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We study online control of time-varying linear systems with unknown dynamics in the nonstochastic control model. At a high level, we demonstrate that this setting is \emph{qualitatively harder} than that of either unknown time-invariant or…
The ability to achieve precise and smooth trajectory tracking is crucial for ensuring the successful execution of various tasks involving robotic manipulators. State-of-the-art techniques require accurate mathematical models of the robot…
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…
The parameters for a Markov Decision Process (MDP) often cannot be specified exactly. Uncertain MDPs (UMDPs) capture this model ambiguity by defining sets which the parameters belong to. Minimax regret has been proposed as an objective for…
In an optimal control strategy, an important point is to define the cost of the control. Usually it is added to the control criterion and multiplied by a small coefficient denoted by $\varepsilon$ which is known as the marginal cost of the…
A fundamental problem in control is to learn a model of a system from observations that is useful for controller synthesis. To provide good performance guarantees, existing methods must assume that the real system is in the class of models…
This paper considers an ergodic version of the bounded velocity follower problem, assuming that the decision maker lacks knowledge of the underlying system parameters and must learn them while simultaneously controlling. We propose…
Feedback is a most important concept in control systems, its main purpose is to deal with internal and/or external uncertainties in dynamical systems, by using the on-line observed information. Thus, a fundamental problem in control theory…
In this paper, we consider the multi-armed bandit problem with high-dimensional features. First, we prove a minimax lower bound, $\mathcal{O}\big((\log d)^{\frac{\alpha+1}{2}}T^{\frac{1-\alpha}{2}}+\log T\big)$, for the cumulative regret,…
We propose an online learning algorithm that adaptively designs a decentralized linear quadratic regulator when the system model is unknown a priori and new data samples from a single system trajectory become progressively available. The…
We consider the problem of nonstochastic control with a sequence of quadratic losses, i.e., LQR control. We provide an efficient online algorithm that achieves an optimal dynamic (policy) regret of $\tilde{O}(\text{max}\{n^{1/3}…
We consider measurement-feedback control in linear dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing an online controller which competes with the optimal…
Policy learning in modern operations environments faces a fundamental tension between limited operational data and the large, often continuous, state and action spaces over which good decisions must be identified and deployed. We study…
This paper studies distributionally robust regret-optimal (DRRO) control with purified output feedback for linear systems subject to additive disturbances and measurement noise. These uncertainties (including the initial system state) are…
We introduce a new algorithm for online linear-quadratic control in a known system subject to adversarial disturbances. Existing regret bounds for this setting scale as $\sqrt{T}$ unless strong stochastic assumptions are imposed on the…
This paper investigates the problem of non-stationary linear bandits, where the unknown regression parameter is evolving over time. Existing studies develop various algorithms and show that they enjoy an…
Some of the most compelling applications of online convex optimization, including online prediction and classification, are unconstrained: the natural feasible set is R^n. Existing algorithms fail to achieve sub-linear regret in this…
We revisit the classic regret-minimization problem in the stochastic multi-armed bandit setting when the arm-distributions are allowed to be heavy-tailed. Regret minimization has been well studied in simpler settings of either bounded…
We consider a stochastic bandit problem with infinitely many arms. In this setting, the learner has no chance of trying all the arms even once and has to dedicate its limited number of samples only to a certain number of arms. All previous…
We consider an LQR optimal control problem with partially unknown dynamics. We propose a new model-based online algorithm to obtain an approximation of the dynamics $and$ the control at the same time during a single simulation.