Many social programs attempt to allocate scarce resources to people with the greatest need. Indeed, public services increasingly use algorithmic risk assessments motivated by this goal. However, targeting the highest-need recipients often conflicts with attempting to evaluate the causal effect of the program as a whole, as the best evaluations would be obtained by randomizing the allocation. We propose a framework to design randomized allocation rules which optimally balance targeting high-need individuals with learning treatment effects, presenting policymakers with a Pareto frontier between the two goals. We give sample complexity guarantees for the policy learning problem and provide a computationally efficient strategy to implement it. We then collaborate with the human services department of Allegheny County, Pennsylvania to evaluate our methods on data from real service delivery settings. Optimized policies can substantially mitigate the tradeoff between learning and targeting. For example, it is often possible to obtain 90% of the optimal utility in targeting high-need individuals while ensuring that the average treatment effect can be estimated with less than 2 times the samples that a randomized controlled trial would require. Mechanisms for targeting public services often focus on measuring need as accurately as possible. However, our results suggest that algorithmic systems in public services can be most impactful if they incorporate program evaluation as an explicit goal alongside targeting.