We consider the non-stochastic Multi-Armed Bandit problem in a setting where there is a fixed and known metric on the action space that determines a cost for switching between any pair of actions. The loss of the online learner has two components: the first is the usual loss of the selected actions, and the second is an additional loss due to switching between actions. Our main contribution giv...

We consider a sequential treatment problem with covariates. Given realization of the covariate vector, instead targeting highest conditional expectation, decision-maker targets which maximizes general functional potential outcome distribution, e.g., quantile, trimmed mean, or socioeconomic such as an inequality, welfare, poverty measure. develop expected regret lower bounds for this and constru...

First, we study online learning with an extended notion of regret, which is defined with respect to a set of strategies. We develop tools for analyzing the minimax rates and deriving efficient learning algorithms in this scenario. While the standard methods for minimizing the usual notion of regret fail, through our analysis we demonstrate the existence of regret-minimization methods that compe...

A major challenge to develop optimal strategies for allocation of flexible demand toward the smart grid paradigm is uncertainty associated with real-time price and electricity demand. This article presents a regret-based model novel iterative algorithm which solves minimax regret optimization problem. algorithms exhibits low computational burden compared traditional linear programming methods a...