We propose a new clustering approach, called optimality-based clustering, that clusters data points based on their latent decision-making preferences. assume each point is decision generated by decision-maker who (approximately) solves an optimization problem and cluster the identifying common objective function of problems for such worst-case optimality error minimized. three different models ...

Classical combinatorial optimization concerns finding a feasible subset of ground set in order to optimize an objective function. We address this article the inverse problem with k-max In other words, we attempt perturb weights elements at minimum total cost make predetermined optimal fashion respect perturbed weights. first show that is general NP-hard. Regarding case independent subsets, O(n2...

We present a learning method to learn the mapping from an input space action space, which is particularly suitable when optimal decision with respect certain unknown cost function. use inverse optimization approach retrieve function by introducing new loss and hypothesis class of mappings. A tractable convex reformulation problem also presented. The effective for input-action in continuous inpu...

PURPOSE To introduce the concept of dose-mass-based inverse optimization for radiotherapy applications. MATERIALS AND METHODS Mathematical derivation of the dose-mass-based formalism is presented. This mathematical representation is compared to the most commonly used dose-volume-based formulation used in inverse optimization. A simple example on digitally created phantom is presented. The pha...

We study the problems of offline and online contextual optimization with feedback information, where instead observing loss, we observe, after-the-fact, optimal action an oracle full knowledge objective function would have taken. aim to minimize regret, which is defined as difference between our losses ones incurred by all-knowing oracle. In setting, decision-maker has information available fro...