Related papers: Multi Timescale Stochastic Approximation: Stabilit…
Adaptive gradient optimizers (AdaGrad), which dynamically adjust the learning rate based on iterative gradients, have emerged as powerful tools in deep learning. These adaptive methods have significantly succeeded in various deep learning…
Based on the stochastic maximum principle for the partially coupled forward-backward stochastic control system (FBSCS for short), a modified method of successive approximations (MSA for short) is established for stochastic recursive optimal…
This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel…
We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines…
We consider a general asynchronous Stochastic Approximation (SA) scheme featuring a weighted infinity-norm contractive operator, and prove a bound on its finite-time convergence rate on a single trajectory. Additionally, we specialize the…
Stochastic gradient descent is the method of choice for large scale optimization of machine learning objective functions. Yet, its performance is greatly variable and heavily depends on the choice of the stepsizes. This has motivated a…
The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly…
We study stochastic approximation procedures for approximately solving a $d$-dimensional linear fixed point equation based on observing a trajectory of length $n$ from an ergodic Markov chain. We first exhibit a non-asymptotic bound of the…
Machine learning has made tremendous progress in recent years, with models matching or even surpassing humans on a series of specialized tasks. One key element behind the progress of machine learning in recent years has been the ability to…
This paper focuses on stochastic partial differential equations (SPDEs) under two-time-scale formulation. Distinct from the work in the existing literature, the systems are driven by $\alpha$-stable processes with $\alpha \in(1,2)$. In…
We study the unconstrained and the minimax saddle point variants of the convex multi-stage stochastic programming problem, where consecutive decisions are coupled through the objective functions, rather than through the constraints. We…
This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group \mathbb{SO}\left(3\right) with the tracking error of the normalized Euclidean distance meeting predefined transient and…
Based on SGD, previous works have proposed many algorithms that have improved convergence speed and generalization in stochastic optimization, such as SGDm, AdaGrad, Adam, etc. However, their convergence analysis under non-convex conditions…
In this paper we develop a stochastic heavy ball method for solving ill-posed inverse problems. The method updates the iterate using only a randomly selected equation at each iteration step while incorporating a momentum term into the…
Adaptive gradient methods have attracted much attention of machine learning communities due to the high efficiency. However their acceleration effect in practice, especially in neural network training, is hard to analyze, theoretically. The…
Large-scale optimization problems require algorithms both effective and efficient. One such popular and proven algorithm is Stochastic Gradient Descent which uses first-order gradient information to solve these problems. This paper studies…
This paper establishes the first almost sure convergence rate and the first maximal concentration bound with exponential tails for general contractive stochastic approximation algorithms with Markovian noise. As a corollary, we also obtain…
We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…
Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…
We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…