Accelerating Nonconvex Learning via Replica Exchange Langevin Diffusion
This addresses optimization challenges in machine learning by improving escape from local minima, though it appears incremental as it builds on existing Langevin diffusion methods.
The paper tackles the problem of nonconvex optimization by proposing replica exchange Langevin diffusion to accelerate learning, achieving faster convergence to global minima through theoretical analysis and practical demonstrations.
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 χ^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.