  Risk management in dynamic decision problems is a primary concern in many
fields, including financial investment, autonomous driving, and healthcare. The
mean-variance function is one of the most widely used objective functions in
risk management due to its simplicity and interpretability. Existing algorithms
for mean-variance optimization are based on multi-time-scale stochastic
approximation, whose learning rate schedules are often hard to tune, and have
only asymptotic convergence proof. In this paper, we develop a model-free
policy search framework for mean-variance optimization with finite-sample error
bound analysis (to local optima). Our starting point is a reformulation of the
original mean-variance function with its Fenchel dual, from which we propose a
stochastic block coordinate ascent policy search algorithm. Both the asymptotic
convergence guarantee of the last iteration's solution and the convergence rate
of the randomly picked solution are provided, and their applicability is
demonstrated on several benchmark domains.
