Online learning with feedback graphs and switching costs

TL;DR

This paper investigates online learning with feedback graphs and switching costs, establishing regret lower bounds, highlighting the limitations of existing algorithms, and proposing new algorithms that are order optimal in various settings.

Contribution

It provides the first lower bounds for general feedback graphs with switching costs and introduces two new algorithms, Threshold Based EXP3 and EXP3. SC, that are order optimal in key scenarios.

Findings

Threshold Based EXP3 outperforms previous algorithms with switching costs.

Both proposed algorithms are order optimal in symmetric PI and MAB settings.

Threshold Based EXP3 is order optimal in switching costs.

Abstract

We study online learning when partial feedback information is provided following every action of the learning process, and the learner incurs switching costs for changing his actions. In this setting, the feedback information system can be represented by a graph, and previous works studied the expected regret of the learner in the case of a clique (Expert setup), or disconnected single loops (Multi-Armed Bandits (MAB)). This work provides a lower bound on the expected regret in the Partial Information (PI) setting, namely for general feedback graphs --excluding the clique. Additionally, it shows that all algorithms that are optimal without switching costs are necessarily sub-optimal in the presence of switching costs, which motivates the need to design new algorithms. We propose two new algorithms: Threshold Based EXP3 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 the duration of the learning process. Additionally, Threshold Based EXP3 is order optimal in the switching cost, whereas EXP3. SC is not. Finally, empirical evaluations show that Threshold Based EXP3 outperforms the previously proposed order-optimal algorithms EXP3 SET in the presence of switching costs, and Batch EXP3 in the MAB setting with switching costs.