# Adaptive Hedging under Delayed Feedback

## TL;DR

This paper introduces a new adaptive hedging algorithm for online expert weight allocation that effectively handles delayed feedback, extending classical algorithms and providing theoretical regret bounds in adversarial settings.

## Contribution

We develop the General Hedging algorithm $$ based on exponential reweighing, extending classical Hedge and Fixed Share algorithms to delayed feedback scenarios.

## Key findings

- The algorithm $$ achieves adversarial loss bounds under delay.
- It extends classical Hedge and Fixed Share algorithms to delayed feedback.
- Provides regret bounds for both countable and continuous expert sets.

## Abstract

The article is devoted to investigating the application of hedging strategies to online expert weight allocation under delayed feedback. As the main result, we develop the General Hedging algorithm $\mathcal{G}$ based on the exponential reweighing of experts' losses. We build the artificial probabilistic framework and use it to prove the adversarial loss bounds for the algorithm $\mathcal{G}$ in the delayed feedback setting. The designed algorithm $\mathcal{G}$ can be applied to both countable and continuous sets of experts. We also show how algorithm $\mathcal{G}$ extends classical Hedge (Multiplicative Weights) and adaptive Fixed Share algorithms to the delayed feedback and derive their regret bounds for the delayed setting by using our main result.