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This paper studies the control of safety-critical dynamical systems in the presence of adversarial disturbances. We seek to synthesize state-feedback controllers to minimize a cost incurred due to the disturbance, while respecting a safety…
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…
We study the control of finite-state systems driven by exogenous disturbances, and design causal policies that track the performance of a lookahead benchmark controller. This objective is formalized through dynamic regret, so that favorable…
We consider the task of learning to control a linear dynamical system under fixed quadratic costs, known as the Linear Quadratic Regulator (LQR) problem. While model-free approaches are often favorable in practice, thus far only model-based…
This paper addresses an online convex optimization problem where the cost function at each step depends on a history of past decisions (i.e., memory), and the decision maker has access to limited predictions of future cost values within a…
Projection-free online learning has drawn increasing interest due to its efficiency in solving high-dimensional problems with complicated constraints. However, most existing projection-free online methods focus on minimizing the static…
This paper presents a synthesis method for the generalised dynamic regret problem, comparing the performance of a strictly causal controller to the optimal non-causal controller under a weighted disturbance. This framework encompasses both…
Recently, adaptive control systems with relaxed persistent excitation (PE) conditions have been proposed to guarantee true parameter convergence and improve the transient response. However, in some cases, sufficient control performance and…
We consider an agent interacting with an environment in a single stream of actions, observations, and rewards, with no reset. This process is not assumed to be a Markov Decision Process (MDP). Rather, the agent has several representations…
This paper proposes a robust regret control framework in which the performance baseline adapts to the realization of system uncertainty. The plant is modeled as a discrete-time, uncertain linear time-invariant system with real-parametric…
We study online inverse linear optimization, also known as contextual recommendation, where a learner sequentially infers an agent's hidden objective vector from observed optimal actions over feasible sets that change over time. The learner…
This paper considers online convex optimization with long term constraints, where constraints can be violated in intermediate rounds, but need to be satisfied in the long run. The cumulative constraint violation is used as the metric to…
We consider the problem of adaptive Model Predictive Control (MPC) for uncertain linear-systems with additive disturbances and with state and input constraints. We present STT-MPC (Self-Tuning Tube-based Model Predictive Control), an online…
We study the problem of dynamic regret minimization in online convex optimization, in which the objective is to minimize the difference between the cumulative loss of an algorithm and that of an arbitrary sequence of comparators. While the…
We investigate online convex optimization in non-stationary environments and choose dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
For linear systems, many data-driven control methods rely on the behavioral framework, using historical data of the system to predict the future trajectories. However, measurement noise introduces errors in predictions. When the noise is…
Real world evolves in continuous time but computations are done from finite samples. Therefore, we study algorithms using finite observations in continuous-time linear dynamical systems. We first study the system identification problem, and…
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…
We study the problem of controlling linear time-invariant systems with known noisy dynamics and adversarially chosen quadratic losses. We present the first efficient online learning algorithms in this setting that guarantee $O(\sqrt{T})$…
This paper presents a synthesis method for robust, regret optimal control. The plant is modeled in discrete-time by an uncertain linear time-invariant (LTI) system. An optimal non-causal controller is constructed using the nominal plant…