相关论文: A Minibatch-SGD-Based Learning Meta-Policy for Inv…

We present the first finite time global convergence analysis of policy gradient in the context of infinite horizon average reward Markov decision processes (MDPs). Specifically, we focus on ergodic tabular MDPs with finite state and action…

We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly…

Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…

We introduce Multi-Iteration Stochastic Optimizers, a novel class of first-order stochastic methods that control the relative $L^2$ error using successive control variates along the iteration path. By exploiting correlations between…

In this work, we focus on the design of optimal controllers that must comply with an information structure. State-of-the-art approaches do so based on the H2 or Hinfty norm to minimize the expected or worst-case cost in the presence of…

Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong framework to guarantee convergence properties. We hereby…

This study presents a comprehensive approach to optimizing inventory management under stochastic demand by leveraging Monte Carlo Simulation (MCS) with grid search and Bayesian optimization. By using a business case of historical demand…

We study reinforcement learning for episodic Markov Decision Processes (MDPs) whose transitions are modelled by a multinomial logistic (MNL) model. Existing algorithms for MNL mixture MDPs yield a regret of $\smash{\tilde{O}(dH^2\sqrt{T})}$…

This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…

Machine learning models trained with \emph{stochastic} gradient descent (SGD) can generalize better than those trained with deterministic gradient descent (GD). In this work, we study SGD's impact on generalization through the lens of the…

In this paper, we study the minimax optimization problem in the smooth and strongly convex-strongly concave setting when we have access to noisy estimates of gradients. In particular, we first analyze the stochastic Gradient Descent Ascent…

We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a…

Stochastic Gradient Descent (SGD) is the workhorse algorithm of deep learning technology. At each step of the training phase, a mini batch of samples is drawn from the training dataset and the weights of the neural network are adjusted…

The problem of stopping stochastic gradient descent (SGD) in an online manner, based solely on the observed trajectory, is a challenging theoretical problem with significant consequences for applications. While SGD is routinely monitored as…

Dynamic pricing of goods in a competitive environment to maximize revenue is a natural objective and has been a subject of research over the years. In this paper, we focus on a class of markets exhibiting the substitutes property with…

This paper presents a novel adaptation of the Stochastic Gradient Descent (SGD), termed AdaBatchGrad. This modification seamlessly integrates an adaptive step size with an adjustable batch size. An increase in batch size and a decrease in…

Stochastic Gradient Descent (SGD) is a popular optimization method which has been applied to many important machine learning tasks such as Support Vector Machines and Deep Neural Networks. In order to parallelize SGD, minibatch training is…

Stochastic gradient descent (SGD) is the optimization algorithm of choice in many machine learning applications such as regularized empirical risk minimization and training deep neural networks. The classical convergence analysis of SGD is…

Dynamic resource allocation problems are ubiquitous, arising in inventory management, order fulfillment, online advertising, and other applications. We initially focus on one of the simplest models of online resource allocation: the…

The performance of mini-batch stochastic gradient descent (SGD) strongly depends on setting the batch size and learning rate to minimize the empirical loss in training the deep neural network. In this paper, we present theoretical analyses…