# Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs

arXiv: https://arxiv.org/abs/1408.4439 · HTML: https://mlsanity.com/paper/1408.4439/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2014.

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

- [MDP modeling for multi-stage stochastic programs](https://mlsanity.com/paper/2509.22981/) (2025)

## Abstract (arXiv)

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the almost sure convergence of these decomposition methods when the relatively complete recourse assumption holds. We also prove the almost sure convergence of these algorithms when applied to risk-averse multistage stochastic linear programs that do not satisfy the relatively complete recourse assumption. The analysis is first done assuming the underlying stochastic process is interstage independent and discrete, with a finite set of possible realizations at each stage. We then indicate two ways of extending the methods and convergence analysis to the case when the process is interstage dependent.