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.
A new optimization algorithm improves convergence in unconstrained problems.
Revisits life insurance surplus models with new technical bases.
Implicit Q-learning and SARSA adjust step-sizes automatically, improving stability and performance.
The paper analyzes fixed step-size SA schemes on Riemannian manifolds.
The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation, where the step size is adapted measuring the length of a so-called cumulative path. The cumulative path is a combination of the previous steps realized by the algorithm, where the importance of each step decreases with time. This article studies …
In this paper, we introduce a method for adapting the step-sizes of temporal difference (TD) learning. The performance of TD methods often depends on well chosen step-sizes, yet few algorithms have been developed for setting the step-size automatically for TD learning. An important limitation of current methods is that…
New algorithm improves stability of optimization algorithms by adapting step-size.
AutoStep MCMC adapts step size locally for better sampling efficiency.
Polyak step size GD reaches final radius of convergence after log iterations.
Stochastic Gradient Descent (SGD) is a popular tool in training large-scale machine learning models. Its performance, however, is highly variable, depending crucially on the choice of the step sizes. Accordingly, a variety of strategies for tuning the step sizes have been proposed, ranging from coordinate-wise approach…
Adaptive step-size improves optimization in complex geometries.
Negative step sizes improve second-order methods for neural networks.
New convergence results for NGVI with various step sizes and sample sizes.
Adaptive step-size method improves compressed SGD performance in machine learning.
The practical performance of online stochastic gradient descent algorithms is highly dependent on the chosen step size, which must be tediously hand-tuned in many applications. The same is true for more advanced variants of stochastic gradients, such as SAGA, SVRG, or AdaGrad. Here we propose to adapt the step size by …
The main goal of this work is equipping convex and nonconvex problems with Barzilai-Borwein (BB) step size. With the adaptivity of BB step sizes granted, they can fail when the objective function is not strongly convex. To overcome this challenge, the key idea here is to bridge (non)convex problems and strongly convex …
Proposes a neural network for learning step-size policies for L-BFGS optimization.
New insights into SGD and SGD-M in high dimensions.
Improved variational inequality algorithms using adaptive step sizes.
We consider -dimensional linear stochastic approximation algorithms (LSAs) with a constant step-size and the so called Polyak-Ruppert (PR) averaging of iterates. LSAs are widely applied in machine learning and reinforcement learning (RL), where the aim is to compute an appropriate (that is a…
Sparse coding is typically solved by iterative optimization techniques, such as the Iterative Shrinkage-Thresholding Algorithm (ISTA). Unfolding and learning weights of ISTA using neural networks is a practical way to accelerate estimation. In this paper, we study the selection of adapted step sizes for ISTA. We show t…
New adaptive step-size method for convex optimization without tuning.
New step-size methods improve SHB convergence for stochastic optimization.
One of the major issues in stochastic gradient descent (SGD) methods is how to choose an appropriate step size while running the algorithm. Since the traditional line search technique does not apply for stochastic optimization algorithms, the common practice in SGD is either to use a diminishing step size, or to tune a…
Sparse Polyak improves high-dimensional statistical estimation.
A new scaling law predicts optimal batch size for training models.
Step decay schedules improve convergence in non-convex optimization.
Large SGD step sizes lead to sparse feature learning in neural networks.
Deep unfolding is a promising deep-learning technique in which an iterative algorithm is unrolled to a deep network architecture with trainable parameters. In the case of gradient descent algorithms, as a result of the training process, one often observes the acceleration of the convergence speed with learned non-const…
A major challenge in current optimization research for deep learning is to automatically find optimal step sizes for each update step. The optimal step size is closely related to the shape of the loss in the update step direction. However, this shape has not yet been examined in detail. This work shows empirically that…
A recent algorithmic family for distributed optimization, DIGing's, have been shown to have geometric convergence over time-varying undirected/directed graphs. Nevertheless, an identical step-size for all agents is needed. In this paper, we study the convergence rates of the Adapt-Then-Combine (ATC) variation of the DI…
Develops a generalized version of Chung's Lemma for stochastic optimization methods.
The variance reduction class of algorithms including the representative ones, SVRG and SARAH, have well documented merits for empirical risk minimization problems. However, they require grid search to tune parameters (step size and the number of iterations per inner loop) for optimal performance. This work introduces `…
Gradient descent with large steps leads to chaotic parameter space and unpredictable outcomes.
We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide an asymptotic expansion up to explicit exponentially decaying terms. Our analysis…
Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally infeasible. The recently proposed stochastic gradient Langevin dynamics (SGLD) method circumvents this problem in three ways: it generates proposed moves using only a subset of the data, it skips the Metropolis-Hastings a…
Study optimizes step size for Metropolis algorithm in non-identifiable cases.
We propose a new stochastic first-order algorithmic framework to solve stochastic composite nonconvex optimization problems that covers both finite-sum and expectation settings. Our algorithms rely on the SARAH estimator introduced in (Nguyen et al, 2017) and consist of two steps: a proximal gradient and an averaging s…
Proposes an exponentially increasing step-size for faster parameter estimation in statistical models.
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with step size compared to normal distribution. Thus it is essential to cut-off these di…
SGD converges almost surely in non-convex problems, avoiding saddle points and accelerating convergence.
Paper develops an online learning algorithm for functional data models.
A new method approximates expected empirical loss for stochastic deep learning tasks.
Motivated by their broad applications in reinforcement learning, we study the linear two-time-scale stochastic approximation, an iterative method using two different step sizes for finding the solutions of a system of two equations. Our main focus is to characterize the finite-time complexity of this method under time-…
New TD algorithms stabilize RL tasks by reformulating updates into fixed point equations.
This manuscript shows that AdaBoost and its immediate variants can produce approximate maximum margin classifiers simply by scaling step size choices with a fixed small constant. In this way, when the unscaled step size is an optimal choice, these results provide guarantees for Friedman's empirically successful "shrink…
The correspondence between residual networks and dynamical systems motivates researchers to unravel the physics of ResNets with well-developed tools in numeral methods of ODE systems. The Runge-Kutta-Fehlberg method is an adaptive time stepping that renders a good trade-off between the stability and efficiency. Can we …
Recently it has been shown that the step sizes of a family of variance reduced gradient methods called the JacSketch methods depend on the expected smoothness constant. In particular, if this expected smoothness constant could be calculated a priori, then one could safely set much larger step sizes which would result i…