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Langevin diffusion is a powerful method for nonconvex optimization, whichenables the escape from local minima by injecting noise into the gradient. Inparticular, the temperature parameter controlling the noise level gives rise toa tradeoff between ``global exploration'' and ``local exploitation'', whichcorrespond to high and low temperatures. To attain the advantages of bothregimes, we propose to use replica exchange, which swaps between two Langevindiffusions with different temperatures. We theoretically analyze theacceleration effect of replica exchange from two perspectives: (i) theconvergence in \chi^2-divergence, and (ii) the large deviation principle. Suchan acceleration effect allows us to faster approach the global minima.Furthermore, by discretizing the replica exchange Langevin diffusion, we obtaina discrete-time algorithm. For such an algorithm, we quantify itsdiscretization error in theory and demonstrate its acceleration effect inpractice.

Accelerating Nonconvex Learning via Replica Exchange Langevin Diffusion