Semi-Parametric Efficient Policy Learning with Continuous Actions
This work addresses policy learning from observational data for applications like personalized pricing, but it is incremental as it extends existing methods to continuous actions.
The paper tackles off-policy evaluation and optimization with continuous actions using observational data, proposing a doubly robust estimate that is robust to estimation errors and extends prior discrete-action methods, with experimental validation in synthetic examples like personalized pricing.
We consider off-policy evaluation and optimization with continuous action spaces. We focus on observational data where the data collection policy is unknown and needs to be estimated. We take a semi-parametric approach where the value function takes a known parametric form in the treatment, but we are agnostic on how it depends on the observed contexts. We propose a doubly robust off-policy estimate for this setting and show that off-policy optimization based on this estimate is robust to estimation errors of the policy function or the regression model. Our results also apply if the model does not satisfy our semi-parametric form, but rather we measure regret in terms of the best projection of the true value function to this functional space. Our work extends prior approaches of policy optimization from observational data that only considered discrete actions. We provide an experimental evaluation of our method in a synthetic data example motivated by optimal personalized pricing and costly resource allocation.