# Hindsight Value Function for Variance Reduction in Stochastic Dynamic Environment

arXiv: https://arxiv.org/abs/2107.12216 · HTML: https://mlsanity.com/paper/2107.12216/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 26 Jul 2021.

## Builds on (most cited first, 14 of 14)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Dynamics-Aware Unsupervised Discovery of Skills](https://mlsanity.com/paper/1907.01657/) (2019)
- [CLUB: A Contrastive Log-ratio Upper Bound of Mutual Information](https://mlsanity.com/paper/2006.12013/) (2020)
- [Q-Prop: Sample-Efficient Policy Gradient with An Off-Policy Critic](https://mlsanity.com/paper/1611.02247/) (2016)
- [Variance Reduction for Policy Gradient with Action-Dependent Factorized Baselines](https://mlsanity.com/paper/1803.07246/) (2018)
- [Unsupervised Multi-Target Domain Adaptation: An Information Theoretic Approach](https://mlsanity.com/paper/1810.11547/) (2018)
- [Variance Reduction for Reinforcement Learning in Input-Driven Environments](https://mlsanity.com/paper/1807.02264/) (2018)
- [Novelty Search in Representational Space for Sample Efficient Exploration](https://mlsanity.com/paper/2009.13579/) (2020)

## Built on by (most cited first, 7 of 7)

- [Generalized Decision Transformer for Offline Hindsight Information Matching](https://mlsanity.com/paper/2111.10364/) (2021)
- [Hindsight Learning for MDPs with Exogenous Inputs](https://mlsanity.com/paper/2207.06272/) (2022)
- [Causality-driven Hierarchical Structure Discovery for Reinforcement Learning](https://mlsanity.com/paper/2210.06964/) (2022)
- [Context Shift Reduction for Offline Meta-Reinforcement Learning](https://mlsanity.com/paper/2311.03695/) (2023)
- [Contrastive Modules with Temporal Attention for Multi-Task Reinforcement Learning](https://mlsanity.com/paper/2311.01075/) (2023)
- [Conceptual Reinforcement Learning for Language-Conditioned Tasks](https://mlsanity.com/paper/2303.05069/) (2023)
- [Object-Category Aware Reinforcement Learning](https://mlsanity.com/paper/2210.07802/) (2022)

## Abstract (arXiv)

Policy gradient methods are appealing in deep reinforcement learning but suffer from high variance of gradient estimate. To reduce the variance, the state value function is applied commonly. However, the effect of the state value function becomes limited in stochastic dynamic environments, where the unexpected state dynamics and rewards will increase the variance. In this paper, we propose to replace the state value function with a novel hindsight value function, which leverages the information from the future to reduce the variance of the gradient estimate for stochastic dynamic environments. Particularly, to obtain an ideally unbiased gradient estimate, we propose an information-theoretic approach, which optimizes the embeddings of the future to be independent of previous actions. In our experiments, we apply the proposed hindsight value function in stochastic dynamic environments, including discrete-action environments and continuous-action environments. Compared with the standard state value function, the proposed hindsight value function consistently reduces the variance, stabilizes the training, and improves the eventual policy.