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• W3040604566 abstract "Langevin diffusion is a powerful method for nonconvex optimization, which enables the escape from local minima by injecting noise into the gradient. In particular, the temperature parameter controlling the noise level gives rise to a tradeoff between ``global exploration'' and ``local exploitation'', which correspond to high and low temperatures. To attain the advantages of both regimes, we propose to use replica exchange, which swaps between two Langevin diffusions with different temperatures. We theoretically analyze the acceleration effect of replica exchange from two perspectives: (i) the convergence in chi^2-divergence, and (ii) the large deviation principle. Such an acceleration effect allows us to faster approach the global minima. Furthermore, by discretizing the replica exchange Langevin diffusion, we obtain a discrete-time algorithm. For such an algorithm, we quantify its discretization error in theory and demonstrate its acceleration effect in practice." @default.
• W3040604566 created "2020-07-10" @default.
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• W3040604566 date "2020-07-04" @default.
• W3040604566 modified "2023-10-18" @default.
• W3040604566 title "Accelerating Nonconvex Learning via Replica Exchange Langevin Diffusion" @default.
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