Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adam (1806.04854v3)

Abstract: Uncertainty computation in deep learning is essential to design robust and reliable systems. Variational inference (VI) is a promising approach for such computation, but requires more effort to implement and execute compared to maximum-likelihood methods. In this paper, we propose new natural-gradient algorithms to reduce such efforts for Gaussian mean-field VI. Our algorithms can be implemented within the Adam optimizer by perturbing the network weights during gradient evaluations, and uncertainty estimates can be cheaply obtained by using the vector that adapts the learning rate. This requires lower memory, computation, and implementation effort than existing VI methods, while obtaining uncertainty estimates of comparable quality. Our empirical results confirm this and further suggest that the weight-perturbation in our algorithm could be useful for exploration in reinforcement learning and stochastic optimization.

• The paper presents novel adaptive algorithms, including Vprop and Vadam, that integrate variational inference directly into the Adam optimizer.
• It demonstrates significant computational savings while maintaining quality uncertainty estimates compared to traditional VI techniques.
• The approach enhances exploration in reinforcement learning tasks by efficiently perturbing network weights during gradient evaluations.

Bayesian Deep Learning by Weight-Perturbation in Adam: A Technical Overview

The paper "Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adam" presents novel approaches to Bayesian deep learning, focusing particularly on overcoming the implementation challenges associated with achieving uncertainty estimates via Variational Inference (VI). The authors propose strategies that integrate these Bayesian methods into the widely-used Adam optimizer by leveraging weight perturbations during the gradient evaluations—a technique intended to streamline the process and reduce operational overhead compared to existing VI techniques.

Summary of Methodological Contributions

The primary methodological advancement is the development of an algorithm that enables VI to be effectively managed within the framework of the Adam optimizer, through the perturbation of network weights in the gradient step. This is achieved through a suite of new natural-gradient algorithms designed to simplify Gaussian mean-field VI. The key contributions of this work involve:

1. Variational RMSprop (Vprop) and Variational Adam (Vadam): These are novel adaptive-learning rate algorithms adapted for Bayesian inference. They utilize existing architectures of RMSprop and Adam but employ stochastic perturbations of network weights to achieve scalable estimation of uncertainty.
2. Variational Online-Newton (VON) and Variational Online Gauss-Newton (VOGN): These algorithms provide a streamlined means to perform VI using stochastic Hessian approximations to reduce computational expense and to manage scalability issues, with VON employing a full-covariance marginal, while VOGN assumes a diagonal structure.
3. Weight-perturbation Exploration: This technique, crucial for exploration in deep reinforcement learning, serves as a method for efficiently guiding the network through the parameter space.

Empirical Results

The empirical evidence presented in the paper underscores that the uncertainty estimates delivered by the proposed methods attain quality on par with more complex VI methods, yet they significantly economize computational resources and ease implementation. Notably, Vadam's and Vprop's performances are substantiated against various benchmarks like Bayesian logistic regression and Bayesian neural networks for regression tasks, exhibiting comparable uncertainty estimation with noticeable computational savings. Moreover, the results suggest advantages in exploration tasks when applied to reinforcement learning environments.

Implications and Future Directions

This research has considerable implications for the fields of AI and machine learning. Practically, the proposed methods make the deployment of Bayesian neural networks more accessible due to reduced complexity and resource requirements. Theoretically, it opens pathways for integrating natural-gradient concepts with adaptive methods, potentially enhancing computational efficiency and convergence rates.

In future work, exploration of variants using richer posterior distributions and extensions to non-Gaussian models could further enhance applicability. Additionally, refining these methods for broader reinforcement learning applications might lead to improved exploration strategies and learning efficiencies in complex environments.

Conclusion

This paper moves the needle towards making Bayesian deep learning more practical for broad applications, enhancing both efficiency and ease of implementation. By embedding Bayesian principles within the constructs of widely-adopted optimizers such as Adam, it simplifies the acquisition of reliable uncertainty estimates—a critical capability in domains such as robotic control and medical diagnostics, where model reliability cannot be compromised. The augmentation of reinforcement learning strategies with Bayesian methods also highlights a promising direction for future AI advancements.