Before revision:  We numerically show that the local control regression is more accurate and more efficient than global control regression , and that the overall computational runtime scales polynomially with respect to the dimension of the control. Finally, we further validate our method by solving a portfolio optimization problem with twelve risky assets with transaction cost, liquidity cost and market impact, which involves twelve exogenous risk factors (asset returns) and thirteen endogenous risk factors (portfolio value and asset prices subject to market impact) .
After revision:  We numerically show that the local control regression is more accurate and more efficient than global control regression can be expensive and inaccurate. To overcome this difficulty, we introduce a local control regression technique, combined with adaptive grids. We show that choosing a coarse grid for local regression can produce sufficiently accurate results .