# Are Online Problems always harder than the Offline equivalent?

I am currently studying Online-Algorithms, and I just asked myself if online Problems are always harder than the offline equivalent.

The most probable answer ist yes, but I can’t figure the reason out why.

Actually I have a second more specific question. When an offline Problem has some integrality gap ($$IG\in[1,\infty)$$) we know in an offline setting, that there is generally no randomized rounding algorithm which achieves a ratio $$C\geq IG$$.

Can this just be adapted to the online problem? If some fractional algorithm has competitive ratio $$c_{frac}$$ can some randomized rounding scheme only reach competitive ratio as good as $$\frac{c_{frac}}{IG}$$?

Thanks in advance.