Prediction with Expert Advice by Following the Perturbed Leader for General Weights

Title: Prediction with Expert Advice by Following the Perturbed Leader for General Weights

Abstract: This research article explores the concept of Prediction with Expert Advice (PEA) using the Follow the Perturbed Leader (FPL) algorithm. The study focuses on the adaptive learning rate and its application to countable expert classes with arbitrary weights. The analysis of the FPL algorithm is easier compared to other PEA algorithms, making it a promising approach for general weight scenarios. The research provides loss bounds for adaptive learning rate and both finite expert classes with uniform weights and countable expert classes with arbitrary weights. The results are significant as they extend the bounds for WM algorithms and apply to a wider range of predictors.

Main Research Question: How can the Follow the Perturbed Leader (FPL) algorithm be used to improve the performance of Prediction with Expert Advice (PEA) for countable expert classes with arbitrary weights using an adaptive learning rate?

Methodology: The study employs the FPL algorithm, which is based on Hannan's algorithm. The methodology involves analyzing the FPL algorithm for PEA and deriving loss bounds for adaptive learning rate. The analysis is conducted for both finite expert classes with uniform weights and countable expert classes with arbitrary weights.

Results: The research provides loss bounds for adaptive learning rate and both finite expert classes with uniform weights and countable expert classes with arbitrary weights. The results are significant as they extend the bounds for WM algorithms and apply to a wider range of predictors.

Implications: The findings of this research have several implications. First, the FPL algorithm provides a simpler and more elegant approach to PEA compared to other WM algorithms. Second, the adaptive learning rate used in the study allows for better performance in a wider range of scenarios. Lastly, the research extends the applicability of PEA to countable expert classes with arbitrary weights, which was not possible with previous WM algorithms.

Conclusion: In conclusion, the research demonstrates that the Follow the Perturbed Leader (FPL) algorithm can be used to improve the performance of Prediction with Expert Advice (PEA) for countable expert classes with arbitrary weights using an adaptive learning rate. The study provides loss bounds for adaptive learning rate and both finite expert classes with uniform weights and countable expert classes with arbitrary weights, which are significant contributions to the field.

Link to Article: https://arxiv.org/abs/0405043v2 Authors: arXiv ID: 0405043v2