Social capital brings individuals benefits and advantages in societies. In this paper, we formalize two types of social capital: bonding capital refers to links to neighbours, while bridging capital refers to brokerages between others. We ask the questions: How would a marginal individual gain social capital with imperfect information of the society? We formalize this issue as the partially observable network building problem and propose two reinforcement learning algorithms: one guarantees the convergence to optimal values in theory, while the other is efficient in practice. We conduct simulations over a real-world dataset, and experimental results coincide with our theoretical analysis.