Accelerated convergence conjecture for Algorithm HOT-2

Let $\bar{L}$ be a continuously differentiable, smooth, and strongly convex function, and consider constant regressors. Let $\{\theta_k\}_{k=0}^{\infty}$ denote the iterates generated by Algorithm HOT-2. Accelerated convergence conjecture. The iterates $\{\theta_k\}_{k=0}^{\infty}$ should satisfy a convergence rate of $\mathcal{O}(\log(1/\epsilon))$. The conjecture predicts accelerated convergence for the proposed high-order tuner in the general strongly convex setting, where the superposition property used by Nesterov's estimating-sequence method is unavailable. Its status is not established in the supplied text.