Unbiased Gradients for a Class of Conditional Stochastic Optimization Problems

Miguel Alvarez; Ajay Jasra

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arXiv · 2605.18786

Unbiased Gradients for a Class of Conditional Stochastic Optimization Problems

Miguel Alvarez·Ajay Jasra

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Abstract

In this paper we consider the conditional stochastic optimization (CSO) problem. This consists of optimizing a function which can be written as the expectation of a function which is itself a function of a conditional expectation, i.e.~of the type $F(\xi) := \mathbb{E}\left[f\left(Z,\mathbb{E}[g(Z,X,\xi)|Z]\right)\right]$, where precise definitions are given in the main text. We address a particular class of CSO problems where the joint law of the random variables $X,Z$ cannot be exactly sampled; this case has been addressed in Goda & Kitade (2023). We introduce a method that combines Markovian stochastic approximation with unbiased approximation methods which allows one to find the optimizer of $F(\xi)$ in the context of interest. We illustrate our methodology on two examples associated to parameter estimation with model averaging and portfolio selection associated to high-dimensional full factor multivariate stochastic volatility models.

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BibTeX RIS

Miguel Alvarez, Ajay Jasra. 2026-05-07. Unbiased Gradients for a Class of Conditional Stochastic Optimization Problems. https://arxiv.org/abs/2605.18786

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