In this paper we study online caching problems where predictions of future requests, e.g., provided by a machine learning model, are available. We consider different optimistic caching policies which are based on the Follow-The-Regularized-Leader algorithm and enjoy strong theoretical guarantees in terms of regret. These new policies have a higher computational cost than classic ones like LRU, LFU, as each update of the cache state requires to solve a constrained optimization problem. We study then their performance when the cache is updated less frequently in order to amortize the update cost over time or over multiple requests.