Reviews: Near Minimax Optimal Players for the Finite-Time 3-Expert Prediction Problem

The paper studies the classic prediction with experts advice problem. There are a finite number k of experts and a finite number T of rounds. There is a player that makes sequential decisions for T rounds based on the advice of the k experts, and his goal is to minimize the maximum regret he can experience (minimax regret). Naturally, the optimal adversarial strategy is a key quantity to study here. This paper takes up the conjectured minimax optimal adversarial strategy called "Comb strategy" in the Gravin et al. paper and shows that it is indeed minimax optimal in the case of 3 experts.