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.
Negative step sizes improve second-order methods for neural networks.
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…
GOLS finds activation functions affect training robustness, especially ReLU.
We develop a projected Nesterov's proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov's momentum acceleration. The objective function that we wish to minimize is the sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a conv…
Boosted Frank-Wolfe accelerates optimization for nonconvex problems.
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 paper analyzes and validates two step size schedules for SGD: exponential and cosine, proving their adaptivity and performance.
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 optimizes AUC in binary classification and changepoint detection.
We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such directions, eliminating the need for the user to tune the learning rate. The pro…
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.
Adaptive step-size improves optimization in complex geometries.
New convergence results for NGVI with various step sizes and sample sizes.
ELU algorithm improves on EM for over-specified Gaussian mixtures.
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…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset of the sample to be dependent on the sample size, a feature not presented in a …
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.
Learning rates in stochastic neural network training are currently determined a priori to training, using expensive manual or automated iterative tuning. This study proposes gradient-only line searches to resolve the learning rate for neural network training algorithms. Stochastic sub-sampling during training decreases…
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…
Proposes a new adaptive learning rate for SGD.
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.