Safe Data Collection for Offline and Online Policy Learning

Motivated by practical needs of experimentation and policy learning in online platforms, we study the problem of safe data collection. Specifically, our goal is to develop a logging policy that efficiently explores different actions to elicit information while achieving competitive reward with a baseline production policy. We first show that a common practice of mixing the production policy with randomized exploration, despite being safe, is sub-optimal in maximizing information gain. Then, we propose a safe optimal logging policy via a novel water-filling technique for the case when no side information about the actions' expected reward is available. We improve upon this design by considering side information and also extend our approaches to the linear contextual model to account for a large number of actions. Along the way, we analyze how our data logging policies impact errors in off(line)-policy learning and empirically validate the benefit of our design by conducting extensive numerical experiments with synthetic and MNIST datasets. To further demonstrate the generality of our approach, we also consider the safe online learning setting. By adaptively applying our techniques, we develop the Safe Phased-Elimination (SafePE) algorithm that can achieve optimal regret bound with only logarithmic number of policy updates.