# Magnetic Field-Based Reward Shaping for Goal-Conditioned Reinforcement Learning

arXiv: https://arxiv.org/abs/2307.08033 · HTML: https://mlsanity.com/paper/2307.08033/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 69 references that are in the map.
- First posted on arXiv 16 Jul 2023.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [Benchmarking Deep Reinforcement Learning for Continuous Control](https://mlsanity.com/paper/1604.06778/) (2016)
- [Multi-Goal Reinforcement Learning: Challenging Robotics Environments and Request for Research](https://mlsanity.com/paper/1802.09464/) (2018)
- [Learning Continuous Control Policies by Stochastic Value Gradients](https://mlsanity.com/paper/1510.09142/) (2015)
- [Goal-conditioned Imitation Learning](https://mlsanity.com/paper/1906.05838/) (2019)
- [Goal-Conditioned Reinforcement Learning: Problems and Solutions](https://mlsanity.com/paper/2201.08299/) (2022)
- [Unsupervised Control Through Non-Parametric Discriminative Rewards](https://mlsanity.com/paper/1811.11359/) (2018)
- [Maximum Entropy Gain Exploration for Long Horizon Multi-goal Reinforcement Learning](https://mlsanity.com/paper/2007.02832/) (2020)
- [Automatic Curriculum Learning through Value Disagreement](https://mlsanity.com/paper/2006.09641/) (2020)
- [The Laplacian in RL: Learning Representations with Efficient Approximations](https://mlsanity.com/paper/1810.04586/) (2018)
- [Keeping Your Distance: Solving Sparse Reward Tasks Using Self-Balancing Shaped Rewards](https://mlsanity.com/paper/1911.01417/) (2019)
- [Dynamical Distance Learning for Semi-Supervised and Unsupervised Skill Discovery](https://mlsanity.com/paper/1907.08225/) (2019)
- [Learning Actionable Representations with Goal-Conditioned Policies](https://mlsanity.com/paper/1811.07819/) (2018)
- [Adversarial Intrinsic Motivation for Reinforcement Learning](https://mlsanity.com/paper/2105.13345/) (2021)
- [Lifelong Incremental Reinforcement Learning with Online Bayesian Inference](https://mlsanity.com/paper/2007.14196/) (2020)
- [Prioritized Experience-based Reinforcement Learning with Human Guidance for Autonomous Driving](https://mlsanity.com/paper/2109.12516/) (2021)
- [Reinforcement Learning and Deep Learning based Lateral Control for Autonomous Driving](https://mlsanity.com/paper/1810.12778/) (2018)
- [A Dirichlet Process Mixture of Robust Task Models for Scalable Lifelong Reinforcement Learning](https://mlsanity.com/paper/2205.10787/) (2022)
- [Fidelity-based Probabilistic Q-learning for Control of Quantum Systems](https://mlsanity.com/paper/1806.03145/) (2018)
- [Imaginary Hindsight Experience Replay: Curious Model-based Learning for Sparse Reward Tasks](https://mlsanity.com/paper/2110.02414/) (2021)

## Built on by (most cited first, 2 of 2)

- [Building Open-Ended Embodied Agent via Language-Policy Bidirectional Adaptation](https://mlsanity.com/paper/2401.00006/) (2023)
- [Hybrid Energy-Aware Reward Shaping: A Unified Lightweight Physics-Guided Methodology for Policy Optimization](https://mlsanity.com/paper/2603.11600/) (2026)

## Abstract (arXiv)

Goal-conditioned reinforcement learning (RL) is an interesting extension of the traditional RL framework, where the dynamic environment and reward sparsity can cause conventional learning algorithms to fail. Reward shaping is a practical approach to improving sample efficiency by embedding human domain knowledge into the learning process. Existing reward shaping methods for goal-conditioned RL are typically built on distance metrics with a linear and isotropic distribution, which may fail to provide sufficient information about the ever-changing environment with high complexity. This paper proposes a novel magnetic field-based reward shaping (MFRS) method for goal-conditioned RL tasks with dynamic target and obstacles. Inspired by the physical properties of magnets, we consider the target and obstacles as permanent magnets and establish the reward function according to the intensity values of the magnetic field generated by these magnets. The nonlinear and anisotropic distribution of the magnetic field intensity can provide more accessible and conducive information about the optimization landscape, thus introducing a more sophisticated magnetic reward compared to the distance-based setting. Further, we transform our magnetic reward to the form of potential-based reward shaping by learning a secondary potential function concurrently to ensure the optimal policy invariance of our method. Experiments results in both simulated and real-world robotic manipulation tasks demonstrate that MFRS outperforms relevant existing methods and effectively improves the sample efficiency of RL algorithms in goal-conditioned tasks with various dynamics of the target and obstacles.