No-Regret Learning with Unbounded Losses: The Case of Logarithmic Pooling Supplementary Appendix May 10, 2023 A. Omitted Proofs

We now prove the first bullet. This is a contradiction, so in fact c κ. The first claim of the second bullet is analogous. To do so, we note the following technical lemma (proof below). To prove (#1), we proceed by induction on t.