Second-order quantile bounds in online learning

These notes reflect the contents of the oral presentation of the paper Koolen and van Erven (2015) given in the journal club. After introducing the Hedge setting and providing some context, including a minimax regret bound, we discuss two kinds of adaptivity to “easy” data: second-order bounds and quantile bounds. We then describe the Squint algorithm proposed by Koolen and van Erven (2015) and show how this strategy can combine those two kinds of adaptivity (something that previous methods could not achieve), while at the same time leading to an efficiently implementable closed-form algorithm.