Move from Perturbed scheme to exponential weighting average

TL;DR

This paper explores the relationship between exponential weighting and follow-the-perturbed-leader algorithms in online decision problems, showing their equivalence under certain conditions and extending their applicability to complex structured problems.

Contribution

It demonstrates the shared properties of the two algorithms, establishes their equivalence for specific perturbations, and extends the algorithms to structured online problems.

Findings

Exponential weighting and follow-the-perturbed-leader share common properties.

Under specific perturbations, the two algorithms are identical.

Follow-the-leader algorithms can be extended to structured problems where exponential algorithms are inefficient.

Abstract

In an online decision problem, one makes decisions often with a pool of decision sequence called experts but without knowledge of the future. After each step, one pays a cost based on the decision and observed rate. One reasonal goal would be to perform as well as the best expert in the pool. The modern and well-known way to attain this goal is the algorithm of exponential weighting. However, recently, another algorithm called follow the perturbed leader is developed and achieved about the same performance. In our work, we first show the properties shared in common by the two algorithms which explain the similarities on the performance. Next we will show that for a specific perturbation, the two algorithms are identical. Finally, we show with some examples that follow-the-leader style algorithms extend naturally to a large class of structured online problems for which the exponential algorithms are inefficient.