# Entropy-regularized Gradient Estimators for Approximate Bayesian Inference

arXiv: https://arxiv.org/abs/2503.11964 · HTML: https://mlsanity.com/paper/2503.11964/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 35 references that are in the map.
- First posted on arXiv 15 Mar 2025.

## Builds on (most cited first, 28 of 28)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Stochastic Gradient Descent as Approximate Bayesian Inference](https://mlsanity.com/paper/1704.04289/) (2017)
- [Randomized Ensembled Double Q-Learning: Learning Fast Without a Model](https://mlsanity.com/paper/2101.05982/) (2021)
- [Improving Adversarial Robustness via Promoting Ensemble Diversity](https://mlsanity.com/paper/1901.08846/) (2019)
- [SUNRISE: A Simple Unified Framework for Ensemble Learning in Deep Reinforcement Learning](https://mlsanity.com/paper/2007.04938/) (2020)
- [Functional Variational Bayesian Neural Networks](https://mlsanity.com/paper/1903.05779/) (2019)
- [On Linear Identifiability of Learned Representations](https://mlsanity.com/paper/2007.00810/) (2020)
- [Repulsive Deep Ensembles are Bayesian](https://mlsanity.com/paper/2106.11642/) (2021)
- [Better Exploration with Optimistic Actor-Critic](https://mlsanity.com/paper/1910.12807/) (2019)
- [Deep Ensembles Work, But Are They Necessary?](https://mlsanity.com/paper/2202.06985/) (2022)
- [Bayesian Optimization with Gradients](https://mlsanity.com/paper/1703.04389/) (2017)
- [Cooperative Exploration for Multi-Agent Deep Reinforcement Learning](https://mlsanity.com/paper/2107.11444/) (2021)
- [Message Passing Stein Variational Gradient Descent](https://mlsanity.com/paper/1711.04425/) (2017)
- [A Unified Particle-Optimization Framework for Scalable Bayesian Sampling](https://mlsanity.com/paper/1805.11659/) (2018)
- [Annealed Stein Variational Gradient Descent](https://mlsanity.com/paper/2101.09815/) (2021)
- [Why do classifier accuracies show linear trends under distribution shift?](https://mlsanity.com/paper/2012.15483/) (2020)
- [When are ensembles really effective?](https://mlsanity.com/paper/2305.12313/) (2023)
- [Pathologies of Predictive Diversity in Deep Ensembles](https://mlsanity.com/paper/2302.00704/) (2023)
- [(Implicit) Ensembles of Ensembles: Epistemic Uncertainty Collapse in Large Models](https://mlsanity.com/paper/2409.02628/) (2024)
- [Model-based Lifelong Reinforcement Learning with Bayesian Exploration](https://mlsanity.com/paper/2210.11579/) (2022)

## Abstract (arXiv)

Effective uncertainty quantification is important for training modern predictive models with limited data, enhancing both accuracy and robustness. While Bayesian methods are effective for this purpose, they can be challenging to scale. When employing approximate Bayesian inference, ensuring the quality of samples from the posterior distribution in a computationally efficient manner is essential. This paper addresses the estimation of the Bayesian posterior to generate diverse samples by approximating the gradient flow of the Kullback-Leibler (KL) divergence and the cross entropy of the target approximation under the metric induced by the Stein Operator. It presents empirical evaluations on classification tasks to assess the method's performance and discuss its effectiveness for Model-Based Reinforcement Learning that uses uncertainty-aware network dynamics models.