  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.
