text: This paper studies off-policy learning in the bandit setting.  It develops a new learning objective where the empirical risk is regularized by the squared Chi-2 divergence between the new and old policy.  This objective is motivated by a bound on the empirical risk, where this divergence appears.  The authors propose to solve this objective by using generative adversarial networks for variational divergence minimization (f-GAN).  The algorithm is then evaluated on settings derived from supervised learning tasks and compared to other algorithms. I find the paper well written and clear.  I like that the proposed method is both supported by theory and empirical results.  Minor point: I do not really agree with the discussion on the impact of the stochasticity of the logging policy in section 5.6.  Based on Figure 5 a and b, it seems that the learned policy is performing equally well no matter how stochastic the logging policy is.  So I find it a bit misleading to suggest that the learned policy are not being improved when the logging policy is more deterministic.  Rather, the gap reduces between the two policies  because the logging policy gets better.  In order to better showcase this mechanism, perhaps you could try using a logging policy that does not favor the best action. quality and clarity: ++ code made available + well written and clear - The proof of theorem 2 is not in the paper nor appendix  (the authors say it is similar to another work). originality + good extension of the work by Swaminathan & Joachims (2015a): derivation of an alternative objective and use of a deep networks.  This paper leverages a set of diverse results significance - The proposed method can only be applied if propensity scores were recorded when the data was generated. - no test on a real setting ++ The proposed method is supported both by theoretical insights and empirical experiments. + empirical improvement with respect to previous methods details/typos: 3.1, p3: R^(h) has an indexed parenthesis 5.2; and we more details 5.3: so that results more comparable