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In recent years, information relaxation and duality in dynamic programs have been studied extensively, and the resulted primal-dual approach has become a powerful procedure in solving dynamic programs by providing lower-upper bounds on the…

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…

We consider the problem of preference based reinforcement learning (PbRL), where, unlike traditional reinforcement learning, an agent receives feedback only in terms of a 1 bit (0/1) preference over a trajectory pair instead of absolute…

One of the largest drivers of social inequality is unequal access to personal tutoring, with wealthier individuals able to afford it, while the majority cannot. Affordable, effective AI tutors offer a scalable solution. We focus on adaptive…

We propose smoothed primal-dual algorithms for solving stochastic and smooth nonconvex optimization problems with linear inequality constraints. Our algorithms are single-loop and only require a single stochastic gradient based on one…

We propose a primal-dual smoothing framework for finding a near-stationary point of a class of non-smooth non-convex optimization problems with max-structure. We analyze the primal and dual gradient complexities of the framework via two…

We consider an online two-stage stochastic optimization with long-term constraints over a finite horizon of $T$ periods. At each period, we take the first-stage action, observe a model parameter realization and then take the second-stage…

We study adaptive estimation and inference in ill-posed linear inverse problems defined by conditional moment restrictions. Existing regularized estimators such as Regularized DeepIV (RDIV) require prior knowledge of the smoothness of the…

Model-free reinforcement learning methods lack an inherent mechanism to impose behavioural constraints on the trained policies. Although certain extensions exist, they remain limited to specific types of constraints, such as value…

We consider the question of how to employ next-token prediction algorithms in adversarial online decision-making environments. Specifically, if we train a next-token prediction model on a distribution $\mathcal{D}$ over sequences of…

We study the $K$-armed contextual dueling bandit problem, a sequential decision making setting in which the learner uses contextual information to make two decisions, but only observes \emph{preference-based feedback} suggesting that one…

We investigate the challenging problem of adversarial multi-armed bandits operating under time-varying constraints, a scenario motivated by numerous real-world applications. To address this complex setting, we propose a novel primal-dual…

This paper develops a distributed model predictive control (DMPC) strategy for a class of discrete-time linear systems with consideration of globally coupled constraints. The DMPC under study is based on the dual problem concerning all…

The goal of robust constrained reinforcement learning (RL) is to optimize an agent's performance under the worst-case model uncertainty while satisfying safety or resource constraints. In this paper, we demonstrate that strong duality does…

With the unprecedented growth of signal processing and machine learning application domains, there has been a tremendous expansion of interest in distributed optimization methods to cope with the underlying large-scale problems.…

This paper studies a distributed stochastic optimization problem over random networks with imperfect communications subject to a global constraint, which is the intersection of local constraint sets assigned to agents. The global cost…

A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…

To accommodate low latency and computation-intensive services, such as the Internet-of-Things (IoT), 5G networks are expected to have cloud and edge computing capabilities. To this end, we consider a generic network setup where devices,…

This paper develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This paper analyzes critical values for parameters in…

This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…