# The Parametric Cost Function Approximation: A new approach for multistage stochastic programming

arXiv: https://arxiv.org/abs/2201.00258 · HTML: https://mlsanity.com/paper/2201.00258/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 81 references that are in the map.
- First posted on arXiv 1 Jan 2022.

## Builds on (most cited first, 4 of 4)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Deep Learning Approximation for Stochastic Control Problems](https://mlsanity.com/paper/1611.07422/) (2016)
- [PEGASUS: A Policy Search Method for Large MDPs and POMDPs](https://mlsanity.com/paper/1301.3878/) (2013)

## Built on by (most cited first, 1 of 1)

- [Learning Optimal Power Flow Value Functions with Input-Convex Neural Networks](https://mlsanity.com/paper/2310.04605/) (2023)

## Abstract (arXiv)

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.