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We study online learning when partial feedback information is providedfollowing every action of the learning process, and the learner incursswitching costs for changing his actions. In this setting, the feedbackinformation system can be represented by a graph, and previous works studiedthe expected regret of the learner in the case of a clique (Expert setup), ordisconnected single loops (Multi-Armed Bandits (MAB)). This work provides alower bound on the expected regret in the Partial Information (PI) setting,namely for general feedback graphs --excluding the clique. Additionally, itshows that all algorithms that are optimal without switching costs arenecessarily sub-optimal in the presence of switching costs, which motivates theneed to design new algorithms. We propose two new algorithms: Threshold BasedEXP3 and EXP3. SC. For the two special cases of symmetric PI setting and MAB,the expected regret of both of these algorithms is order optimal in theduration of the learning process. Additionally, Threshold Based EXP3 is orderoptimal in the switching cost, whereas EXP3. SC is not. Finally, empiricalevaluations show that Threshold Based EXP3 outperforms the previously proposedorder-optimal algorithms EXP3 SET in the presence of switching costs, and BatchEXP3 in the MAB setting with switching costs.

Online learning with feedback graphs and switching costs