Unbiased Gradients for a Class of Conditional Stochastic Optimization Problems
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| Format: | Preprint |
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2026
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| _version_ | 1866916024301912064 |
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| author | Alvarez, Miguel Jasra, Ajay |
| author_facet | Alvarez, Miguel Jasra, Ajay |
| contents | 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 $F(ξ) := \mathbb{E}\left[f\left(Z,\mathbb{E}[g(Z,X,ξ)|Z]\right)\right]$, 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 $F(ξ)$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_18786 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unbiased Gradients for a Class of Conditional Stochastic Optimization Problems Alvarez, Miguel Jasra, Ajay Optimization and Control Numerical Analysis Methodology 62L20, 65C40, 65C05 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 $F(ξ) := \mathbb{E}\left[f\left(Z,\mathbb{E}[g(Z,X,ξ)|Z]\right)\right]$, 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 $F(ξ)$ 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. |
| title | Unbiased Gradients for a Class of Conditional Stochastic Optimization Problems |
| topic | Optimization and Control Numerical Analysis Methodology 62L20, 65C40, 65C05 |
| url | https://arxiv.org/abs/2605.18786 |