A continuous-time approach to online optimization

Panayotis Mertikopoulos, Joon Kwon
2017 Journal of Dynamics & Games  
We consider a family of learning strategies for online optimization problems that evolve in continuous time and we show that they lead to no regret. From a more traditional, discrete-time viewpoint, this continuous-time approach allows us to derive the no-regret properties of a large class of discretetime algorithms including as special cases the exponential weight algorithm, online mirror descent, smooth fictitious play and vanishingly smooth fictitious play. In so doing, we obtain a unified
more » ... obtain a unified view of many classical regret bounds, and we show that they can be decomposed into a term stemming from continuoustime considerations and a term which measures the disparity between discrete and continuous time. As a result, we obtain a general class of infinite horizon learning strategies that guarantee an O(n −1/2 ) regret bound without having to resort to a doubling trick.
doi:10.3934/jdg.2017008 fatcat:kqyfekfxgndcxfbt7ve3lq7lgm