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We study Constrained Online Convex Optimization with Memory (COCO-M), where both the loss and the constraints depend on a finite window of past decisions made by the learner. This setting extends the previously studied unconstrained online…
This paper focuses on adaptive control of the discrete-time linear quadratic regulator (adaptive LQR). Recent literature has made significant contributions in proving non-asymptotic convergence rates, but existing approaches have a few…
This article develops a control method for linear time-invariant systems subject to time-varying and a priori unknown cost functions, that satisfies state and input constraints, and is robust to exogenous disturbances. To this end, we…
Online learning aims to perform nearly as well as the best hypothesis in hindsight. For some hypothesis classes, though, even finding the best hypothesis offline is challenging. In such offline cases, local search techniques are often…
We propose a data-driven online convex optimization algorithm for controlling dynamical systems. In particular, the control scheme makes use of an initially measured input-output trajectory and behavioral systems theory which enable it to…
We consider the problem of online adaptive control of the linear quadratic regulator, where the true system parameters are unknown. We prove new upper and lower bounds demonstrating that the optimal regret scales as…
Predicting the output of a dynamical system from streaming data is fundamental to real-time feedback control and decision-making. We first derive an autoregressive representation that relates future local outputs to asynchronous past…
This paper considers the problem of online trajectory design under time-varying environments. We formulate the general trajectory optimization problem within the framework of time-varying constrained convex optimization and proposed a novel…
We study the problem of controlling a linear dynamical system with adversarial perturbations where the only feedback available to the controller is the scalar loss, and the loss function itself is unknown. For this problem, with either a…
This paper considers the stability of online learning algorithms and its implications for learnability (bounded regret). We introduce a novel quantity called {\em forward regret} that intuitively measures how good an online learning…
Online learning has traditionally focused on the expected rewards. In this paper, a risk-averse online learning problem under the performance measure of the mean-variance of the rewards is studied. Both the bandit and full information…
We study the problem of non-stationary dueling bandits and provide the first adaptive dynamic regret algorithm for this problem. The only two existing attempts in this line of work fall short across multiple dimensions, including…
This paper considers distributed online nonconvex optimization with time-varying inequality constraints over a network of agents, where the nonconvex local loss and convex local constraint functions can vary arbitrarily across iterations.…
Non-stationary online learning has drawn much attention in recent years. Despite considerable progress, dynamic regret minimization has primarily focused on convex functions, leaving the functions with stronger curvature (e.g., squared or…
We study online decision making problems under resource constraints, where both reward and cost functions are drawn from distributions that may change adversarially over time. We focus on two canonical settings: $(i)$ online resource…
Stochastic and adversarial data are two widely studied settings in online learning. But many optimization tasks are neither i.i.d. nor fully adversarial, which makes it of fundamental interest to get a better theoretical understanding of…
We study online learning problems in which a decision maker has to take a sequence of decisions subject to $m$ long-term constraints. The goal of the decision maker is to maximize their total reward, while at the same time achieving small…
This paper addresses safe distributed online optimization over an unknown set of linear safety constraints. A network of agents aims at jointly minimizing a global, time-varying function, which is only partially observable to each…
We consider control of uncertain linear time-varying stochastic systems from the perspective of regret minimization. Specifically, we focus on the problem of designing a feedback controller that minimizes the loss relative to a clairvoyant…
We consider the problem of controlling an unknown linear dynamical system under a stochastic convex cost and full feedback of both the state and cost function. We present a computationally efficient algorithm that attains an optimal…