The article introduces a new method called contextual stochastic bilevel optimization (CSBO) that extends traditional optimization by considering additional information. This method is useful for tasks like meta-learning and personalized federated learning. The researchers developed a double-loop gradient method based on Multilevel Monte-Carlo (MLMC) technique to handle this complexity. Their method matches existing lower bounds for stochastic nonconvex optimization and is not affected by the number of tasks in meta-learning. Numerical experiments support their theoretical findings.