2022/12/20 by Adrien Le Franc, Jean‐Philippe Chancelier, Franc, Adrien Le +5 · 1 citation
Decision Sciences · Computer Science · Economics, Econometrics and Finance · #Risk and Portfolio Optimization #Optimization and Variational Analysis #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2212.10384
In multistage decision problems, it is often the case that an initial\nstrategic decision (such as investment) is followed by many operational ones\n(operating the investment). Such initial strategic decision can be seen as a\nparameter affecting a multistage decision problem. More generally, we study in\nthis paper a standard multistage stochastic optimization problem depending on a\nparameter. When the parameter is fixed, Stochastic Dynamic Programming provides\na way to compute the optimal value of the problem. Thus, the value function\ndepends both on the state (as usual) and on the parameter. Our aim is to\ninvestigate on the possibility to efficiently compute gradients of the value\nfunction with respect to the parameter, when these objects exist. When\nnondifferentiable, we propose a regularization method based on the\nMoreau-Yosida envelope. We present a numerical test case from day-ahead power\nscheduling.\n