In online reinforcement learning theory, how to judge the complexity order of regret, if there are two or more terms in there?
For example, the state space is $X$, the action space is $A$, the episode number is $K$, and the horizon number is $H$. If we have an algorithm with regret $R_K=2X^2A H \ln K \ln H + 3XAH^2\ln K$.
How can I decide the order of this algorithm? Should we look at which term is dominant with respect to the episode number $K$ or total steps $T=HK$? Then it might be $O(XAH^2\ln K)$
Or also consider the relationship with the state and action space? Then it might be $O(X^2AH^2\ln K)$, here I choose the highest order of each variable in both terms.