# On prediction from expert advice with more than five experts

arXiv: https://arxiv.org/abs/2610.05186 · HTML: https://mlsanity.com/paper/2610.05186/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 18 of 18)

- [Prediction with Expert Advice: a PDE Perspective](https://mlsanity.com/paper/1904.11401/) (2019)
- [New Potential-Based Bounds for Prediction with Expert Advice](https://mlsanity.com/paper/1911.01641/) (2019)
- [Finite-Time 4-Expert Prediction Problem](https://mlsanity.com/paper/1911.10936/) (2019)
- [Towards Optimal Algorithms for Prediction with Expert Advice](https://mlsanity.com/paper/1409.3040/) (2014)
- [On the asymptotic optimality of the comb strategy for prediction with expert advice](https://mlsanity.com/paper/1902.02368/) (2019)
- [Tight Lower Bounds for Multiplicative Weights Algorithmic Families](https://mlsanity.com/paper/1607.02834/) (2016)
- [A PDE Approach to the Prediction of a Binary Sequence with Advice from Two History-Dependent Experts](https://mlsanity.com/paper/2007.12732/) (2020)
- [Towards Minimax Online Learning with Unknown Time Horizon](https://mlsanity.com/paper/1307.8187/) (2013)
- [Experimental Evidence for Asymptotic Non-Optimality of Comb Adversary Strategy](https://mlsanity.com/paper/1912.01548/) (2019)
- [New Potential-Based Bounds for the Geometric-Stopping Version of Prediction with Expert Advice](https://mlsanity.com/paper/1912.03132/) (2019)
- [Malicious Experts versus the multiplicative weights algorithm in online prediction](https://mlsanity.com/paper/2003.08457/) (2020)
- [Online Prediction With History-Dependent Experts: The General Case](https://mlsanity.com/paper/2008.00052/) (2020)
- [Asymptotically optimal strategies for online prediction with history-dependent experts](https://mlsanity.com/paper/2008.13703/) (2020)
- [Numerical solution of a PDE arising from prediction with expert advice](https://mlsanity.com/paper/2406.05754/) (2024)
- [An explicit solution of the five-expert prediction PDE and the exact optimality set of COMB](https://mlsanity.com/paper/2609.14892/) (2026)
- [Prediction with Five Experts and Geometric Stopping: A Probabilistic Construction and Analytic Verification](https://mlsanity.com/paper/2609.17986/) (2026)
- [Prediction with Expert Advice: Anytime Regret with Many Experts Matches the Fixed-Time Constant](https://mlsanity.com/paper/2609.27206/) (2026)
- [The finite-horizon five-expert prediction problem](https://mlsanity.com/paper/2609.38035/) (2026)

## Abstract (arXiv)

We prove that no single rank ordered adversary strategy is globally optimal for the prediction with expert advice problem with six or more experts, in both the geometric stopping and finite time horizon settings. The proof is based on establishing a leading order correction when one expert moves far ahead of the others. This allows us to connect optimal strategies between n and j<n experts and utilize recent results on the exact optimality set for the five expert problem.