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We consider a stochastic system whose uncontrolled state dynamics are modelled by a general one-dimensional It\^{o} diffusion. The control effort that can be applied to this system takes the form that is associated with the so-called…
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…
In contrast to the classic formulation of partial monitoring, linear partial monitoring can model infinite outcome spaces, while imposing a linear structure on both the losses and the observations. This setting can be viewed as a…
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…
This paper considers the distributed bandit convex optimization problem with time-varying constraints. In this problem, the global loss function is the average of all the local convex loss functions, which are unknown beforehand. Each agent…
We study predictive control in a setting where the dynamics are time-varying and linear, and the costs are time-varying and well-conditioned. At each time step, the controller receives the exact predictions of costs, dynamics, and…
In this paper, we consider a class of stochastic optimal control problems with risk constraints that are expressed as bounded probabilities of failure for particular initial states. We present here a martingale approach that diffuses a risk…
We present an optimal control-based strategy to enhance the estimation of impulse-like disturbances in continuously monitored linear classical and quantum systems by exploiting non-equilibrium states. Using optimal estimation techniques for…
We study the control of an \emph{unknown} linear dynamical system under general convex costs. The objective is minimizing regret vs. the class of disturbance-feedback-controllers, which encompasses all stabilizing…
We study the non-stationary stochastic multiarmed bandit (MAB) problem and propose two generic algorithms, namely, the limited memory deterministic sequencing of exploration and exploitation (LM-DSEE) and the Sliding-Window Upper Confidence…
Stochastic Model Predictive Control addresses uncertainties by incorporating chance constraints that provide probabilistic guarantees of constraint satisfaction. However, simultaneously optimizing over the risk allocation and the feedback…
We study the non-stationary stochastic multi-armed bandit problem, where the reward statistics of each arm may change several times during the course of learning. The performance of a learning algorithm is evaluated in terms of their…
We provide consistent random algorithms for sequential decision under partial monitoring, i.e. when the decision maker does not observe the outcomes but receives instead random feedback signals. Those algorithms have no internal regret in…
This paper investigates the problem of impact-time-control and proposes a learning-based computational guidance algorithm to solve this problem. The proposed guidance algorithm is developed based on a general prediction-correction concept:…
Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper we consider a class of infinite time-horizon singular stochastic control problems for…
Multi-armed bandit problems are the most basic examples of sequential decision problems with an exploration-exploitation trade-off. This is the balance between staying with the option that gave highest payoffs in the past and exploring new…
Reliable optimal control is challenging when the dynamics of a nonlinear system are unknown and only infrequent, noisy output measurements are available. This work addresses this setting of limited sensing by formulating a Bayesian prior…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
Dual control explicitly addresses the problem of trading off active exploration and exploitation in the optimal control of partially unknown systems. While the problem can be cast in the framework of stochastic dynamic programming, exact…
We study the problem of determining an effective exploration strategy in static and non-linear optimization problems, which depend on an unknown scalar parameter to be learned from online collected noisy data. An optimal trade-off between…