Regret Minimization and Job Scheduling

Regret minimization has proven to be a very powerful tool in both computational learning theory and online algorithms. Regret minimization algorithms can guarantee, for a single decision maker, a near optimal behavior under fairly adversarial assumptions. I will discuss a recent extensions of the classical regret minimization model, which enable to handle many different settings related to job scheduling, and guarantee the near optimal online behavior. 1 Regret Minimization Consider a single decision maker attempting to optimize it performance in face of an uncertain environment. This simple online setting has attracted attention from multiple disciplines, including operations research, game theory, and computer science. In computer science, computational learning theory and online algorithms both focus on this task from different perspectives. I will concentrate only on a certain facet of this general issue of decision making, and consider settings related to regret minimization, where the performance of the online decision maker is compared to a benchmark based on a class of comparison policies. Regret minimization has its roots in computational learning theory and game theory. While the motivation for the research in the two fields have been very different, the basic model that both fields has studied have been very similar. They both consider an online setting, where an agent needs to select actions, while having only information about the past performance and having no (or very limited) information regarding the future. Many natural computer science problems give rise to such online settings; typical examples include scheduling problems, paging, routing protocols, and many more. Online regret minimization learning algorithms have been introduced and studied in the computational learning community [27, 19, 2, 13, 24] and also in the game theory community [20, 17, 16, 21]. (See [11] for an excellent book on the topic.) ? This work was supported in part by the IST Programme of the European Community, under the PASCAL2 Network of Excellence, IST-2007-216886, by a grant from the Israel Science Foundation (grant No. 709/09) and grant No. 2008-321 from the United States-Israel Binational Science Foundation (BSF). This publication reflects the authors’ views only.