  Given any algorithm for convex optimization that uses exact first-order
information (i.e., function values and subgradients), we show how to use such
an algorithm to solve the problem with access to inexact first-order
information. This is done in a ``black-box'' manner without knowledge of the
internal workings of the algorithm. This complements previous work that
considers the performance of specific algorithms like (accelerated) gradient
descent with inexact information. In particular, our results apply to a wider
range of algorithms beyond variants of gradient descent, e.g., projection-free
methods, cutting-plane methods, or any other first-order methods formulated in
the future. Further, they also apply to algorithms that handle structured
nonconvexities like mixed-integer decision variables.
