A new first-order method for online bilevel optimization achieves regret O(1 + V_T + H_{2,T}) over O(T log T) iterations without Hessian-vector products.
Online min-max problems with non-convexity and non-stationarity.Transactions on Machine Learning Research
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Algorithms achieve optimal regret bounds of Ω(1+V_T) for standard bilevel local regret with O(T log T) inner gradients and Ω(T/W²) for window-averaged regret using adaptive and window-based analyses.
Introduces a novel search direction enabling sublinear stochastic bilevel regret guarantees for first- and zeroth-order online bilevel optimization algorithms without relying on window smoothing.
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Fully First-Order Algorithms for Online Bilevel Optimization
A new first-order method for online bilevel optimization achieves regret O(1 + V_T + H_{2,T}) over O(T log T) iterations without Hessian-vector products.
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Achieving Better Local Regret Bound for Online Non-Convex Bilevel Optimization
Algorithms achieve optimal regret bounds of Ω(1+V_T) for standard bilevel local regret with O(T log T) inner gradients and Ω(T/W²) for window-averaged regret using adaptive and window-based analyses.
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Stochastic Regret Guarantees for Online Zeroth- and First-Order Bilevel Optimization
Introduces a novel search direction enabling sublinear stochastic bilevel regret guarantees for first- and zeroth-order online bilevel optimization algorithms without relying on window smoothing.