  We propose a new model for augmenting algorithms with predictions by
requiring that they are formally learnable and instance robust. Learnability
ensures that predictions can be efficiently constructed from a reasonable
amount of past data. Instance robustness ensures that the prediction is robust
to modest changes in the problem input, where the measure of the change may be
problem specific. Instance robustness insists on a smooth degradation in
performance as a function of the change. Ideally, the performance is never
worse than worst-case bounds. This also allows predictions to be objectively
compared.
  We design online algorithms with predictions for a network flow allocation
problem and restricted assignment makespan minimization. For both problems, two
key properties are established: high quality predictions can be learned from a
small sample of prior instances and these predictions are robust to errors that
smoothly degrade as the underlying problem instance changes.
