Yubo Zhou

Yubo Zhou, Jun Shu, Junmin Liu et al.

Gradient-based hyperparameter optimization (HPO) have emerged recently, leveraging bilevel programming techniques to optimize hyperparameter by estimating hypergradient w.r.t. validation loss. Nevertheless, previous theoretical works mainly focus on reducing the gap between the estimation and ground-truth (i.e., the bias), while ignoring the error due to data distribution (i.e., the variance), which degrades performance. To address this issue, we conduct a bias-variance decomposition for hypergradient estimation error and provide a supplemental detailed analysis of the variance term ignored by previous works. We also present a comprehensive analysis of the error bounds for hypergradient estimation. This facilitates an easy explanation of some phenomena commonly observed in practice, like overfitting to the validation set. Inspired by the derived theories, we propose an ensemble hypergradient strategy to reduce the variance in HPO algorithms effectively. Experimental results on tasks including regularization hyperparameter learning, data hyper-cleaning, and few-shot learning demonstrate that our variance reduction strategy improves hypergradient estimation. To explain the improved performance, we establish a connection between excess error and hypergradient estimation, offering some understanding of empirical observations.

Yubo Zhou, Luo Luo, Guang Dai et al.

Stochastic Bilevel Optimization has emerged as a fundamental framework for meta-learning and hyperparameter optimization. Despite the practical prevalence of single-loop algorithms--which update lower and upper variables concurrently--their theoretical understanding, particularly in the stochastic regime, remains significantly underdeveloped compared to their multi-loop counterparts. Existing analyses often yield suboptimal convergence rates or obscure the critical dependence on the lower-level condition number $κ$, frequently burying it within generic Lipschitz constants. In this paper, we bridge this gap by providing a refined convergence analysis of the Single-loop Stochastic Approximate Implicit Differentiation (SSAID) algorithm. We prove that SSAID achieves an $ε$-stationary point with an oracle complexity of $\mathcal{O}(κ^7 ε^{-2})$. Our result is noteworthy in two aspects: (i) it matches the optimal $\mathcal{O}(ε^{-2})$ rate of state-of-the-art multi-loop methods (e.g., stocBiO) while maintaining the computational efficiency of a single-loop update; and (ii) it provides the first explicit, fine-grained characterization of the $κ$-dependence for stochastic AID-based single-loop methods. This work demonstrates that SSAID is not merely a heuristic approach, but admits a rigorous theoretical foundation with convergence guarantees competitive with mainstream multi-loop frameworks.