Non-Convex Optimization via Non-Reversible Stochastic Gradient Langevin Dynamics
arXiv:2004.02823
Abstract
Stochastic Gradient Langevin Dynamics (SGLD) is a powerful algorithm for optimizing a non-convex objective, where a controlled and properly scaled Gaussian noise is added to the stochastic gradients to steer the iterates towards a global minimum. SGLD is based on the overdamped Langevin diffusion which is reversible in time. By adding an anti-symmetric matrix to the drift term of the overdamped Langevin diffusion, one gets a non-reversible diffusion that converges to the same stationary distribution with a faster convergence rate. In this paper, we study the non reversible Stochastic Gradient Langevin Dynamics (NSGLD) which is based on discretization of the non-reversible Langevin diffusion. We provide finite-time performance bounds for the global convergence of NSGLD for solving stochastic non-convex optimization problems. Our results lead to non-asymptotic guarantees for both population and empirical risk minimization problems. Numerical experiments for Bayesian independent component analysis and neural network models show that NSGLD can outperform SGLD with proper choices of the anti-symmetric matrix.
arXiv comment45 pages
References in corpus (9)
- Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks
- Optimal non-reversible linear drift for the convergence to equilibrium of a diffusion
- Variance Reduction using Nonreversible Langevin Samplers
- Accelerating diffusions
- Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations
- Improving the convergence of reversible samplers
- Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Acceleration
- Breaking Reversibility Accelerates Langevin Dynamics for Global Non-Convex Optimization
- Nonreversible Langevin Samplers: Splitting Schemes, Analysis and Implementation