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.
Extends DCP framework to Hadamard manifolds for geodesically convex functions.
Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain problems, but existing software for differentiable optimization layers is rigid…
In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for solving them in which each iteration is obtained by solving a convex programming pro…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search step (gradient descent or Quasi-Newton iteration) into these uniformly optimal conv…
Novel approximation hierarchy for sparse quadratic programs.
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…
In this paper we consider regularized convex cone programming problems. In particular, we first propose an iterative hard thresholding (IHT) method and its variant for solving regularized box constrained convex programming. We show that the sequence generated by these methods converges to a local minimizer.…
Convex optimization refines neural network training, improving model performance and reducing hyperparameter sensitivity.
Neural networks solve copositive programs, revealing insights into training problems.
Max-linear regression problem solved with convex programming.
New method finds arbitrage opportunities in fluctuating asset bands.
Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods are fast and scalable, but can have instability when used to approximate constraints or objective functions for optimization. Ensemble methods, like bagging, sm…
We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that the algorithm has super-linear convergence with exponentially high probability, wi…
This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers, and (3) missing data. This problem, often dubbed as robust principal component analysis (robust PCA), finds applications in various domai…
Paper develops exact convex optimization for neural networks with polynomial activations.
We introduce a convex approach for mixed linear regression over features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in for each data point. These estimates can then be clustered using, for example, -means. For problem…
Bayesian optimization tackles non-convex, two-stage stochastic problems efficiently.
We develop exact representations of training two-layer neural networks with rectified linear units (ReLUs) in terms of a single convex program with number of variables polynomial in the number of training samples and the number of hidden neurons. Our theory utilizes semi-infinite duality and minimum norm regularization…
We study a distributionally robust mean square error estimation problem over a nonconvex Wasserstein ambiguity set containing only normal distributions. We show that the optimal estimator and the least favorable distribution form a Nash equilibrium. Despite the non-convex nature of the ambiguity set, we prove that the …
The closed string field theory minimal-area problem asks for the conformal metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2π. This is an extremal length problem in conformal geometry as well as a problem in systolic geometry. We consider the ana…
Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a lower-dimensional problem. Such dimensionality reduction is essential in computation-limite…
We consider the question of estimating a solution to a system of equations that involve convex nonlinearities, a problem that is common in machine learning and signal processing. Because of these nonlinearities, conventional estimators based on empirical risk minimization generally involve solving a non-convex optimiza…
SOC-ICNN expands neural network representational capacity by using conic optimization.
Polynomial-time convex optimization for CNNs with ReLU activations.
Optimizes distributions robustly with Sinkhorn distance.
This paper reports applications of Difference of Convex functions (DC) programming to Learning from Demonstrations (LfD) and Reinforcement Learning (RL) with expert data. This is made possible because the norm of the Optimal Bellman Residual (OBR), which is at the heart of many RL and LfD algorithms, is DC. Improvement…
Many problems in machine learning and other fields can be (re)for-mulated as linearly constrained separable convex programs. In most of the cases, there are multiple blocks of variables. However, the traditional alternating direction method (ADM) and its linearized version (LADM, obtained by linearizing the quadratic p…
This paper tackles multi-marginal optimal transport problems using DC programming.
Data-driven optimization improves mean-variance portfolios by penalizing norms.
We consider the problem of estimating the phases of K mixed complex signals from a multichannel observation, when the mixing matrix and signal magnitudes are known. This problem can be cast as a non-convex quadratically constrained quadratic program which is known to be NP-hard in general. We propose three approaches t…
We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the relevant variables. Our approach is a two-stage quadratic programming method that…
A new method solves diagonally constrained SDPs quickly and accurately.
We study the problem of estimating multiple predictive functions from a dictionary of basis functions in the nonparametric regression setting. Our estimation scheme assumes that each predictive function can be estimated in the form of a linear combination of the basis functions. By assuming that the coefficient matrix …
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a binary, continuous and multi-class target type, incorporating constraints not p…
New method approximates neural network training for robustness.
New method uses DC functions for piecewise linear regression.
Differential privacy enables organizations to collect accurate aggregates over sensitive data with strong, rigorous guarantees on individuals' privacy. Previous work has found that under differential privacy, computing multiple correlated aggregates as a batch, using an appropriate \emph{strategy}, may yield higher acc…
We propose a formulation for nonlinear recurrent models that includes simple parametric models of recurrent neural networks as a special case. The proposed formulation leads to a natural estimator in the form of a convex program. We provide a sample complexity for this estimator in the case of stable dynamics, where th…
Maximizes determinant of vector sums under matroid constraints.
New algorithms improve submodular minimization via DC programming.
We consider a multi-objective risk-averse two-stage stochastic programming problem with a multivariate convex risk measure. We suggest a convex vector optimization formulation with set-valued constraints and propose an extended version of Benson's algorithm to solve this problem. Using Lagrangian duality, we develop sc…
The paper develops mixed-integer formulations for neural networks using partitioning.
New method trains quantized neural networks to global optimality.
This work connects neural network training to convex optimization via the NTK.
A new algorithm solves semidefinite programs using Langevin diffusion.
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of a…
Strong geodesic convex function and strong monotone vector field of order on Riemannian manifolds have been established. A characterization of strong geodesic convex function of order for the continuously differentiable functions has been discussed. The relation between the solution of a new variational inequal…
Convex optimization method infers latent structure in random dot product graphs.