Counterfactual risk minimization is a framework for offline policy
optimization with logged data which consists of context, action, propensity
score, and reward for each sample point. In this work, we build on this
framework and propose a learning method for settings where the rewards for some
samples are not observed, and so the logged data consists of a subset of
samples with unknown rewards and a subset of samples with known rewards. This
setting arises in many application domains, including advertising and
healthcare. While reward feedback is missing for some samples, it is possible
to leverage the unknown-reward samples in order to minimize the risk, and we
refer to this setting as semi-counterfactual risk minimization. To approach
this kind of learning problem, we derive new upper bounds on the true risk
under the inverse propensity score estimator. We then build upon these bounds
to propose a regularized counterfactual risk minimization method, where the
regularization term is based on the logged unknown-rewards dataset only; hence
it is reward-independent. We also propose another algorithm based on generating
pseudo-rewards for the logged unknown-rewards dataset. Experimental results
with neural networks and benchmark datasets indicate that these algorithms can
leverage the logged unknown-rewards dataset besides the logged known-reward
dataset
