Dec 10, 2023
Řečník · 6 sledujících
Řečník · 5 sledujících
We introduce contextual stochastic bilevel optimization (CSBO) – a stochastic bilevel optimization template with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision variable. This framework captures important applications such as meta-learning, Wasserstein distributionally robust optimization with side information (WDRO-SI), and instrumental variable regression (IV). Due to the presence of contextual information, existing single-loop methods for classical stochastic bilevel optimization are unable to converge. To overcome this challenge, we introduce an efficient double-loop gradient method based on the Multilevel Monte-Carlo (MLMC) technique and establish its sample and computational complexities. When specialized to stochastic nonconvex optimization, our method matches existing lower bounds. Numerical experiments further validate our theoretical results.We introduce contextual stochastic bilevel optimization (CSBO) – a stochastic bilevel optimization template with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision variable. This framework captures important applications such as meta-learning, Wasserstein distributionally robust optimization with side information (WDRO-SI), and instrumental variable regression (IV). Due to the presence of contextual information, existing sing…
Účet · 648 sledujících
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