We apply empirical likelihood techniques to contextual bandit policy value estimation, confidence intervals, and learning. We propose a tighter estimator for off-policy evaluation with improved statistical performance over previous proposals. Coupled with this estimator is a confidence interval which also improves over previous proposals. We then harness these to improve learning from contextual bandit data. Each of these is empirically evaluated to show good performance against strong baselines in finite sample regimes.
Optimizing an interactive system against a predefined online metric is particularly challenging, especially when the metric is computed from user feedback such as clicks and payments. The key challenge is the counterfactual nature: in the case of Web search, any change to a component of the search engine may result in a different search result page for the same query, but we normally cannot infer reliably from search log how users would react to the new result page. Consequently, it appears impossible to accurately estimate online metrics that depend on user feedback, unless the new engine is actually run to serve live users and compared with a baseline in a controlled experiment. This approach, while valid and successful, is unfortunately expensive and time-consuming. In this paper, we propose to address this problem using causal inference techniques, under the contextual-bandit framework. This approach effectively allows one to run potentially many online experiments offline from search log, making it possible to estimate and optimize online metrics quickly and inexpensively. Focusing on an important component in a commercial search engine, we show how these ideas can be instantiated and applied, and obtain very promising results that suggest the wide applicability of these techniques.