The Hedge Algorithm on a Continuum
published: Dec. 5, 2015, recorded: October 2015, views: 1658
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
We consider an online optimization problem on a subset S of Rn (not necessarily convex), in which a decision maker chooses, at each iteration t, a probability distribution x(t) over S, and seeks to minimize a cumulative expected loss, where each loss is a Lipschitz function revealed at the end of iteration t. Building on previous work, we propose a generalized Hedge algorithm and show a O(tlogt−−−−−√) bound on the regret when the losses are uniformly Lipschitz and S is uniformly fat (a weaker condition than convexity). Finally, we propose a generalization to the dual averaging method on the set of Lebesgue-continuous distributions over S.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !