Before revision:  As random coloring incurs \Omega(T^{1/2}) discrepancy, while the offline bounds are \Theta( (n\log T) ^{1/2 for vector balancing and 1 for interval balancing, a natural question is whether one can (nearly) match the offline bounds in the online setting for these problems.
After revision:  As random coloring incurs \Omega(T^{1/2}) discrepancy, while the offline bounds are \Theta( \sqrt{n \log (T/n) for vector balancing and 1 for interval balancing, a natural question is whether one can (nearly) match the offline bounds in the online setting for these problems.