# Learning in complex action spaces without policy gradients

arXiv: https://arxiv.org/abs/2410.06317 · HTML: https://mlsanity.com/paper/2410.06317/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 54 of its 84 references that are in the map.
- First posted on arXiv 8 Oct 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 30 of 54)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Rainbow: Combining Improvements in Deep Reinforcement Learning](https://mlsanity.com/paper/1710.02298/) (2017)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [QT-Opt: Scalable Deep Reinforcement Learning for Vision-Based Robotic Manipulation](https://mlsanity.com/paper/1806.10293/) (2018)
- [Solving Rubik's Cube with a Robot Hand](https://mlsanity.com/paper/1910.07113/) (2019)
- [Learning to Communicate with Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1605.06676/) (2016)
- [Value-Decomposition Networks For Cooperative Multi-Agent Learning](https://mlsanity.com/paper/1706.05296/) (2017)
- [Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2003.08839/) (2020)
- [Maximum a Posteriori Policy Optimisation](https://mlsanity.com/paper/1806.06920/) (2018)
- [Revisiting the Arcade Learning Environment: Evaluation Protocols and Open Problems for General Agents](https://mlsanity.com/paper/1709.06009/) (2017)
- [Distributed Distributional Deterministic Policy Gradients](https://mlsanity.com/paper/1804.08617/) (2018)
- [Equivalence Between Policy Gradients and Soft Q-Learning](https://mlsanity.com/paper/1704.06440/) (2017)
- [Deep Reinforcement Learning in Large Discrete Action Spaces](https://mlsanity.com/paper/1512.07679/) (2015)
- [Continuous Deep Q-Learning with Model-based Acceleration](https://mlsanity.com/paper/1603.00748/) (2016)
- [Bigger, Better, Faster: Human-level Atari with human-level efficiency](https://mlsanity.com/paper/2305.19452/) (2023)
- [Acme: A Research Framework for Distributed Reinforcement Learning](https://mlsanity.com/paper/2006.00979/) (2020)

## Abstract (arXiv)

While conventional wisdom holds that policy gradient methods are better suited to complex action spaces than action-value methods, foundational work has shown that the two paradigms are equivalent in small, finite action spaces (O'Donoghue et al., 2017; Schulman et al., 2017a). This raises the question of why their computational applicability and performance diverge as the complexity of the action space increases. We hypothesize that the apparent superiority of policy gradients in such settings stems not from intrinsic qualities of the paradigm but from universal principles that can also be applied to action-value methods, enabling similar functions. We identify three such principles and provide a framework for incorporating them into action-value methods. To support our hypothesis, we instantiate this framework in what we term QMLE, for Q-learning with maximum likelihood estimation. Our results show that QMLE can be applied to complex action spaces at a computational cost comparable to that of policy gradient methods, all without using policy gradients. Furthermore, QMLE exhibits strong performance on the DeepMind Control Suite, even when compared to state-of-the-art methods such as DMPO and D4PG.