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

TL;DR

This paper analyzes the asymptotic behavior of the comb strategy in prediction with expert advice, proving its optimality for four experts in an adversarial setting with geometric stopping.

Contribution

It provides the exact leading order expansion of the value function and confirms the asymptotic optimality of comb strategies for four experts.

Findings

Exact leading order expansion of the value function computed

Proved asymptotic optimality of comb strategies for four experts

Supports conjecture by Gravin et al. on strategy optimality

Abstract

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.