# Multistage Conditional Compositional Optimization

arXiv: https://arxiv.org/abs/2604.14075 · HTML: https://mlsanity.com/paper/2604.14075/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 72 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Builds on (most cited first, 2 of 2)

- [Unbiased Simulation for Optimizing Stochastic Function Compositions](https://mlsanity.com/paper/1711.07564/) (2017)
- [Multi-level Monte-Carlo Gradient Methods for Stochastic Optimization with Biased Oracles](https://mlsanity.com/paper/2408.11084/) (2024)

## Abstract (arXiv)

We introduce Multistage Conditional Compositional Optimization (MCCO) as a new paradigm for decision-making under uncertainty that combines aspects of multistage stochastic programming and conditional stochastic optimization. MCCO minimizes a nest of conditional expectations and nonlinear cost functions. It has numerous applications and arises, for example, in optimal stopping, linear-quadratic regulator problems, distributionally robust contextual bandits, as well as in problems involving dynamic risk measures. The na"ive nested sampling approach for MCCO suffers from the curse of dimensionality familiar from scenario tree-based multistage stochastic programming, that is, its scenario complexity grows exponentially with the number of nests. We develop new multilevel Monte Carlo techniques for MCCO whose scenario complexity grows only polynomially with the desired accuracy.