I was reading Stanford's CS 229 materials on Linear Quadratic Regulation ( Lecture note 13, youtube Lecture 18, around time 36 min). And it mentions that:
" the quadratic formulation of the reward is equivalent to saying that we want our state to be close to the origin.For example, if $U_t = I_n $(the identity matrix) and $W_t = I_d$, then $R_t = -\Vert(s_t)\Vert^2-\Vert(a_t)\Vert^2$, meaning that we want to take smooth actions (small norm of $a_t$) to go back to the origin (small norm of $s_t$)."
but why is that? Why the norm of the origin is smaller? $s_t$ for any time point are just a vector of n dimension which can take any value, right?