相关论文: Finite-Sample Analysis of Stochastic Approximation…

This paper presents a stochastic approximation proximal subgradient (SAPS) method for stochastic convex-concave minimax optimization. By accessing unbiased and variance bounded approximate subgradients, we show that this algorithm exhibits…

Discrete stochastic optimization considers the problem of minimizing (or maximizing) loss functions defined on discrete sets, where only noisy measurements of the loss functions are available. The discrete stochastic optimization problem is…

Safe reinforcement learning (RL) aims to learn policies that satisfy certain constraints before deploying them to safety-critical applications. Previous primal-dual style approaches suffer from instability issues and lack optimality…

In this paper, we study ordinary differential equations (ODE) coupled with solutions of a stochastic nonsmooth convex optimization problem (SNCOP). We use the regularization approach, the sample average approximation and the time-stepping…

We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…

Stochastic approximation (SA) algorithms are widely used in system optimization problems when only noisy measurements of the system are available. This paper studies two types of SA algorithms in a multivariate Kiefer-Wolfowitz setting:…

We study a decentralized variant of stochastic approximation, a data-driven approach for finding the root of an operator under noisy measurements. A network of agents, each with its own operator and data observations, cooperatively find the…

We consider a class of nonconvex nonsmooth optimization problems whose objective is the sum of a smooth function and a finite number of nonnegative proper closed possibly nonsmooth functions (whose proximal mappings are easy to compute),…

We consider saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence…

This paper intends to apply the sample-average-approximation (SAA) scheme to solve a system of stochastic equations (SSE), which has many applications in a variety of fields. The SAA is an effective paradigm to address risks and uncertainty…

This paper presents the first sufficient conditions that guarantee the stability and almost sure convergence of multi-timescale stochastic approximation (SA) iterates. It extends the existing results on one-timescale and two-timescale SA…

Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…

Most existing approximate Thompson Sampling (TS) algorithms for multi-armed bandits use Stochastic Gradient Langevin Dynamics (SGLD) or its variants in each round to sample from the posterior, relaxing the need for conjugacy assumptions…

In this paper, we investigate an optimal control problem with terminal stochastic linear complementarity constraints (SLCC), and its discrete approximation using the relaxation, the sample average approximation (SAA) and the implicit Euler…

Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…

In this paper, we examine the Sample Average Approximation (SAA) procedure within a framework where the Monte Carlo estimator of the expectation is biased. We also introduce Multilevel Monte Carlo (MLMC) in the SAA setup to enhance the…

We study the safe reinforcement learning problem with nonlinear function approximation, where policy optimization is formulated as a constrained optimization problem with both the objective and the constraint being nonconvex functions. For…

We apply the sample average approximation (SAA) method to risk-neutral optimization problems governed by nonlinear partial differential equations (PDEs) with random inputs. We analyze the consistency of the SAA optimal values and SAA…

Stochastic Approximation (SA) is a widely used algorithmic approach in various fields, including optimization and reinforcement learning (RL). Among RL algorithms, Q-learning is particularly popular due to its empirical success. In this…

Asynchronous stochastic approximations (SAs) are an important class of model-free algorithms, tools and techniques that are popular in multi-agent and distributed control scenarios. To counter Bellman's curse of dimensionality, such…