Applying CVaR to generating diverse responses, we can define the random cost Z as − log P (Y |X), the corresponding CVaR is: where ν r (θ) = inf{ν ∈ R|P (− log P (Y |X) ≤ ν) ≥ r}, and θ are parameters of the Seq2Seq model.
we have: for a given post X and its ground- ), optimizing CVaR is equivalent to maximizing the following objective function: where Y 1−α is a collection of ground-truth responses such that: We can see that maximizing the above objective function requires the worst 1 − α responses to be close to the post.