# Understanding Hindsight Goal Relabeling from a Divergence Minimization Perspective

arXiv: https://arxiv.org/abs/2209.13046 · HTML: https://mlsanity.com/paper/2209.13046/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 56 of its 74 references that are in the map.
- First posted on arXiv 26 Sep 2022.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [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)
- [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)
- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [BC-Z: Zero-Shot Task Generalization with Robotic Imitation Learning](https://mlsanity.com/paper/2202.02005/) (2022)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Learning Robust Rewards with Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1710.11248/) (2017)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Overcoming Exploration in Reinforcement Learning with Demonstrations](https://mlsanity.com/paper/1709.10089/) (2017)
- [Learning Latent Plans from Play](https://mlsanity.com/paper/1903.01973/) (2019)
- [Behavior Transformers: Cloning k modes with one stone](https://mlsanity.com/paper/2206.11251/) (2022)
- [Multi-Goal Reinforcement Learning: Challenging Robotics Environments and Request for Research](https://mlsanity.com/paper/1802.09464/) (2018)
- [DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections](https://mlsanity.com/paper/1906.04733/) (2019)
- [Contrastive Learning as Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2206.07568/) (2022)
- [Visual Reinforcement Learning with Imagined Goals](https://mlsanity.com/paper/1807.04742/) (2018)
- [One-Shot Imitation Learning](https://mlsanity.com/paper/1703.07326/) (2017)
- [Language Conditioned Imitation Learning over Unstructured Data](https://mlsanity.com/paper/2005.07648/) (2020)
- [Reverse Curriculum Generation for Reinforcement Learning](https://mlsanity.com/paper/1707.05300/) (2017)
- [IQ-Learn: Inverse soft-Q Learning for Imitation](https://mlsanity.com/paper/2106.12142/) (2021)
- [A Divergence Minimization Perspective on Imitation Learning Methods](https://mlsanity.com/paper/1911.02256/) (2019)
- [AlgaeDICE: Policy Gradient from Arbitrary Experience](https://mlsanity.com/paper/1912.02074/) (2019)
- [Imitation Learning via Off-Policy Distribution Matching](https://mlsanity.com/paper/1912.05032/) (2019)
- [Skew-Fit: State-Covering Self-Supervised Reinforcement Learning](https://mlsanity.com/paper/1903.03698/) (2019)
- [Equivalence Between Policy Gradients and Soft Q-Learning](https://mlsanity.com/paper/1704.06440/) (2017)

## Abstract (arXiv)

Hindsight goal relabeling has become a foundational technique in multi-goal reinforcement learning (RL). The essential idea is that any trajectory can be seen as a sub-optimal demonstration for reaching its final state. Intuitively, learning from those arbitrary demonstrations can be seen as a form of imitation learning (IL). However, the connection between hindsight goal relabeling and imitation learning is not well understood. In this paper, we propose a novel framework to understand hindsight goal relabeling from a divergence minimization perspective. Recasting the goal reaching problem in the IL framework not only allows us to derive several existing methods from first principles, but also provides us with the tools from IL to improve goal reaching algorithms. Experimentally, we find that under hindsight relabeling, Q-learning outperforms behavioral cloning (BC). Yet, a vanilla combination of both hurts performance. Concretely, we see that the BC loss only helps when selectively applied to actions that get the agent closer to the goal according to the Q-function. Our framework also explains the puzzling phenomenon wherein a reward of (-1, 0) results in significantly better performance than a (0, 1) reward for goal reaching.