e7663e974c4ee7a2b475a4775201ce1f-Supplemental-Conference.pdf

The key challenge in making this connection is grounding the skills, so that each skill corresponds to a specific goal-conditioned policy. We start by recalling the definition of the discounted state occupancymeasure(Eq.3): p(st+=sg)=(1 γ) X On the second line, we havechanged the bounds of the summation to start at 0, and changed the terms inside the summation accordingly. On the third line, we applied linearity of expectation to movethesummation insidetheexpectation. Onthefourthline,weappliedlinearity ofexpectation again to move the term fort = 0 inside the expectation. Finally, we substituted the definition of rg(s,a)toobtainthedesiredresult. This result means that we are doing policy improvement with approximate Q-values.