  Off-policy learning methods are intended to learn a policy from logged data,
which includes context, action, and feedback (cost or reward) for each sample
point. In this work, we build on the counterfactual risk minimization
framework, which also assumes access to propensity scores. We propose learning
methods for problems where feedback is missing for some samples, so there are
samples with feedback and samples missing-feedback in the logged data. We refer
to this type of learning as semi-supervised batch learning from logged data,
which arises in a wide range of application domains. We derive a novel upper
bound for the true risk under the inverse propensity score estimator to address
this kind of learning problem. Using this bound, we propose a regularized
semi-supervised batch learning method with logged data where the regularization
term is feedback-independent and, as a result, can be evaluated using the
logged missing-feedback data. Consequently, even though feedback is only
present for some samples, a learning policy can be learned by leveraging the
missing-feedback samples. The results of experiments derived from benchmark
datasets indicate that these algorithms achieve policies with better
performance in comparison with logging policies.
