  We study the problem of online learning (OL) from revealed preferences: a
learner wishes to learn a non-strategic agent's private utility function
through observing the agent's utility-maximizing actions in a changing
environment. We adopt an online inverse optimization setup, where the learner
observes a stream of agent's actions in an online fashion and the learning
performance is measured by regret associated with a loss function. We first
characterize a special but broad class of agent's utility functions, then
utilize this structure in designing a new convex loss function. We establish
that the regret with respect to our new loss function also bounds the regret
with respect to all other usual loss functions in the literature. This allows
us to design a flexible OL framework that enables a unified treatment of loss
functions and supports a variety of online convex optimization algorithms. We
demonstrate with theoretical and empirical evidence that our framework based on
the new loss function (in particular online Mirror Descent) has significant
advantages in terms of regret performance and solution time over other OL
algorithms from the literature and bypasses the previous technical assumptions
as well.
