6 problems

Constant-strategy nonexistence conjecture. For $n\geq 6$ experts, there is no globally asymptotically optimal adversary strategy that is constant on $\mathbb{S}_n$. The paper repor…

Non-COMB uniqueness conjecture. The non-COMB strategy $(1,0,1,0,0)$ is the only globally asymptotically optimal strategy for $n=5$ experts. The claim is supported by strong numeric…

COMB optimality conjecture. The COMB strategy is globally asymptotically optimal on $\mathbb{S}_n$ only for $n\leq 4$ experts. The paper reports strong numerical evidence against g…

Gravin's COMB strategy conjecture. The COMB strategy is asymptotically optimal as $T\to\infty$ for all $n$. This was proved in the cited source only for $n=2$ and $n=3$ experts. De…

Let $a^c$ be the comb adversary on $N$ experts: after ranking the coordinates so that $x_{(1)}\geq x_{(2)}\geq\cdots\geq x_{(N)}$, it assigns probability $\frac{1}{2}$ to each of…

Let there be $k$ experts, with cumulative gains and gain increments as in the prediction-with-expert-advice setting. Partition the experts into the two teams … At each step, choose…