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.

翻译：我们提出了一种处理漂移博弈的新方法，该类二人博弈在提升算法和在线学习场景中具有广泛应用。本方法包含两个步骤：(a) 通过求解关联偏微分方程（PDE）推测渐近最优势；接着 (b) 通过证明最终时刻损失的上界与下界之差随时间步数负幂次增长的关系来验证该猜想。基于势的上界证明仅需泰勒展开等初等数学工具，而基于势的下界证明同样简洁，仅需结合泰勒展开与概率或组合论证。本方法不仅更为初等，而且我们给出了新的势函数，并推导出在渐近条件下相互匹配的对应上界与下界。