# On the asymptotic optimality of the comb strategy for prediction with expert advice

arXiv: https://arxiv.org/abs/1902.02368 · HTML: https://mlsanity.com/paper/1902.02368/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2019.

## Built on by (most cited first, 10 of 10)

- [PDE-Based Optimal Strategy for Unconstrained Online Learning](https://mlsanity.com/paper/2201.07877/) (2022)
- [Optimal Comparator Adaptive Online Learning with Switching Cost](https://mlsanity.com/paper/2205.06846/) (2022)
- [Continuous Prediction with Experts' Advice](https://mlsanity.com/paper/2206.00236/) (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)
- [Prediction with Expert Advice: Anytime Regret with Many Experts Matches the Fixed-Time Constant](https://mlsanity.com/paper/2609.27206/) (2026)
- [A PDE approach for regret bounds under partial monitoring](https://mlsanity.com/paper/2209.01256/) (2022)
- [On prediction from expert advice with more than five experts](https://mlsanity.com/paper/2610.05186/) (2026)

## Abstract (arXiv)

For the problem of prediction with expert advice in the adversarial setting with geometric stopping, we compute the exact leading order expansion for the long time behavior of the value function. Then, we use this expansion to prove that as conjectured in Gravin et al. [12], the comb strategies are indeed asymptotically optimal for the adversary in the case of 4 experts.