Why is it useful to define the return as the sum of the rewards from time $t$ onward rather than up to $t$?
The return for an MDP is usually defined as
$$G_t=R_{t+1}+R_{t+2}+ \dots +R_T$$
Why is this defined as the return? Is there anything useful about this?
It seems like it's more useful to define the return as $$G_t=R_0+ \dots+R_t,$$ because your "return", so to speak, is the "profit from investment" so it seems like your return will be your accumulated reward from taking actions up to that point.