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Monte Carlo (MC) methods are the most widely used methods to estimate theperformance of a policy. Given an interested policy, MC methods give estimatesby repeatedly running this policy to collect samples and taking the average ofthe outcomes. Samples collected during this process are called online samples.To get an accurate estimate, MC methods consume massive online samples. Whenonline samples are expensive, e.g., online recommendations and inventorymanagement, we want to reduce the number of online samples while achieving thesame estimate accuracy. To this end, we use off-policy MC methods that evaluatethe interested policy by running a different policy called behavior policy. Wedesign a tailored behavior policy such that the variance of the off-policy MCestimator is provably smaller than the ordinary MC estimator. Importantly, thistailored behavior policy can be efficiently learned from existing offline data,i,e., previously logged data, which are much cheaper than online samples. Withreduced variance, our off-policy MC method requires fewer online samples toevaluate the performance of a policy compared with the ordinary MC method.Moreover, our off-policy MC estimator is always unbiased.

Improving Monte Carlo Evaluation with Offline Data