Stochastic Gradient Langevin Dynamics Algorithms with Adaptive Drifts
This work addresses the bottleneck of slow posterior sampling in Bayesian deep learning, which is crucial for improving AI safety aspects like uncertainty and bias, though it appears incremental as an enhancement to existing SGMCMC techniques.
The authors tackled the inefficiency of Monte Carlo sampling for Bayesian deep learning by proposing adaptive stochastic gradient MCMC algorithms with biased drift functions, which significantly outperformed existing methods like SGLD and SGHMC in simulations and optimization tasks.
Bayesian deep learning offers a principled way to address many issues concerning safety of artificial intelligence (AI), such as model uncertainty,model interpretability, and prediction bias. However, due to the lack of efficient Monte Carlo algorithms for sampling from the posterior of deep neural networks (DNNs), Bayesian deep learning has not yet powered our AI system. We propose a class of adaptive stochastic gradient Markov chain Monte Carlo (SGMCMC) algorithms, where the drift function is biased to enhance escape from saddle points and the bias is adaptively adjusted according to the gradient of past samples. We establish the convergence of the proposed algorithms under mild conditions, and demonstrate via numerical examples that the proposed algorithms can significantly outperform the existing SGMCMC algorithms, such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian Monte Carlo (SGHMC) and preconditioned SGLD, in both simulation and optimization tasks.