# DiSProD: Differentiable Symbolic Propagation of Distributions for Planning

arXiv: https://arxiv.org/abs/2302.01491 · HTML: https://mlsanity.com/paper/2302.01491/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 61 references that are in the map.
- First posted on arXiv 3 Feb 2023.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Integrated Task and Motion Planning](https://mlsanity.com/paper/2010.01083/) (2020)
- [Learning Continuous Control Policies by Stochastic Value Gradients](https://mlsanity.com/paper/1510.09142/) (2015)
- [Value Iteration Networks](https://mlsanity.com/paper/1602.02867/) (2016)
- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Efficient Model-Based Reinforcement Learning through Optimistic Policy Search and Planning](https://mlsanity.com/paper/2006.08684/) (2020)
- [PIPPS: Flexible Model-Based Policy Search Robust to the Curse of Chaos](https://mlsanity.com/paper/1902.01240/) (2019)
- [Data-Efficient Reinforcement Learning with Probabilistic Model Predictive Control](https://mlsanity.com/paper/1706.06491/) (2017)
- [Learning and Policy Search in Stochastic Dynamical Systems with Bayesian Neural Networks](https://mlsanity.com/paper/1605.07127/) (2016)
- [An Online Learning Approach to Model Predictive Control](https://mlsanity.com/paper/1902.08967/) (2019)
- [Stein Variational Model Predictive Control](https://mlsanity.com/paper/2011.07641/) (2020)
- [Towards Target-Driven Visual Navigation in Indoor Scenes via Generative Imitation Learning](https://mlsanity.com/paper/2009.14509/) (2020)
- [Model-Based Policy Search Using Monte Carlo Gradient Estimation with Real Systems Application](https://mlsanity.com/paper/2101.12115/) (2021)
- [Dual Online Stein Variational Inference for Control and Dynamics](https://mlsanity.com/paper/2103.12890/) (2021)
- [Autonomous Navigation of AGVs in Unknown Cluttered Environments: log-MPPI Control Strategy](https://mlsanity.com/paper/2203.16599/) (2022)
- [Admissible Abstractions for Near-optimal Task and Motion Planning](https://mlsanity.com/paper/1806.00805/) (2018)

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

- [Novelty Adaptation Through Hybrid Large Language Model (LLM)-Symbolic Planning and LLM-guided Reinforcement Learning](https://mlsanity.com/paper/2603.11351/) (2026)
- [Improving planning and MBRL with temporally-extended actions](https://mlsanity.com/paper/2505.15754/) (2025)

## Abstract (arXiv)

The paper introduces DiSProD, an online planner developed for environments with probabilistic transitions in continuous state and action spaces. DiSProD builds a symbolic graph that captures the distribution of future trajectories, conditioned on a given policy, using independence assumptions and approximate propagation of distributions. The symbolic graph provides a differentiable representation of the policy's value, enabling efficient gradient-based optimization for long-horizon search. The propagation of approximate distributions can be seen as an aggregation of many trajectories, making it well-suited for dealing with sparse rewards and stochastic environments. An extensive experimental evaluation compares DiSProD to state-of-the-art planners in discrete-time planning and real-time control of robotic systems. The proposed method improves over existing planners in handling stochastic environments, sensitivity to search depth, sparsity of rewards, and large action spaces. Additional real-world experiments demonstrate that DiSProD can control ground vehicles and surface vessels to successfully navigate around obstacles.