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.
This work shows neural networks can solve non-convex constraints problems.
We show that many machine learning goals, such as improved fairness metrics, can be expressed as constraints on the model's predictions, which we call rate constraints. We study the problem of training non-convex models subject to these rate constraints (or any non-convex and non-differentiable constraints). In the non…
Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the -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…
The paper tackles MAP inference over non-convex constraints in safety-critical settings.
Paper tackles constrained learning with non-convex losses, overcoming challenges with new approach.
Paper solves high-order portfolio optimization with cardinality constraint.
Study on policy testing in MDPs with lower bounds and new algorithm.
Quantum computing tackles non-convex portfolio optimization with cardinality constraints.
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints corresponding to first-order stochastic dominance. We propose new discretization sch…
We describe two nonconventional algorithms for linear regression, called GAME and CLASH. The salient characteristics of these approaches is that they exploit the convex -ball and non-convex -sparsity constraints jointly in sparse recovery. To establish the theoretical approximation guarantees of GAME an…
Proposes r2SGLD for efficient constrained exploration in non-convex learning.
We analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank constraint is locally identical to the proximal operator of its convex envelope, hen…
In recent years, constrained optimization has become increasingly relevant to the machine learning community, with applications including Neyman-Pearson classification, robust optimization, and fair machine learning. A natural approach to constrained optimization is to optimize the Lagrangian, but this is not guarantee…
The paper shows regularization can't always find all optimal solutions in constrained ML.
New algorithm optimizes DAGs by swapping node pairs to avoid cycles.
Non-convex optimization is ubiquitous in machine learning. Majorization-Minimization (MM) is a powerful iterative procedure for optimizing non-convex functions that works by optimizing a sequence of bounds on the function. In MM, the bound at each iteration is required to \emph{touch} the objective function at the opti…
We study the projected gradient descent method on low-rank matrix problems with a strongly convex objective. We use the Burer-Monteiro factorization approach to implicitly enforce low-rankness; such factorization introduces non-convexity in the objective. We focus on constraint sets that include both positive semi-defi…
The non-negative matrix factorization (NMF) model with an additional orthogonality constraint on one of the factor matrices, called the orthogonal NMF (ONMF), has been found a promising clustering model and can outperform the classical K-means. However, solving the ONMF model is a challenging optimization problem becau…
Algorithm ensures safe optimization under unknown constraints.
This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally intractable, we first show that generic instances of the problem can be solved efficientl…
We study power utility maximization for exponential Lévy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the Lévy triplet is constructed under minimal assumptions by solving the Bellman equation. We use a nove…
The problem of low-rank approximation with convex constraints, which appears in data analysis, system identification, model order reduction, low-order controller design and low-complexity modelling is considered. Given a matrix, the objective is to find a low-rank approximation that meets rank and convex constraints, w…
This paper explores the nonconvexity of push-forward constraints in machine learning.
In this paper, the online variants of the classical Frank-Wolfe algorithm are considered. We consider minimizing the regret with a stochastic cost. The online algorithms only require simple iterative updates and a non-adaptive step size rule, in contrast to the hybrid schemes commonly considered in the literature. Seve…
New methods solve sparse estimation robustly, even with outliers.
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…
Develops a new fairness learning approach for multi-task regression models.
Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead to unwanted shrinkage. This paper explores instead penalizing the squared distanc…
A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few hundreds variables (in the underlying combinatorial problem). On the other hand…
Paper examines financial engineering problems and introduces AlphaZero for better replication strategies.
Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the nuclear norm, which acts as a convenient convex surrogate. While elegant theoretical c…
SnareNet adds repair layers to neural networks to ensure outputs meet physical constraints.
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…
In classification models fairness can be ensured by solving a constrained optimization problem. We focus on fairness constraints like Disparate Impact, Demographic Parity, and Equalized Odds, which are non-decomposable and non-convex. Researchers define convex surrogates of the constraints and then apply convex optimiz…
New single-loop algorithm tackles weakly convex constraints in stochastic optimization.
We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization problems. Recently, it was shown that the underlying principle behind their succ…
Motivated by an application in computational biology, we consider low-rank matrix factorization with -constraints on one of the factors and optionally convex constraints on the second one. In addition to the non-convexity shared with other matrix factorization schemes, our problem is further complicated by a c…
New algorithm solves -norm constrained multilinear logistic regression for tensor data.
Bayesian inference over admissible histories leads to irreversible kinetics.
A new optimization method, BPM, converges linearly in non-convex, non-smooth problems.
New algorithms for differentially private optimization in convex and non-convex settings with near-optimal rates.
The study establishes risk bounds for distributional regression estimators.
Paper solves optimal portfolio deleveraging with cross asset impacts.
Counterexample shows state-constrained optimal control problems can have Young measure gaps.
Optimizes binary regression models with gradient ascent-descent methods.
Boosted Difference of Convex Functions Algorithm solves VaR constrained portfolio optimization.
Method identifies shifts leading to large model performance differences.
Federated edge learning improves with CSIT-free model aggregation using RIS.