Contextual Inverse Optimization: Offline and Online Learning

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 from past periods needs make one decision, while in optimizes decisions dynamically over time based a new set feasible actions functions each period. For characterize minimax policy, establishing performance that can be achieved underlying geometry induced data. leverage this geometric characterization optimize cumulative regret. develop algorithm yields first regret bound for problem logarithmic horizon.