# New Potential-Based Bounds for the Geometric-Stopping Version of Prediction with Expert Advice

arXiv: https://arxiv.org/abs/1912.03132 · HTML: https://mlsanity.com/paper/1912.03132/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2019.

## Built on by (most cited first, 6 of 6)

- [PDE-Based Optimal Strategy for Unconstrained Online Learning](https://mlsanity.com/paper/2201.07877/) (2022)
- [A PDE-Based Analysis of the Symmetric Two-Armed Bernoulli Bandit](https://mlsanity.com/paper/2202.05767/) (2022)
- [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)
- [A New Approach to Drifting Games, Based on Asymptotically Optimal Potentials](https://mlsanity.com/paper/2207.11405/) (2022)
- [On prediction from expert advice with more than five experts](https://mlsanity.com/paper/2610.05186/) (2026)

## Abstract (arXiv)

This work addresses the classic machine learning problem of online prediction with expert advice. A new potential-based framework for the fixed horizon version of this problem has been recently developed using verification arguments from optimal control theory. This paper extends this framework to the random (geometric) stopping version. To obtain explicit bounds, we construct potentials for the geometric version from potentials used for the fixed horizon version of the problem. This construction leads to new explicit lower and upper bounds associated with specific adversary and player strategies. While there are several known lower bounds in the fixed horizon setting, our lower bounds appear to be the first such results in the geometric stopping setting with an arbitrary number of experts. Our framework also leads in some cases to improved upper bounds. For two and three experts, our bounds are optimal to leading order.