  Robust optimization (RO) has emerged as one of the leading paradigms to
efficiently model parameter uncertainty. The recent connections between RO and
problems in statistics and machine learning domains demand for solving RO
problems in ever more larger scale. However, the traditional approaches for
solving RO formulations based on building and solving robust counterparts or
the iterative approaches utilizing nominal feasibility oracles can be
prohibitively expensive and thus significantly hinder the scalability of RO
paradigm. In this paper, we present a general and flexible iterative framework
to approximately solve robust convex optimization problems that is built on a
fully online first-order paradigm. In comparison to the existing literature, a
key distinguishing feature of our approach is that it only requires access to
first-order oracles that are remarkably cheaper than pessimization or nominal
feasibility oracles, while maintaining the same convergence rates. This, in
particular, makes our approach much more scalable and hence preferable in
large-scale applications, specifically those from machine learning and
statistics domains. We also provide new interpretations of existing iterative
approaches in our framework and illustrate our framework on robust quadratic
programming.
