  In this paper, we initiate the study of the weighted paging problem with
predictions. This continues the recent line of work in online algorithms with
predictions, particularly that of Lykouris and Vassilvitski (ICML 2018) and
Rohatgi (SODA 2020) on unweighted paging with predictions. We show that unlike
unweighted paging, neither a fixed lookahead nor knowledge of the next request
for every page is sufficient information for an algorithm to overcome existing
lower bounds in weighted paging. However, a combination of the two, which we
call the strong per request prediction (SPRP) model, suffices to give a
2-competitive algorithm. We also explore the question of gracefully degrading
algorithms with increasing prediction error, and give both upper and lower
bounds for a set of natural measures of prediction error.
