The Parametric Cost Function Approximation: A new approach for multistage stochastic programming
This approach addresses the challenge of managing uncertainty in complex decision-making for industries like energy, offering a simpler and more practical solution compared to existing methods, though it introduces new offline tuning requirements.
The paper tackles the complexity of solving multistage stochastic programming problems by proposing a parameterized deterministic optimization model as an alternative to traditional methods like dynamic programming or scenario trees, demonstrating its effectiveness in handling uncertainty without the usual approximations in applications such as a nonstationary energy storage problem.
The most common approaches for solving multistage stochastic programming problems in the research literature have been to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the impact of a decision now on the future. By contrast, common industry practice is to use a deterministic approximation of the future which is easier to understand and solve, but which is criticized for ignoring uncertainty. We show that a parameterized version of a deterministic optimization model can be an effective way of handling uncertainty without the complexity of either stochastic programming or dynamic programming. We present the idea of a parameterized deterministic optimization model, and in particular a deterministic lookahead model, as a powerful strategy for many complex stochastic decision problems. This approach can handle complex, high-dimensional state variables, and avoids the usual approximations associated with scenario trees or value function approximations. Instead, it introduces the offline challenge of designing and tuning the parameterization. We illustrate the idea by using a series of application settings, and demonstrate its use in a nonstationary energy storage problem with rolling forecasts.