From our theoretical analysis and empirical evaluation, we conclude that the model selection procedure needs tobe guided by careful considerations regardingtheobserveddata,thefactorsusedforcorrection,andthestructureofthe data-generatingprocess.

These assumptions are not strong and can be satisfied in most of environments includes MuJoCo, Atarigamesandsoon. Let f be an Lebesgue integrable function, P and Q are two probability distributions, |f| C,then EP(x)f(x) EQ(x)f(x) CDTV(P,Q) (5) Proof. Suppose there are two actions a1, a2 under state s, and let Q1(s,a1) = u, Q1(s,a2) = v. In this way, we can derive the upper bound of Ea π2Q1(s,a) Ea π1Q1(s,a)asabove. Since both sides of the above equation have the same minimum (here the minima are given by Qk = Q), we can replace the objective in Problem 2 with the upper bound in Eq. (10) and solve therelaxedoptimizationproblem.

Therefore, a series of attempts Chung et al. [2020], Wu et al. [2020], Wang et al. [2020c], Gordon et al. [2020a], Tang et al. [2019], Aguilar et al. [2019] have been made to review the techniques for effective