A Drifting-Games Analysis for Online Learning and Applications to Boosting
This work provides a unified framework for online learning that addresses efficiency and generalization issues, though it is incremental as it builds on existing minimax and drifting-games concepts.
The authors tackled the problem of designing online learning algorithms by introducing a drifting-games framework that generalizes minimax analysis, resulting in new parameter-free algorithms with improved computational efficiency in boosting applications.
We provide a general mechanism to design online learning algorithms based on a minimax analysis within a drifting-games framework. Different online learning settings (Hedge, multi-armed bandit problems and online convex optimization) are studied by converting into various kinds of drifting games. The original minimax analysis for drifting games is then used and generalized by applying a series of relaxations, starting from choosing a convex surrogate of the 0-1 loss function. With different choices of surrogates, we not only recover existing algorithms, but also propose new algorithms that are totally parameter-free and enjoy other useful properties. Moreover, our drifting-games framework naturally allows us to study high probability bounds without resorting to any concentration results, and also a generalized notion of regret that measures how good the algorithm is compared to all but the top small fraction of candidates. Finally, we translate our new Hedge algorithm into a new adaptive boosting algorithm that is computationally faster as shown in experiments, since it ignores a large number of examples on each round.