Lower Complexity Bounds for Nonconvex-Strongly-Convex Bilevel Optimization with First-Order Oracles
arXiv:2511.19656v3 Announce Type: replace Abstract: Although upper bound guarantees for bilevel optimization have been widely studied, progress on lower bounds has been limited due to the complexity of the bilevel structure. In this work, we focus on the smooth nonconvex-strongly-convex setting and develop new hard instances that yield nontrivial lower bounds under deterministic and stochastic first-order oracle models. In the deterministic case, we prove that any first-order zero-respecting algorithm requires at least $\Omega(\kappa^{3/2}\epsilon^{-2})$ oracle calls to find an $\epsilon$-accu
This academic paper, published in 2026, details theoretical complexity bounds for a specific optimization problem, representing ongoing foundational research in AI/ML.
For a sophisticated reader, this provides a glimpse into the ongoing theoretical efforts to understand the fundamental limits of certain machine learning algorithms, which underpins future practical advancements.
This particular research publication does not immediately change current practices or market conditions, but it contributes to the incremental advancement of AI optimization theory.
- · Machine Learning Researchers
- · Academic Institutions
It provides a deeper theoretical understanding of the computational cost for bilevel optimization problems.
Improved theoretical bounds could eventually guide the development of more efficient and robust algorithms for complex AI tasks.
These foundational insights, over a very long time horizon, might contribute to breakthroughs in AI systems requiring advanced optimization techniques.
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Read at arXiv cs.LG