Non-Stationary Functional Bilevel Optimization
Existing function-space bilevel optimization methods struggle to handle online non-stationary environments. This work proposes SmoothFBO, the first algorithm to extend function-space bilevel optimization to such settings. By employing a time-smoothed stochastic hypergradient estimator, SmoothFBO reduces variance in gradient estimates, enabling stable outer-loop updates and achieving sublinear regret. The method offers strong theoretical guarantees and scalability, while naturally encompassing classical parametric bilevel optimization as a special case. Empirical evaluations on non-stationary hyperparameter optimization and model-based reinforcement learning tasks demonstrate that SmoothFBO significantly outperforms existing approaches, confirming its effectiveness and broad applicability.