arXiv
Open Access
2025
A law of large numbers for predicting several steps ahead
Vladimir Vovk
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
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Vladimir Vovk
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Informasi Jurnal
- Tahun Terbit
- 2025
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- en
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- arXiv
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- Open Access ✓