in nonlinear programs on Hadamard manifolds.

method Introduces Disciplined Geodesically Convex Programming (DGCP) framework, defining compositions and transformations for geodesically convex functions.

result Allows verification of geodesic convexity for a broader range of functions, including statistical estimators and matrix-valued optimization.

Convex Programming Geodesic Convexity Hadamard Manifolds Statistical Estimators Matrix Optimization

2024-07-07abs ↗pdf ↗

Deep Learning Generalization and the Convex Hull of Training Setscs.LG

Deep learning models generalize by extending decision boundaries outside the convex hull of training data.

problem Understanding how deep learning models generalize beyond their training data.

method Investigation of decision boundaries inside and outside the convex hull of training sets, using various neural network architectures and training regimes.

result Over-parameterization is necessary for deep learning models to extend decision boundaries outside the convex hull of their training data.

deep learning generalization convex hull decision boundaries over-parameterization

2021-01-25abs ↗pdf ↗

Constrained episodic reinforcement learning in concave-convex and knapsack settingscs.LG

Algorithm tackles constrained reinforcement learning with concave-convex and knapsack constraints.

problem Constrained episodic reinforcement learning with concave rewards and convex constraints.

method Modular analysis with strong theoretical guarantees for concave-convex and knapsack settings.

result Significantly outperforms existing approaches in constrained episodic environments.

reinforcement learning constrained optimization episodic concave-convex knapsack

2020-06-09abs ↗pdf ↗

Learning Variational Inequalities from Data: Fast Generalization Rates under Strong Monotonicitycs.LG

This paper shows how to learn variational inequalities fast with strong monotonicity.

problem Learning variational inequalities efficiently.

method Extending convex optimization techniques to variational inequalities with strong monotonicity.

result Fast generalization rates of

Θ(1/ε)

for learning variational inequalities.

Variational Inequalities Fast Learning Rates Strong Monotonicity Stability-Based Generalization Convex Optimization

2024-10-28abs ↗pdf ↗

Online Episodic Convex Reinforcement Learningcs.LG

New algorithm for online learning in episodic MDPs with convex objectives.

problem Online episodic convex reinforcement learning.

method Online mirror descent algorithm with varying constraint sets and exploration bonus.

result Near-optimal regret bounds for online CURL without prior knowledge of transition function.

online learning reinforcement learning convex optimization mirror descent regret bounds

2025-05-12abs ↗pdf ↗

Sparse projections onto the simplexcs.LG

Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the $\ell_1$ -norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank a…

2012-06-07abs ↗pdf ↗

Provably Training Overparameterized Neural Network Classifiers with Non-convex Constraintsstat.ML

This work shows neural networks can solve non-convex constraints problems.

problem Training neural networks under non-convex constraints.

method Project stochastic gradient descent with no-regret analysis of online learning.

result Overparameterized neural networks achieve near-optimal and near-feasible solutions.

neural networks non-convex constraints project stochastic gradient descent no-regret analysis overparameterization

2020-12-30abs ↗pdf ↗

Non-Convex Projected Gradient Descent for Generalized Low-Rank Tensor Regressionstat.ML

In this paper, we consider the problem of learning high-dimensional tensor regression problems with low-rank structure. One of the core challenges associated with learning high-dimensional models is computation since the underlying optimization problems are often non-convex. While convex relaxations could lead to polyn…

2016-11-30abs ↗pdf ↗

Optimal learning rate schedules in high-dimensional non-convex optimization problemscs.LG

Analyzes optimal learning rate schedules in high-dimensional non-convex optimization problems.

problem Optimizing high-dimensional non-convex loss landscapes.

method Langevin optimization with learning rate decaying as $η(t) = t^{-β}$.

result To speed up optimization without getting stuck in saddles, a decay rate $β < 1$ is optimal, contrary to convex setups where $β = 1$.

learning rate schedules high-dimensional optimization non-convex problems Langevin optimization signal recovery

2022-02-09abs ↗pdf ↗

Optimal transport mapping via input convex neural networkscs.LG

In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal transport map. This involves learning two convex functions, by solving a novel mi…

2019-08-28abs ↗pdf ↗

Iso-Riemannian Optimization on Learned Data Manifoldsmath.OC

Develops iso-Riemannian optimization for data manifolds.

problem Challenges in performing optimization on learned data manifolds.

method Introduces iso-connection and iso-Riemannian descent algorithm.

result Demonstrates efficient solutions to inverse problems on learned data manifolds.

data manifolds Riemannian optimization iso-connection euclidean convexity geodesic convexity

2025-10-23abs ↗pdf ↗

Optimal Stochastic Non-smooth Non-convex Optimization through Online-to-Non-convex Conversioncs.LG

New algorithms optimize non-smooth, non-convex objectives with improved complexity.

problem Optimizing non-smooth, non-convex stochastic objectives.

method Reduction to online learning, applying optimistic online learning techniques.

result Improved complexity for finding

(δ,ε)

-stationary points.

Optimization Non-smooth Non-convex Stochastic Online Learning

2023-02-07abs ↗pdf ↗

Greedy Convex Ensemblecs.LG

We consider learning a convex combination of basis models, and present some new theoretical and empirical results that demonstrate the effectiveness of a greedy approach. Theoretically, we first consider whether we can use linear, instead of convex, combinations, and obtain generalization results similar to existing on…

2019-10-09abs ↗pdf ↗

Online Learning on Hidden-Convex Losses via Algorithmic Equivalence: Optimal Regret, Geometric Barrier, and Bandit Feedbackcs.LG

Improved online learning for hidden-convex losses achieves optimal regret.

problem Adversarial online learning with nonconvex losses that become convex after reparameterization.

method Algorithmic equivalence between OGD and OMD on convex losses, with Hessian compatibility condition.

result OGD achieves

\mathcal{O}(\sqrt{T})

regret for hidden-convex losses, matching optimal rate.

online learning hidden-convex losses algorithmic equivalence regret minimization Hessian compatibility

2026-05-25abs ↗pdf ↗

Jensen: An Easily-Extensible C++ Toolkit for Production-Level Machine Learning and Convex Optimizationcs.LG

This paper introduces Jensen, an easily extensible and scalable toolkit for production-level machine learning and convex optimization. Jensen implements a framework of convex (or loss) functions, convex optimization algorithms (including Gradient Descent, L-BFGS, Stochastic Gradient Descent, Conjugate Gradient, etc.), …

2018-07-17abs ↗pdf ↗

Algorithmic Connections Between Active Learning and Stochastic Convex Optimizationcs.LG

Interesting theoretical associations have been established by recent papers between the fields of active learning and stochastic convex optimization due to the common role of feedback in sequential querying mechanisms. In this paper, we continue this thread in two parts by exploiting these relations for the first time …

2015-05-15abs ↗pdf ↗

On the complexity of PAC learning in Hilbert spacescs.LG

Study improves learning algorithms for convex polyhedra in Hilbert spaces.

problem Learning convex polyhedra in Hilbert spaces.

method Proposes an algorithm for learning a polyhedron in a Hilbert space.

result Correctly classifies at least 1-ε of the distribution with high probability.

Hilbert space convex polyhedra PAC learning binary classification

2023-03-03abs ↗pdf ↗

CoNES: Convex Natural Evolutionary Strategiescs.LG

CoNES optimizes blackbox functions using convex optimization and information geometry.

problem Optimizing high-dimensional blackbox functions efficiently.

method Formulated as a convex program that adapts evolutionary strategies gradient estimates.

result Vastly outperforms conventional blackbox optimization methods on benchmarks and MuJoCo tasks.

Convex optimization Evolutionary strategies Blackbox optimization Information geometry Reinforcement learning

2020-07-16abs ↗pdf ↗

Muon Does Not Converge on Convex Lipschitz Functionscs.LG

Muon fails to converge on convex Lipschitz functions.

problem Understanding the convergence of Muon on convex and Lipschitz functions.

method Analyzing Muon's performance on convex and Lipschitz functions without error feedback.

result Muon does not converge on convex and Lipschitz functions, regardless of learning rate schedule.

Muon Convex Lipschitz Convergence Error Feedback

2026-05-09abs ↗pdf ↗

Learning with Stochastic Ordersstat.ML

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

problem Learning high-dimensional distributions with stochastic orders.

method Introduces Choquet-Toland distance and Variational Dominance Criterion, uses input convex maxout networks (ICMNs).

result Proposes surrogates for Choquet-Toland distance and Variational Dominance Criterion with parametric rates.

stochastic orders Choquet-Toland distance Variational Dominance Criterion input convex maxout networks curse of dimensionality

2022-05-27abs ↗pdf ↗

Learning in Non-convex Games with an Optimization Oraclecs.LG

We consider online learning in an adversarial, non-convex setting under the assumption that the learner has an access to an offline optimization oracle. In the general setting of prediction with expert advice, Hazan et al. (2016) established that in the optimization-oracle model, online learning requires exponentially …

2018-10-17abs ↗pdf ↗

Catalyst Acceleration for Gradient-Based Non-Convex Optimizationstat.ML

We introduce a generic scheme to solve nonconvex optimization problems using gradient-based algorithms originally designed for minimizing convex functions. Even though these methods may originally require convexity to operate, the proposed approach allows one to use them on weakly convex objectives, which covers a larg…

2017-03-31abs ↗pdf ↗

Non-Convex SGD Learns Halfspaces with Adversarial Label Noisecs.LG

Non-convex SGD learns halfspaces with adversarial label noise efficiently.

problem Agnostically learning halfspaces in adversarial label noise settings.

method Non-convex SGD optimization for halfspace learning.

result Non-convex SGD achieves misclassification error close to optimal with adversarial noise.

SGD halfspaces PAC model log-concave distributions adversarial noise

2020-06-11abs ↗pdf ↗

Reward is enough for convex MDPscs.AI

Reward suffices for convex MDPs, expanding RL to new problems.

problem Capturing goals as convex functions of stationary distribution.

method Reformulated as a min-max game using Fenchel duality.

result Convex MDPs require non-stationary reward functions.

reinforcement learning Markov decision processes convex optimization Fenchel duality min-max games

2021-06-01abs ↗pdf ↗

Why Do Local Methods Solve Nonconvex Problems?cs.LG

Optimizers find approximate global minima in non-convex problems.

problem Understanding why local methods solve non-convex optimization problems.

method Formalizing the hypothesis that many local minima are approximately global minima.

result Most local minima of practical non-convex objectives are approximately global minima.

non-convex optimization local minima global minima machine learning optimization

2021-03-24abs ↗pdf ↗

Self-Directed Learning of Convex Labelings on Graphscs.LG

Efficient algorithm for self-directed learning of convex clusters on graphs.

problem Self-directed classification of nodes on graphs with convex clusters.

method Developed efficient algorithms for (geodesically) convex clusters on graphs.

result Polynomial runtime algorithm with

3(h(G)+1)^4 \ln n

mistakes for graphs with two convex clusters.

self-directed learning graph classification convex clusters online learning geodesic convexity

2024-09-02abs ↗pdf ↗

Convex Representation Learning for Generalized Invariance in Semi-Inner-Product Spacecs.LG

Convex learning for diverse invariances in semi-inner-product space.

problem Efficiently learning invariant representations for a wide range of invariances.

method Developed a convex representation learning algorithm for generalized invariances modeled as semi-norms, introducing Euclidean embeddings for kernel representers in a semi-inner-product space.

result Accurate invariant representations learned efficiently and effectively, validated by experiments.

representation learning invariance convex optimization semi-inner-product space kernel methods

2020-04-25abs ↗pdf ↗

Momentum via Primal Averaging: Theoretical Insights and Learning Rate Schedules for Non-Convex Optimizationcs.LG

New insights into using momentum for non-convex optimization.

problem Improving training of non-convex models like deep neural networks.

method Developed a Lyapunov analysis of SGD with momentum using stochastic primal averaging.

result Precise conditions under which SGD+M outperforms SGD and optimal hyper-parameter schedules.

momentum non-convex optimization SGD SPA Lyapunov analysis

2020-10-01abs ↗pdf ↗

An Analysis of Constant Step Size SGD in the Non-convex Regime: Asymptotic Normality and Biasstat.ML

SGD's uncertainty quantified in non-convex learning problems.

problem Uncertainty quantification in non-convex learning problems.

method Asymptotic normality of SGD iterates and bias characterization.

result SGD iterates are asymptotically normally distributed around the expected value of the invariant distribution.

SGD non-convex learning asymptotic normality bias Markov chains

2020-06-14abs ↗pdf ↗

Tackling benign nonconvexity with smoothing and stochastic gradientscs.LG

SGD converges to global minimum for certain non-convex functions.

problem Theoretical challenges in optimizing non-convex functions in machine learning.

method Perturbed SGD on a broad class of non-convex functions.

result SGD converges to global minimum for certain non-convex functions.

SGD non-convex optimization stochastic gradient descent global convergence smoothed optimization

2022-02-18abs ↗pdf ↗

Reinforcement learning for linear-convex models with jumps via stability analysis of feedback controlsmath.OC

Study shows how to control jump-diffusion processes with stable feedback controls in reinforcement learning.

problem Control jump-diffusion processes with unknown coefficients in reinforcement learning.

method Lipschitz continuous optimal feedback controls, stability analysis of forward-backward SDEs, least-squares algorithm.

result Achieves

O(\sqrt{N\ln N})

regret for linear-convex learning problems with jumps.

Reinforcement Learning Linear-Convex Models Jump-Diffusion Processes Stability Analysis Least-Squares Algorithm

2021-04-19abs ↗pdf ↗

Multi-Stage Multi-Task Feature Learningstat.ML

Multi-task sparse feature learning aims to improve the generalization performance by exploiting the shared features among tasks. It has been successfully applied to many applications including computer vision and biomedical informatics. Most of the existing multi-task sparse feature learning algorithms are formulated a…

2012-10-22abs ↗pdf ↗

A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problemscs.LG

Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning settings. However, solving the non-convex optimization problems associated with non-conv…

2013-03-18abs ↗pdf ↗

A Distributed Cubic-Regularized Newton Method for Smooth Convex Optimization over Networksmath.OC

A new distributed method for convex optimization over networks with fast convergence.

problem Large-scale convex optimization over networks with limited communication.

method Distributed cubic-regularized Newton method.

result Convergence rate of

O(k^{{-}3})

for convex functions with Lipschitz gradient and Hessian.

distributed optimization Newton method convex optimization federated learning networks

2020-07-07abs ↗pdf ↗