# Action Shaping: Policies Absorb What They Can Express

arXiv: https://arxiv.org/abs/2609.32752 · HTML: https://mlsanity.com/paper/2609.32752/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 56 of its 63 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 30 of 56)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Going deeper with Image Transformers](https://mlsanity.com/paper/2103.17239/) (2021)
- [RepVGG: Making VGG-style ConvNets Great Again](https://mlsanity.com/paper/2101.03697/) (2021)
- [Randomized Ensembled Double Q-Learning: Learning Fast Without a Model](https://mlsanity.com/paper/2101.05982/) (2021)
- [On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization](https://mlsanity.com/paper/1802.06509/) (2018)
- [Residual Reinforcement Learning for Robot Control](https://mlsanity.com/paper/1812.03201/) (2018)
- [ReZero is All You Need: Fast Convergence at Large Depth](https://mlsanity.com/paper/2003.04887/) (2020)
- [Data-Driven Sparse Structure Selection for Deep Neural Networks](https://mlsanity.com/paper/1707.01213/) (2017)
- [Algorithmic Regularization in Learning Deep Homogeneous Models: Layers are Automatically Balanced](https://mlsanity.com/paper/1806.00900/) (2018)
- [Residual Policy Learning](https://mlsanity.com/paper/1812.06298/) (2018)
- [Implicit regularization for deep neural networks driven by an Ornstein-Uhlenbeck like process](https://mlsanity.com/paper/1904.09080/) (2019)
- [Label Noise SGD Provably Prefers Flat Global Minimizers](https://mlsanity.com/paper/2106.06530/) (2021)
- [Jump-Start Reinforcement Learning](https://mlsanity.com/paper/2204.02372/) (2022)
- [Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity](https://mlsanity.com/paper/2106.09524/) (2021)
- [What Happens after SGD Reaches Zero Loss? --A Mathematical Framework](https://mlsanity.com/paper/2110.06914/) (2021)
- [Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics](https://mlsanity.com/paper/2012.04728/) (2020)
- [SKILL0: In-Context Agentic Reinforcement Learning for Skill Internalization](https://mlsanity.com/paper/2604.02268/) (2026)
- [Self-Improving Vision-Language-Action Models with Data Generation via Residual RL](https://mlsanity.com/paper/2511.00091/) (2025)
- [Residual Off-Policy RL for Finetuning Behavior Cloning Policies](https://mlsanity.com/paper/2509.19301/) (2025)
- [ExpandNets: Linear Over-parameterization to Train Compact Convolutional Networks](https://mlsanity.com/paper/1811.10495/) (2018)
- [Action Space Shaping in Deep Reinforcement Learning](https://mlsanity.com/paper/2004.00980/) (2020)
- [Stochastic Collapse: How Gradient Noise Attracts SGD Dynamics Towards Simpler Subnetworks](https://mlsanity.com/paper/2306.04251/) (2023)
- [Privileged Sensing Scaffolds Reinforcement Learning](https://mlsanity.com/paper/2405.14853/) (2024)
- [Revisiting Discrete Soft Actor-Critic](https://mlsanity.com/paper/2209.10081/) (2022)
- [DecAP: Decaying Action Priors for Accelerated Imitation Learning of Torque-Based Legged Locomotion Policies](https://mlsanity.com/paper/2310.05714/) (2023)
- [RaceMOP: Mapless Online Path Planning for Multi-Agent Autonomous Racing using Residual Policy Learning](https://mlsanity.com/paper/2403.07129/) (2024)

## Abstract (arXiv)

Reward shaping has a theorem: a potential-based term can be removed without changing the optimal policy. The same practice on the action channel, an offset added in training and dropped at deployment, has no theorem. Nothing cancels an action offset, so the correction is kept at deployment or removed without a guarantee. We call it action shaping and state its principle. A trainable policy absorbs an offset its own output layer can reproduce exactly, which is what we mean by express; what is absorbed can be removed with the return intact. Its minimal instance is a zero-initialized linear head behind a learnable gate, added to an actor that trains through a learned action-value function, with no penalty or schedule. The gate rises and then falls on its own, for deterministic and stochastic actors alike, and on 20 tasks removing the head costs almost nothing. The condition is exact reproduction, not capacity: a nonlinear head with more parameters is not absorbed, and in a paired control, one linear path added to a nonlinear base head restores absorption. Exact reproduction gives the loss a flat direction that gradient noise drifts along, and the offset's amplitude indicates, before removal, what dropping the head will cost. Action shaping thus gains the counterpart of the shaping theorem, a condition for absorption, together with the mechanism behind it and a diagnostic that reads it. Policies absorb what they can express, and only that.