2016/02/17 by Rodolphe Jenatton, Jim Huang, Jenatton, Rodolphe +7 · 1 citation
Business, Management and Accounting · Computer Science · Decision Sciences · Mathematics · #Advanced Bandit Algorithms Research #Consumer Market Behavior and Pricing #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Optimization and Search Problems #Risk and Portfolio Optimization #Statistics Theory (math.ST) #cs.LG #math.OC #math.ST #stat.ML #stat.TH
paper · pdf · doi:10.48550/arxiv.1602.05394
openalex publication_date 2016/02/17 · arxiv created 2016/06/08 · arxiv updated 2016/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. We conduct experiments on synthetic data to illustrate the benefits of the non-additive penalty and show vanishing regret convergence on live traffic data collected by a display advertising platform in production.