# Learning and Planning in Complex Action Spaces

arXiv: https://arxiv.org/abs/2104.06303 · HTML: https://mlsanity.com/paper/2104.06303/

## Key facts

- Cited by 77 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 52 references that are in the map.
- First posted on arXiv 13 Apr 2021.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [dm_control: Software and Tasks for Continuous Control](https://mlsanity.com/paper/2006.12983/) (2020)
- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [Distributed Distributional Deterministic Policy Gradients](https://mlsanity.com/paper/1804.08617/) (2018)
- [Deep Reinforcement Learning in Large Discrete Action Spaces](https://mlsanity.com/paper/1512.07679/) (2015)
- [Acme: A Research Framework for Distributed Reinforcement Learning](https://mlsanity.com/paper/2006.00979/) (2020)
- [V-MPO: On-Policy Maximum a Posteriori Policy Optimization for Discrete and Continuous Control](https://mlsanity.com/paper/1909.12238/) (2019)
- [An empirical investigation of the challenges of real-world reinforcement learning](https://mlsanity.com/paper/2003.11881/) (2020)
- [Discretizing Continuous Action Space for On-Policy Optimization](https://mlsanity.com/paper/1901.10500/) (2019)
- [Monte-Carlo Tree Search as Regularized Policy Optimization](https://mlsanity.com/paper/2007.12509/) (2020)
- [Relative Entropy Regularized Policy Iteration](https://mlsanity.com/paper/1812.02256/) (2018)
- [Hierarchical visuomotor control of humanoids](https://mlsanity.com/paper/1811.09656/) (2018)
- [Imagined Value Gradients: Model-Based Policy Optimization with Transferable Latent Dynamics Models](https://mlsanity.com/paper/1910.04142/) (2019)
- [A0C: Alpha Zero in Continuous Action Space](https://mlsanity.com/paper/1805.09613/) (2018)
- [Information Theoretic Model Predictive Q-Learning](https://mlsanity.com/paper/2001.02153/) (2019)
- [An operator view of policy gradient methods](https://mlsanity.com/paper/2006.11266/) (2020)
- [Local Search for Policy Iteration in Continuous Control](https://mlsanity.com/paper/2010.05545/) (2020)
- [Dream and Search to Control: Latent Space Planning for Continuous Control](https://mlsanity.com/paper/2010.09832/) (2020)

## Built on by (most cited first, 30 of 77)

- [TD-MPC2: Scalable, Robust World Models for Continuous Control](https://mlsanity.com/paper/2310.16828/) (2023)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [Mastering Atari Games with Limited Data](https://mlsanity.com/paper/2111.00210/) (2021)
- [EfficientZero V2: Mastering Discrete and Continuous Control with Limited Data](https://mlsanity.com/paper/2403.00564/) (2024)
- [Dynamic Search for Inference-Time Alignment in Diffusion Models](https://mlsanity.com/paper/2503.02039/) (2025)
- [Quantum Circuit Optimization with AlphaTensor](https://mlsanity.com/paper/2402.14396/) (2024)
- [Learning Large Neighborhood Search Policy for Integer Programming](https://mlsanity.com/paper/2111.03466/) (2021)
- [Procedural Generalization by Planning with Self-Supervised World Models](https://mlsanity.com/paper/2111.01587/) (2021)
- [A Consciousness-Inspired Planning Agent for Model-Based Reinforcement Learning](https://mlsanity.com/paper/2106.02097/) (2021)
- [A Survey on Self-play Methods in Reinforcement Learning](https://mlsanity.com/paper/2408.01072/) (2024)
- [The Free Energy Principle for Perception and Action: A Deep Learning Perspective](https://mlsanity.com/paper/2207.06415/) (2022)
- [floq: Training Critics via Flow-Matching for Scaling Compute in Value-Based RL](https://mlsanity.com/paper/2509.06863/) (2025)
- [Planning for Sample Efficient Imitation Learning](https://mlsanity.com/paper/2210.09598/) (2022)
- [LightZero: A Unified Benchmark for Monte Carlo Tree Search in General Sequential Decision Scenarios](https://mlsanity.com/paper/2310.08348/) (2023)
- [Scalable Online Planning via Reinforcement Learning Fine-Tuning](https://mlsanity.com/paper/2109.15316/) (2021)
- [Evaluating model-based planning and planner amortization for continuous control](https://mlsanity.com/paper/2110.03363/) (2021)
- [Dynamic Model Predictive Shielding for Provably Safe Reinforcement Learning](https://mlsanity.com/paper/2405.13863/) (2024)
- [BetaZero: Belief-State Planning for Long-Horizon POMDPs using Learned Approximations](https://mlsanity.com/paper/2306.00249/) (2023)
- [MiniZero: Comparative Analysis of AlphaZero and MuZero on Go, Othello, and Atari Games](https://mlsanity.com/paper/2310.11305/) (2023)
- [Improving Pre-Trained Vision-Language-Action Policies with Model-Based Search](https://mlsanity.com/paper/2508.12211/) (2025)
- [UniZero: Generalized and Efficient Planning with Scalable Latent World Models](https://mlsanity.com/paper/2406.10667/) (2024)
- [Bayes Adaptive Monte Carlo Tree Search for Offline Model-based Reinforcement Learning](https://mlsanity.com/paper/2410.11234/) (2024)
- [Guided Search Strategies in Non-Serializable Environments with Applications to Software Engineering Agents](https://mlsanity.com/paper/2505.13652/) (2025)
- [AlphaStar Unplugged: Large-Scale Offline Reinforcement Learning](https://mlsanity.com/paper/2308.03526/) (2023)
- [Efficient Multi-agent Reinforcement Learning by Planning](https://mlsanity.com/paper/2405.11778/) (2024)
- [What model does MuZero learn?](https://mlsanity.com/paper/2306.00840/) (2023)
- [Controllable Graph Generation with Diffusion Models via Inference-Time Tree Search Guidance](https://mlsanity.com/paper/2510.10402/) (2025)
- [Efficient Planning in Combinatorial Action Spaces with Applications to Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2302.04376/) (2023)
- [Improving and Benchmarking Offline Reinforcement Learning Algorithms](https://mlsanity.com/paper/2306.00972/) (2023)
- [Policy-shaped prediction: avoiding distractions in model-based reinforcement learning](https://mlsanity.com/paper/2412.05766/) (2024)

## Abstract (arXiv)

Many important real-world problems have action spaces that are high-dimensional, continuous or both, making full enumeration of all possible actions infeasible. Instead, only small subsets of actions can be sampled for the purpose of policy evaluation and improvement. In this paper, we propose a general framework to reason in a principled way about policy evaluation and improvement over such sampled action subsets. This sample-based policy iteration framework can in principle be applied to any reinforcement learning algorithm based upon policy iteration. Concretely, we propose Sampled MuZero, an extension of the MuZero algorithm that is able to learn in domains with arbitrarily complex action spaces by planning over sampled actions. We demonstrate this approach on the classical board game of Go and on two continuous control benchmark domains: DeepMind Control Suite and Real-World RL Suite.