Lemma A.2. Algorithm ϕ gives a lower bound on the query γ . That is, ϕ (x, R) γ (x, R).

We show that any (possibly non-private) learning rule can be effectively transformed to a private learning rule with only a polynomial overhead in the mistake bound.

Nonetheless, modern machine learning is adaptive in its nature. Prior information about a model's performance on the test set inevitably influences

This gave birth to learning-augmented algorithms, which use these predictions to go beyond the standard long-standing worst-case limitations. The design of such algorithms requires establishing good tradeoffs between consistency and robustness, i.e. having improved performance when the predictions are accurate, and not behaving poorly