Finding new materials with targeted properties with as few experiments as possible is a key goal of accelerated materials discovery. The enormous complexity due to the interplay of structural, chemical and microstructural degrees of freedom in materials makes the rational design of new materials with targeted properties rather difficult. Machine learning and statistical design, used in industry for solving complex problems, are increasingly being adapted for the design of new materials by learning from past data. However, the number of well characterized samples available as sources of data to learn from is typically small; as a result, uncertainties associated with the predictions from model fits, or even those from measurements, become large and important. The choice of the next experiment or calculation solely based on the machine model predictions is prone to be suboptimal. Thus, optimization schemes are needed for decision making to guide experiments using uncertainties to explore the vast material descriptor space. I will discuss how an active learning framework that iteratively combines machine learning, optimization and experiments can lead to the discovery of piezoelectric solid-solutions with targeted properties.