R\'enyi Tracking Bounds for Langevin Dynamics with Moving Targets
These are the first non-asymptotic R\'enyi-divergence tracking bounds for Langevin dynamics with discrete target updates for Langevin diffusion and Langevin Monte Carlo.
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These are the first non-asymptotic R\'enyi-divergence tracking bounds for Langevin dynamics with discrete target updates for Langevin diffusion and Langevin Monte Carlo.
A Lyapunov function is constructed for the gap process between the estimated cumulative loss of the optimal arm and that of the best competing arm, and establishes a lower bound on the exponent of $\operatorname{Err}_t$ for any $\rho>0$, showing that the exponent $2$ is essentially tight.
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