  A framework is introduced for solving a sequence of slowly changing
optimization problems, including those arising in regression and classification
applications, using optimization algorithms such as stochastic gradient descent
(SGD). The optimization problems change slowly in the sense that the minimizers
change at either a fixed or bounded rate. A method based on estimates of the
change in the minimizers and properties of the optimization algorithm is
introduced for adaptively selecting the number of samples needed from the
distributions underlying each problem in order to ensure that the excess risk,
i.e., the expected gap between the loss achieved by the approximate minimizer
produced by the optimization algorithm and the exact minimizer, does not exceed
a target level. Experiments with synthetic and real data are used to confirm
that this approach performs well.
