# Diverse Projection Ensembles for Distributional Reinforcement Learning

arXiv: https://arxiv.org/abs/2306.07124 · HTML: https://mlsanity.com/paper/2306.07124/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 54 references that are in the map.
- First posted on arXiv 12 Jun 2023.

## Builds on (most cited first, 30 of 37)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Is Q-learning Provably Efficient?](https://mlsanity.com/paper/1807.03765/) (2018)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Randomized Ensembled Double Q-Learning: Learning Fast Without a Model](https://mlsanity.com/paper/2101.05982/) (2021)
- [Large-Scale Study of Curiosity-Driven Learning](https://mlsanity.com/paper/1808.04355/) (2018)
- [ViZDoom: A Doom-based AI Research Platform for Visual Reinforcement Learning](https://mlsanity.com/paper/1605.02097/) (2016)
- [Deep Reinforcement Learning and the Deadly Triad](https://mlsanity.com/paper/1812.02648/) (2018)
- [Controlling Overestimation Bias with Truncated Mixture of Continuous Distributional Quantile Critics](https://mlsanity.com/paper/2005.04269/) (2020)
- [Deep Exploration via Randomized Value Functions](https://mlsanity.com/paper/1703.07608/) (2017)
- [Behaviour Suite for Reinforcement Learning](https://mlsanity.com/paper/1908.03568/) (2019)
- [Fully Parameterized Quantile Function for Distributional Reinforcement Learning](https://mlsanity.com/paper/1911.02140/) (2019)
- [The Uncertainty Bellman Equation and Exploration](https://mlsanity.com/paper/1709.05380/) (2017)
- [Estimating Risk and Uncertainty in Deep Reinforcement Learning](https://mlsanity.com/paper/1905.09638/) (2019)
- [An Analysis of Categorical Distributional Reinforcement Learning](https://mlsanity.com/paper/1802.08163/) (2018)
- [Statistics and Samples in Distributional Reinforcement Learning](https://mlsanity.com/paper/1902.08102/) (2019)
- [Distributional Reinforcement Learning for Efficient Exploration](https://mlsanity.com/paper/1905.06125/) (2019)
- [Information-Directed Exploration for Deep Reinforcement Learning](https://mlsanity.com/paper/1812.07544/) (2018)
- [Successor Uncertainties: Exploration and Uncertainty in Temporal Difference Learning](https://mlsanity.com/paper/1810.06530/) (2018)
- [On the Importance of Exploration for Generalization in Reinforcement Learning](https://mlsanity.com/paper/2306.05483/) (2023)

## Built on by (most cited first, 8 of 8)

- [Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'](https://mlsanity.com/paper/2505.04950/) (2025)
- [Contextual Similarity Distillation: Ensemble Uncertainties with a Single Model](https://mlsanity.com/paper/2503.11339/) (2025)
- [Off-Policy Safe Reinforcement Learning with Constrained Optimistic Exploration](https://mlsanity.com/paper/2603.23889/) (2026)
- [Training on Irrelevant States Implies Data Augmentation: Generalization in Contextual MDPs](https://mlsanity.com/paper/2410.03565/) (2024)
- [Universal Value-Function Uncertainties](https://mlsanity.com/paper/2505.21119/) (2025)
- [DVPO: Distributional Value Modeling-based Policy Optimization for LLM Post-Training](https://mlsanity.com/paper/2512.03847/) (2025)
- [On the Equivalence of Random Network Distillation, Deep Ensembles, and Bayesian Inference](https://mlsanity.com/paper/2602.19964/) (2026)
- [Auditing the Risk Claims of Distributional Reinforcement Learning](https://mlsanity.com/paper/2607.11607/) (2026)

## Abstract (arXiv)

In contrast to classical reinforcement learning (RL), distributional RL algorithms aim to learn the distribution of returns rather than their expected value. Since the nature of the return distribution is generally unknown a priori or arbitrarily complex, a common approach finds approximations within a set of representable, parametric distributions. Typically, this involves a projection of the unconstrained distribution onto the set of simplified distributions. We argue that this projection step entails a strong inductive bias when coupled with neural networks and gradient descent, thereby profoundly impacting the generalization behavior of learned models. In order to facilitate reliable uncertainty estimation through diversity, we study the combination of several different projections and representations in a distributional ensemble. We establish theoretical properties of such projection ensembles and derive an algorithm that uses ensemble disagreement, measured by the average 1-Wasserstein distance, as a bonus for deep exploration. We evaluate our algorithm on the behavior suite benchmark and VizDoom and find that diverse projection ensembles lead to significant performance improvements over existing methods on a variety of tasks with the most pronounced gains in directed exploration problems.