A Block Coordinate Ascent Algorithm for Mean-Variance Optimization

Risk management plays a central role in sequential decision-making problems, common in fields such as portfolio management [Lai et al., 2011], autonomous driving [Maurer et al., 2016], and healthcare [Parker, 2009]. A common risk-measure is the variance of the expected sum of rewards/costs and the mean-variance tradeoff function [Sobel, 1982; Mannor and Tsitsiklis, 2011] is one of the most widely used objective functions in risk-sensitive decision-making. Other risk-sensitive objectives have also been studied, for example, Borkar [2002] studied exponential utility functions, Tamar et al. [2012] experimented with the Sharpe Ratio measurement, Chow et al. [2018] studied value at risk (VaR) and mean-VaR optimization, Chow and Ghavamzadeh [2014], Tamar et al. [2015b], and Chow et al. [2018] investigated conditional value at risk (CVaR) and mean-CVaR optimization in a static setting, and Tamar et al. [2015a] investigated coherent risk for both linear and nonlinear system dynamics. Compared with other widely used performance measurements, such as the Sharpe Ratio and CVaR, the mean-variance measurement has explicit interpretability and computational advantages [Markowitz et al., 2000; Li and Ng, 2000]. For example, the Sharpe Ratio tends to lead to solutions with less mean return [Tamar et al., 2012].