Off-policy learning (OPL) in contextual bandits aims to learn a decision-making policy that maximizes the target rewards by using only historical interaction data collected under previously developed policies. Unfortunately, when rewards are only partially observed, the effectiveness of OPL degrades severely. Well-known examples of such partial rewards include explicit ratings in content recommendations, conversion signals on e-commerce platforms that are partial due to delay, and the issue of censoring in medical problems. One possible solution to deal with such partial rewards is to use secondary rewards, such as dwelling time, clicks, and medical indicators, which are more densely observed. However, relying solely on such secondary rewards can also lead to poor policy learning since they may not align with the target reward. Thus, this work studies a new and general problem of OPL where the goal is to learn a policy that maximizes the expected target reward by leveraging densely observed secondary rewards as supplemental data. We then propose a new method called Hybrid Policy Optimization for Partially-Observed Reward (HyPeR), which effectively uses the secondary rewards in addition to the partially observed target reward to achieve effective OPL despite the challenging scenario. We also discuss a case where we aim to optimize not only the expected target reward but also the expected secondary rewards to some extent; counter-intuitively, we will show that leveraging the two objectives is in fact advantageous also for the optimization of only the target reward. Along with statistical analysis of our proposed methods, empirical evaluations on both synthetic and real-world data show that HyPeR outperforms existing methods in various scenarios.

**Off-Policy Evaluation (OPE)** aims to assess the effectiveness of counterfactual policies using offline logged data and is frequently utilized to identify the top-$k$ promising policies for deployment in online A/B tests. Existing evaluation metrics for OPE estimators primarily focus on the "accuracy" of OPE or that of downstream policy selection, neglecting risk-return tradeoff and *efficiency* in subsequent online policy deployment. To address this issue, we draw inspiration from portfolio evaluation in finance and develop a new metric, called **SharpeRatio@k**, which measures the risk-return tradeoff and efficiency of policy portfolios formed by an OPE estimator under varying online evaluation budgets ($k$). We first demonstrate, in two example scenarios, that our proposed metric can clearly distinguish between conservative and high-stakes OPE estimators and reliably identify the most *efficient* estimator capable of forming superior portfolios of candidate policies that maximize return with minimal risk during online deployment, while existing evaluation metrics produce only degenerate results. To facilitate a quick, accurate, and consistent evaluation of OPE via SharpeRatio@k, we have also implemented the proposed metric in an open-source software. Using SharpeRatio@k and the software, we conduct a benchmark experiment of various OPE estimators regarding their risk-return tradeoff, presenting several future directions for OPE research.