Multistage Conditional Compositional Optimization
Buse Şen, Yifan Hu, Daniel Kuhn
TLDR
Introduces Multistage Conditional Compositional Optimization (MCCO) and a novel multilevel Monte Carlo method to efficiently solve its high-dimensional problems.
Key contributions
- Introduces Multistage Conditional Compositional Optimization (MCCO) for decision-making under uncertainty.
- MCCO minimizes nested conditional expectations and nonlinear costs, applicable to optimal stopping and dynamic risk.
- Overcomes exponential scenario complexity of naive MCCO sampling with novel multilevel Monte Carlo methods.
- Achieves polynomial scenario complexity, significantly improving efficiency for high-dimensional problems.
Why it matters
This paper introduces a new framework, MCCO, for complex decision-making under uncertainty, unifying existing approaches. It addresses the critical computational challenge of exponential complexity in such problems. The proposed efficient multilevel Monte Carlo methods make MCCO practically applicable to a wide range of real-world scenarios, from finance to control.
Original Abstract
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 naïve 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.
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