A Block Coordinate Ascent Algorithm for Mean-Variance Optimization
This addresses risk management challenges in fields like finance and autonomous driving, offering a more practical alternative to existing methods with hard-to-tune schedules, though it is incremental in improving optimization techniques.
The paper tackles the problem of mean-variance optimization in risk management by developing a model-free policy search framework with a stochastic block coordinate ascent algorithm, providing finite-sample error bounds and convergence guarantees, as demonstrated on benchmark domains.
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.