arXiv Open Access 2025

A law of large numbers for predicting several steps ahead

Vladimir Vovk
Lihat Sumber

Abstrak

This note proves a law of large numbers for predicting several steps ahead, which, in the case of uniformly bounded random variables, generalizes the standard law of large numbers for martingales; the standard law of large numbers corresponds to predicting one step ahead. Its main result shows that the law of large numbers holds for predicting $N$ uniformly bounded random variables $o(N)$ steps ahead, but it is much more precise and in some respects optimal. This law of large numbers is applied to a problem of decision making with a bounded loss function limiting the impact of each decision to $o(N)$ steps.

Topik & Kata Kunci

Penulis (1)

V

Vladimir Vovk

Format Sitasi

Vovk, V. (2025). A law of large numbers for predicting several steps ahead. https://arxiv.org/abs/2508.17507

Akses Cepat

Lihat di Sumber
Informasi Jurnal
Tahun Terbit
2025
Bahasa
en
Sumber Database
arXiv
Akses
Open Access ✓