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This paper explores the problem of path planning under uncertainty. Specifically, we consider online receding horizon based planners that need to operate in a latent environment where the latent information can be modeled via Gaussian…

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…

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…

This work theoretically studies a ubiquitous reinforcement learning policy for controlling the canonical model of continuous-time stochastic linear-quadratic systems. We show that randomized certainty equivalent policy addresses the…

Various ways for decision making with imprecise probabilities (admissibility, maximal expected utility, maximality, E-admissibility, $\Gamma$-maximax, $\Gamma$-maximin, all of which are well-known from the literature) are discussed and…

In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…

We consider the problem of online learning where the sequence of actions played by the learner must adhere to an unknown safety constraint at every round. The goal is to minimize regret with respect to the best safe action in hindsight…

Many prediction tasks can admit multiple models that can perform almost equally well. This phenomenon can can undermine interpretability and safety when competing models assign conflicting predictions to individuals. In this work, we study…

Performance of adaptive control policies is assessed through the regret with respect to the optimal regulator, which reflects the increase in the operating cost due to uncertainty about the dynamics parameters. However, available results in…

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…

This paper proposes a theoretical analysis of recommendation systems in an online setting, where items are sequentially recommended to users over time. In each round, a user, randomly picked from a population of $m$ users, requests a…

Dealing with uncertainty in optimization parameters is an important and longstanding challenge. Typically, uncertain parameters are predicted accurately, and then a deterministic optimization problem is solved. However, the decisions…

In online convex optimization, the player aims to minimize regret, or the difference between her loss and that of the best fixed decision in hindsight over the entire repeated game. Algorithms that minimize (standard) regret may converge to…

In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the…

Techniques for decision making with knowledge of linear constraints on condition probabilities are examined. These constraints arise naturally in many situations: upper and lower condition probabilities are known; an ordering among the…

Policy learning algorithms are widely used in areas such as personalized medicine and advertising to develop individualized treatment regimes. However, most methods force a decision even when predictions are uncertain, which is risky in…

The setting of an agent making decisions under uncertainty and under dynamic constraints is common for the fields of optimal control, reinforcement learning, and recently also for online learning. In the online learning setting, the quality…

We study the prediction with expert advice setting, where the aim is to produce a decision by combining the decisions generated by a set of experts, e.g., independently running algorithms. We achieve the min-max optimal dynamic regret under…

This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…

In many sequential decision problems, an agent performs a repeated task. He then suffers regret and obtains information that he may use in the following rounds. However, sometimes the agent may also obtain information and avoid suffering…