08b7dc6e8b36bcaac15847827b7951a9-AuthorFeedback.pdf

The setup there is also a special case of our setup, where the reward is linear in the treatment vector, i.e.4 hθ(z),Ti,butwhereT R` m (`isnumber ofitems andmnumber ofslots) and whereT takesvalues inasubset5 of the hypercube. The discreteness of the action space allows Swaminathan et al to apply a more direct propensity6 approach (seee.g. Thiscanindeedlead22 to a benefit if the errors are heteroskedastic as then one should do an optimally re-weighted square loss projection.23 However, these extra moment conditions have no bite in the case of homoskedastic noise. This involves simple matrix computations.