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In this paper, we address \ac{SGNEP} seeking with risk-neutral agents. Our main contribution lies the development of a stochastic variance-reduced gradient (SVRG) technique, modified to contend with general sample spaces, within a…
In this work we study the convergence of gradient methods for nonconvex optimization problems -- specifically the effect of the problem formulation to the convergence behavior of the solution of a gradient flow. We show through a simple…
This paper investigates a multidimensional non-homogeneous stochastic linear-quadratic optimal control problem featuring random coefficients and a terminal mean-field term in the cost functional, enabling its direct application to…
We consider the optimal regulation problem for nonlinear control-affine dynamical systems. Whereas the linear-quadratic regulator (LQR) considers optimal control of a linear system with quadratic cost function, we study polynomial systems…
Vector quantile regression (VQR) is an optimal transport (OT)-based framework that extends linear quantile regression to vector-valued response variables and can be formulated as an OT problem with a mean-independence constraint. In this…
This paper considers a finite-sum optimization problem under first-order queries and investigates the benefits of strategic querying on stochastic gradient-based methods compared to uniform querying strategy. We first introduce Oracle…
We consider a non-convex constrained optimization problem, where the objective function is weakly convex and the constraint function is either convex or weakly convex. To solve this problem, we consider the classical switching subgradient…
This paper considers a distributed stochastic strongly convex optimization, where agents connected over a network aim to cooperatively minimize the average of all agents' local cost functions. Due to the stochasticity of gradient estimation…
As application demands for zeroth-order (gradient-free) optimization accelerate, the need for variance reduced and faster converging approaches is also intensifying. This paper addresses these challenges by presenting: a) a comprehensive…
The Linear Quadratic Regulator (LQR) framework considers the problem of regulating a linear dynamical system perturbed by environmental noise. We compute the policy regret between three distinct control policies: i) the optimal online…
In modern decentralized applications, ensuring communication efficiency and privacy for the users are the key challenges. In order to train machine-learning models, the algorithm has to communicate to the data center and sample data for its…
Regularized empirical risk minimization problem with linear predictor appears frequently in machine learning. In this paper, we propose a new stochastic primal-dual method to solve this class of problems. Different from existing methods,…
Stochastic approximation (SA) algorithms have been widely applied in minimization problems when the loss functions and/or the gradient information are only accessible through noisy evaluations. Stochastic gradient (SG) descent---a…
We study a linear-quadratic, optimal control problem on a discrete, finite time horizon with distributional ambiguity, in which the cost is assessed via Conditional Value-at-Risk (CVaR). We take steps toward deriving a scalable dynamic…
High-dimensional stochastic optimal control (SOC) becomes harder with longer planning horizons: existing methods scale linearly in the horizon $T$, with performance often deteriorating exponentially. We overcome these limitations for a…
Model-free approaches for reinforcement learning (RL) and continuous control find policies based only on past states and rewards, without fitting a model of the system dynamics. They are appealing as they are general purpose and easy to…
We consider the problem of offline reinforcement learning (RL) -- a well-motivated setting of RL that aims at policy optimization using only historical data. Despite its wide applicability, theoretical understandings of offline RL, such as…
Unlike traditional model-based reinforcement learning approaches that estimate system parameters from data, non-model-based data-driven control learns the optimal policy directly from input-state data without any intermediate model…
This paper studies an infinite horizon optimal control problem for discrete-time linear system and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. In this general…
We study reinforcement learning (RL) for a class of continuous-time linear-quadratic (LQ) control problems for diffusions, where states are scalar-valued and running control rewards are absent but volatilities of the state processes depend…