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- W3048592889 abstract "In this paper, we study a class of stochastic optimization problems, referred to as the conditional stochastic optimization (CSO), in the form of $min_{x in mathcal{X}} mathbb{E}_{xi}f_xi({mathbb{E}_{eta|xi}[g_eta(x, xi)]})$, which finds a wide spectrum of applications including portfolio selection, reinforcement learning, robust learning, and causal inference. Assuming availability of samples from the distribution $mathbb{P}(xi)$ and samples from the conditional distribution $mathbb{P}(eta|xi)$, we establish the sample complexity of the sample average approximation (SAA) for CSO, under a variety of structural assumptions, such as Lipschitz continuity, smoothness, and error bound conditions. We show that the total sample complexity improves from $mathcal{O}(d/epsilon^4)$ to $mathcal{O}(d/epsilon^3)$ when assuming smoothness of the outer function, and further to $mathcal{O}(1/epsilon^2)$ when the empirical function satisfies the quadratic growth condition. We also establish the sample complexity of a modified SAA when $xi$ and $eta$ are independent. Several numerical experiments further support our theoretical findings." @default.
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- W3048592889 date "2020-01-01" @default.
- W3048592889 modified "2023-10-17" @default.
- W3048592889 title "Sample Complexity of Sample Average Approximation for Conditional Stochastic Optimization" @default.
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- W3048592889 doi "https://doi.org/10.1137/19m1284865" @default.
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