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 algorithm improves convergence for non-convex problems with boundaries.
Optimizers find approximate global minima in non-convex problems.
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…
SGD's uncertainty quantified in non-convex learning problems.
Machine learning algorithms typically perform optimization over a class of non-convex functions. In this work, we provide bounds on the fundamental hardness of identifying the global minimizer of a non convex function. Specifically, we design a family of parametrized non-convex functions and employ statistical lower bo…
Stochastic gradient descent~(SGD) and its variants have attracted much attention in machine learning due to their efficiency and effectiveness for optimization. To handle large-scale problems, researchers have recently proposed several lock-free strategy based parallel SGD~(LF-PSGD) methods for multi-core systems. Howe…
Adaptive momentum method solves non-convex min-max problems.
Paper solves curvature equations in Minkowski space for non-convex domains.
Heavy Ball method speeds up finding global optima in non-convex problems.
Note on the computational complexity of Gromov-Wasserstein distance.
A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low rank are frequently imposed or else the objective itself is designed to be a non-c…
This work shows neural networks can solve non-convex constraints problems.
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…
Study accelerates optimization methods in non-convex problems, but doesn't improve the algorithm's performance.
Here we study non-convex composite optimization: first, a finite-sum of smooth but non-convex functions, and second, a general function that admits a simple proximal mapping. Most research on stochastic methods for composite optimization assumes convexity or strong convexity of each function. In this paper, we extend t…
Paper proposes a working set algorithm for non-convex sparse regression with provable convergence.
Non-convex optimization problems often arise from probabilistic modeling, such as estimation of posterior distributions. Non-convexity makes the problems intractable, and poses various obstacles for us to design efficient algorithms. In this work, we attack non-convexity by first introducing the concept of \emph{probab…
Survey of advances in non-convex min-max optimization for applications.
The min-max problem, also known as the saddle point problem, is a class of optimization problems which minimizes and maximizes two subsets of variables simultaneously. This class of problems can be used to formulate a wide range of signal processing and communication (SPCOM) problems. Despite its popularity, most exist…
Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies heavily on the assumption that every entry is observed with exactly the same pro…
Improved optimization guarantees for deep learning models with Nesterov acceleration.
A fast method for decentralized non-convex optimization over networks.
Paper develops robust SGLD for solving non-convex DRO problems.
Proves convergence of PSGLA for sampling non-convex potentials.
Recently non-convex optimization approaches for solving machine learning problems have gained significant attention. In this paper we explore non-convex boosting in classification by means of integer programming and demonstrate real-world practicability of the approach while circumventing shortcomings of convex boostin…
Paper tackles non-convex optimization for higher moments in portfolio management.
We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are non-convex but belong to the class of difference of convex (DC) functions. Our contribution is a new general purpose proximal Newton algorithm that is able to deal with such a situation. The algorithm consi…
The TREX is a recently introduced method for performing sparse high-dimensional regression. Despite its statistical promise as an alternative to the lasso, square-root lasso, and scaled lasso, the TREX is computationally challenging in that it requires solving a non-convex optimization problem. This paper shows a remar…
This work explores the non-convex optimization in compressive learning and the performance of heuristics.
New method finds near-optimal solutions for non-convex optimization problems.
Gradient descent solves robust mean estimation in high dimensions.
AGGLIO optimizes non-convex functions with local convexity guarantees.
New methods improve convergence in non-convex non-smooth learning problems.
Develops a new fairness learning approach for multi-task regression models.
This work studies the strong duality of non-convex matrix factorization problems: we show that under certain dual conditions, these problems and its dual have the same optimum. This has been well understood for convex optimization, but little was known for non-convex problems. We propose a novel analytical framework an…
We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a low-rank core and the corresponding sparse residual. Rigorous theoretical analysis of t…
Study uses weak transport for non-convex costs in fixed-income markets.
Quantum annealers aim at solving non-convex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists in designing a classical energy function whose ground states are the sought optimal solutions of the original optimization problem and add a controllable qua…
Paper checks SSC for matrix factorizations using Gurobi.
A meta-learning approach improves the performance of alternating minimization for non-convex optimization problems.
We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order non-convex optimization remain to be full gradient descent that converges in $O(1/\varep…
NSGLD improves SGLD for non-convex optimization problems.
SGD converges to global minimum for certain non-convex functions.
Paper resolves ambiguity in non-convex bilevel optimization problems.
Several recently proposed architectures of neural networks such as ResNeXt, Inception, Xception, SqueezeNet and Wide ResNet are based on the designing idea of having multiple branches and have demonstrated improved performance in many applications. We show that one cause for such success is due to the fact that the mul…
In this paper, we study a family of non-convex and possibly non-smooth inf-projection minimization problems, where the target objective function is equal to minimization of a joint function over another variable. This problem include difference of convex (DC) functions and a family of bi-convex functions as special cas…
Generalizes smoothness conditions for optimization methods.
New method improves efficiency of non-convex matrix reconstruction.