Learning what to remember

We consider a lifelong learning scenario in which a learner faces a neverending and arbitrary stream of facts and has to decide which ones to retain in its limited memory. We introduce a mathematical model based on the online learning framework, in which the learner measures itself against a collection of experts that are also memory-constrained and that reflect different policies for what to remember. Interspersed with the stream of facts are occasional questions, and on each of these the learner incurs a loss if it has not remembered the corresponding fact. Its goal is to do almost as well as the best expert in hindsight, while using roughly the same amount of memory. We identify difficulties with using the multiplicative weights update algorithm in this memory-constrained scenario, and design an alternative scheme whose regret guarantees are close to the best possible.