Online optimization and regret guarantees for non-additive long-term constraints

Understand

We consider online optimization in the 1-lookahead setting, where the objective does not decompose additively over the rounds of the online game.

• The resulting formulation enables us to deal with non-stationary and/or long-term constraints , which arise, for example, in online display advertising problems.
• We propose an on-line primal-dual algorithm for which we obtain dynamic cumulative regret guarantees.
• They depend on the convexity and the smoothness of the non-additive penalty, as well as terms capturing the smoothness with which the residuals of the non-stationary and long-term constraints vary over the rounds.