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.
Study shows tractable generalization in RL is impossible but possible with Strong Proximity.
Improved sampling guarantees for weakly log-concave distributions.
We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the difference of convex (DC) programming, and enjoys both strong computational and statist…
Paper analyzes convergence of proximal algorithm in metric spaces without geodesic convexity.
New method reduces variance in stochastic optimization with high confidence.
The proximal inertial gradient descent is efficient for the composite minimization and applicable for broad of machine learning problems. In this paper, we revisit the computational complexity of this algorithm and present other novel results, especially on the convergence rates of the objective function values. The no…
The paper analyzes convergence rates of Langevin dynamics and Proximal Sampler using -divergence.
We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However, primal-dual algorithms often require explicit strongly convex regularization in …
We consider the class of optimization problems arising from computationally intensive L1-regularized M-estimators, where the function or gradient values are very expensive to compute. A particular instance of interest is the L1-regularized MLE for learning Conditional Random Fields (CRFs), which are a popular class of …
We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth term and multiple stochastic nonsmooth terms. In each iteration, our splitting t…
Two new algorithms improve federated optimization under second-order similarity.
New insights show NAG and FISTA converge linearly without knowing strong convexity modulus.
In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties of this method, both in the exact and inexact setting, in the case when the obje…
We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient descent, coordinate gradient descent, proximal coordinate gradient, and Newton's …
We develop model-based methods for solving stochastic convex optimization problems, introducing the approximate-proximal point, or aProx, family, which includes stochastic subgradient, proximal point, and bundle methods. When the modeling approaches we propose are appropriately accurate, the methods enjoy stronger conv…
Unified framework for causal inference with reliable uncertainty quantification.
Complex embeddings handle non-metric proximity data better than traditional methods.
In this paper we propose a primal-dual proximal extragradient algorithm to solve the generalized Dantzig selector (GDS) estimation problem, based on a new convex-concave saddle-point (SP) reformulation. Our new formulation makes it possible to adopt recent developments in saddle-point optimization, to achieve the optim…
Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are statistically inefficient as estimators of the true parameter value. To address these tw…
A new algorithm solves signed Fréchet regression on manifolds with bounded curvature.
Guarantees convergence for black-box variational inference without modifications.
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 distributed optimization for federated learning with theoretical guarantees.
We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class structure under geometric assumptions. Furthermore, we derive an accelerated proximal …
In many learning settings, it is beneficial to augment the main features with pairwise interactions. Such interaction models can be often enhanced by performing variable selection under the so-called strong hierarchy constraint: an interaction is non-zero only if its associated main features are non-zero. Existing conv…
In 1963, Polyak proposed a simple condition that is sufficient to show a global linear convergence rate for gradient descent. This condition is a special case of the Łojasiewicz inequality proposed in the same year, and it does not require strong convexity (or even convexity). In this work, we show that this much-older…
Algorithm samples from composite log-concave distributions using gradient evaluations and restricted Gaussian oracles.
This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and proximal updates, respectively. The proposed algorithm is closely related to a p…
The paper classifies trades into types based on proximity and measures their impact on stock prices.
The paper analyzes PPM for nonconvex-nonconcave problems, identifying three regions with varying convergence guarantees.
The estimation of multivariate GARCH time series models is a difficult task mainly due to the significant overparameterization exhibited by the problem and usually referred to as the "curse of dimensionality". For example, in the case of the VEC family, the number of parameters involved in the model grows as a polynomi…
Neural architecture search (NAS) recently attracts much research attention because of its ability to identify better architectures than handcrafted ones. However, many NAS methods, which optimize the search process in a discrete search space, need many GPU days for convergence. Recently, DARTS, which constructs a diffe…
Paper solves minimax optimization gap with near-optimal algorithms.
This research introduces an autonomous robot navigation method using reinforcement learning.
The Support Vector Machine (SVM) has been used in a wide variety of classification problems. The original SVM uses the hinge loss function, which is non-differentiable and makes the problem difficult to solve in particular for regularized SVMs, such as with -regularization. This paper considers the Huberized SV…
ALP outperforms other data descriptors in one-class classification.
In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal operator is time-consuming, or the proximal operator does not have an analytic sol…
The paper explores rigidity and proximality in dynamical systems, proving new results about -algebras.
Improves time series classification with forest proximities.
In this paper we propose a randomized primal-dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints. Assuming mere convexity, we establish its convergence rate in terms of the objective value and feasibility m…
In this paper we consider the problem of maximizing the Area under the ROC curve (AUC) which is a widely used performance metric in imbalanced classification and anomaly detection. Due to the pairwise nonlinearity of the objective function, classical SGD algorithms do not apply to the task of AUC maximization. We propo…
In this work we introduce a new optimisation method called SAGA in the spirit of SAG, SDCA, MISO and SVRG, a set of recently proposed incremental gradient algorithms with fast linear convergence rates. SAGA improves on the theory behind SAG and SVRG, with better theoretical convergence rates, and has support for compos…
CFR-Pro enhances treatment effect estimation by incorporating local proximity.
Improved random forest proximities capture data geometry.
Introduces PPMM algorithm for nonconvex robust regression problems.
Extends RF proximities to all supervised distance-based machine learning contexts.
New method improves convergence of SPP for convex optimization problems.
Improved bounds for proximal gradient algorithms with computational errors.