A New Approach to Drifting Games, Based on Asymptotically Optimal Potentials
This provides a more elementary method for analyzing drifting games, which are important for boosting and online learning, but it appears incremental as it builds on existing frameworks with new potentials and proofs.
The paper tackles the problem of drifting games by developing a new approach that uses asymptotically optimal potentials derived from solving a PDE, resulting in upper and lower bounds on the final-time loss that match asymptotically with differences scaling as a negative power of the number of time steps.
We develop a new approach to drifting games, a class of two-person games with many applications to boosting and online learning settings. Our approach involves (a) guessing an asymptotically optimal potential by solving an associated partial differential equation (PDE); then (b) justifying the guess, by proving upper and lower bounds on the final-time loss whose difference scales like a negative power of the number of time steps. The proofs of our potential-based upper bounds are elementary, using little more than Taylor expansion. The proofs of our potential-based lower bounds are also elementary, combining Taylor expansion with probabilistic or combinatorial arguments. Not only is our approach more elementary, but we give new potentials and derive corresponding upper and lower bounds that match each other in the asymptotic regime.