  Prediction with expert advice is a foundational problem in online learning.
In instances with $T$ rounds and $n$ experts, the classical Multiplicative
Weights Update method suffers at most $\sqrt{(T/2)\ln n}$ regret when $T$ is
known beforehand. Moreover, this is asymptotically optimal when both $T$ and
$n$ grow to infinity. However, when the number of experts $n$ is small/fixed,
algorithms with better regret guarantees exist. Cover showed in 1967 a dynamic
programming algorithm for the two-experts problem restricted to $\{0,1\}$ costs
that suffers at most $\sqrt{T/2\pi} + O(1)$ regret with $O(T^2)$ pre-processing
time. In this work, we propose an optimal algorithm for prediction with two
experts' advice that works even for costs in $[0,1]$ and with $O(1)$ processing
time per turn. Our algorithm builds up on recent work on the experts problem
based on techniques and tools from stochastic calculus.
