  Microfinance, despite its significant potential for poverty reduction, is
facing sustainability hardships due to high default rates. Although many
methods in regular finance can estimate credit scores and default
probabilities, these methods are not directly applicable to microfinance due to
the following unique characteristics: a) under-explored (developing) areas such
as rural Africa do not have sufficient prior loan data for microfinance
institutions (MFIs) to establish a credit scoring system; b) microfinance
applicants may have difficulty providing sufficient information for MFIs to
accurately predict default probabilities; and c) many MFIs use group liability
(instead of collateral) to secure repayment. Here, we present a novel
control-theoretic model of microfinance that accounts for these
characteristics. We construct an algorithm to learn microfinance decision
policies that achieve financial inclusion, fairness, social welfare, and
sustainability. We characterize the convergence conditions to Pareto-optimum
and the convergence speeds. We demonstrate, in numerous real and synthetic
datasets, that the proposed method accounts for the complexities induced by
group liability to produce robust decisions before sufficient loans are given
to establish credit scoring systems and for applicants whose default
probability cannot be accurately estimated due to missing information. To the
best of our knowledge, this paper is the first to connect microfinance and
control theory. We envision that the connection will enable safe learning and
control techniques to help modernize microfinance and alleviate poverty.
