Non-Convex Optimization via Non-Reversible Stochastic Gradient Langevin Dynamics
This work addresses faster convergence for stochastic non-convex optimization problems, such as in machine learning, but is incremental as it builds on existing SGLD methods.
The paper tackles non-convex optimization by proposing Non-Reversible Stochastic Gradient Langevin Dynamics (NSGLD), which modifies SGLD with an anti-symmetric matrix to accelerate convergence, showing improved performance in experiments like Bayesian independent component analysis and neural networks.
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.