A Chance-Constrained Generative Framework for Sequence Optimization

Let v be the mean validity of the sequences generated by Gθ, i.e., v = 1 N ∑N i=1 1[g(Gθ(ξi)) > T ], where 1[·] is the indicator function. For notational simplicity, we assume that the function g is a binary indicator, then we will have v = 1 N ∑N i=1 g(Gθ(ξi)), so we know there are Nv valid sequences and N(1 − v) invalid ones. Note that it is not hard to obtain a similar analysis for arbitrary g function.