We study minimax strategies for the online prediction problem with expert advice. It has been conjectured that a simple adversary strategy, called COMB, is near optimal in this game for any number of experts. Our results and new insights make progress in this direction by showing that, up to a small additive term, COMB is minimax optimal in the finite-time three expert problem. In addition, we provide for this setting a new near minimax optimal COMB-based learner. Prior to this work, in this problem, learners obtaining the optimal multiplicative constant in their regret rate were known only when $K=2$ or $K\rightarrow\infty$. We characterize, when $K=3$, the regret of the game scaling as $\sqrt{8/(9\pi)T}\pm \log(T)^2$ which gives for the first time the optimal constant in the leading ($\sqrt{T}$) term of the regret.

We study minimax strategies for the online prediction problem with expert advice.

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.

We study minimax strategies for the online prediction problem with expert advice.

We study minimax strategies for the online prediction problem with expert advice. It has been conjectured that a simple adversary strategy, called COMB, is near optimal in this game for any number of experts. Our results and new insights make progress in this direction by showing that, up to a small additive term, COMB is minimax optimal in the finite-time three expert problem. In addition, we provide for this setting a new near minimax optimal COMB-based learner. Prior to this work, in this problem, learners obtaining the optimal multiplicative constant in their regret rate were known only when $K 2$ or $K\rightarrow\infty$.

We study minimax strategies for the online prediction problem with expert advice. It has been conjectured that a simple adversary strategy, called COMB, is near optimal in this game for any number of experts. Our results and new insights make progress in this direction by showing that, up to a small additive term, COMB is minimax optimal in the finite-time three expert problem. In addition, we provide for this setting a new near minimax optimal COMB-based learner. Prior to this work, in this problem, learners obtaining the optimal multiplicative constant in their regret rate were known only when $K=2$ or $K\rightarrow\infty$. We characterize, when $K=3$, the regret of the game scaling as $\sqrt{8/(9\pi)T}\pm \log(T)^2$ which gives for the first time the optimal constant in the leading ($\sqrt{T}$) term of the regret.