  The goal of counterfactual learning for statistical machine translation (SMT)
is to optimize a target SMT system from logged data that consist of user
feedback to translations that were predicted by another, historic SMT system. A
challenge arises by the fact that risk-averse commercial SMT systems
deterministically log the most probable translation. The lack of sufficient
exploration of the SMT output space seemingly contradicts the theoretical
requirements for counterfactual learning. We show that counterfactual learning
from deterministic bandit logs is possible nevertheless by smoothing out
deterministic components in learning. This can be achieved by additive and
multiplicative control variates that avoid degenerate behavior in empirical
risk minimization. Our simulation experiments show improvements of up to 2 BLEU
points by counterfactual learning from deterministic bandit feedback.
