  We consider a new family of operators for reinforcement learning with the
goal of alleviating the negative effects and becoming more robust to
approximation or estimation errors. Various theoretical results are
established, which include showing on a sample path basis that our family of
operators preserve optimality and increase the action gap. Our empirical
results illustrate the strong benefits of our family of operators,
significantly outperforming the classical Bellman operator and recently
proposed operators.
