Convergence Rate of a Functional Learning Method for Contextual Stochastic Optimization
We consider a stochastic optimization problem involving two random variables: a context variable $X$ and a dependent variable $Y$. The objective is to minimize the expected value of a nonlinear loss functional applied to the conditional expectation $\mathbb{E}[f(X, Y,β) \mid X]$, where $f$ is a nonlinear function and $β$ represents the decision variables. We focus on the practically important setting in which direct sampling from the conditional distribution of $Y \mid X$ is infeasible, and only a stream of i.i.d. observation pairs $\{(X^k, Y^k)\}_{k=0,1,2,\ldots}$ is available. In our approach, the conditional expectation is approximated within a prespecified parametric function class. W...
| Authors | Noel Smith, Andrzej Ruszczynski |
|---|---|
| Primary category | math.OC |
| Published | 13 March 2026 |
| Last updated at source | 2 July 2026 |
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