Stochastic Lie-Bracket Approximations for Zeroth-Order Optimization on Manifolds

arXiv:2609.38069 · math.OC, cs.SY, eess.SY · Submitted 2026-09-29 · Read on arXiv

math.OC, cs.SY, eess.SY

Submitted: 2026-09-29

Updated: 2026-09-29

Terminology

• Spectral Gap — 8× in this paper · explained in 5 episodes
• Convergence Guarantees — 4× in this paper · explained in 3 episodes
• Objective Function — 4× in this paper · explained in 2 episodes
• Gradient Flow — 2× in this paper · explained in 2 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• Hybrid System — 1× in this paper · explained in 2 episodes
• Lyapunov function — 1× in this paper · explained in 2 episodes
• Regret — 1× in this paper · explained in 3 episodes
• Riemannian optimization — 1× in this paper · explained in 2 episodes

Sources

• Two-Timescale Asymptotic Simulations of Hybrid Inclusions with Applications to Stochastic Hybrid Optimization
• Averaging of Random Vibrations in Mechanical Systems in the Sense of Ito, Stratonovich, and Sussmann

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