# Aggregating Strategies for Long-term Forecasting

## TL;DR

This paper explores the adaptation of classic aggregating algorithms, especially Vovk's, for long-term forecasting, proposing theoretical and practical modifications with different regret bounds.

## Contribution

It generalizes Vovk's aggregating algorithm for long-term forecasting and introduces two modifications with distinct theoretical and practical benefits.

## Key findings

- The first modification achieves a time-independent regret bound.
- The second modification offers a practical approach with $O(
oot{T})$ regret.
- The algorithms are tailored for long-term forecasting scenarios.

## Abstract

The article is devoted to investigating the application of aggregating algorithms to the problem of the long-term forecasting. We examine the classic aggregating algorithms based on the exponential reweighing. For the general Vovk's aggregating algorithm we provide its generalization for the long-term forecasting. For the special basic case of Vovk's algorithm we provide its two modifications for the long-term forecasting. The first one is theoretically close to an optimal algorithm and is based on replication of independent copies. It provides the time-independent regret bound with respect to the best expert in the pool. The second one is not optimal but is more practical and has $O(\sqrt{T})$ regret bound, where $T$ is the length of the game.