# Risk-Averse Stochastic Shortest Path Planning

arXiv: https://arxiv.org/abs/2103.14727 · HTML: https://mlsanity.com/paper/2103.14727/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 52 references that are in the map.
- First posted on arXiv 26 Mar 2021.

## Builds on (most cited first, 16 of 16)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [Algorithms for CVaR Optimization in MDPs](https://mlsanity.com/paper/1406.3339/) (2014)
- [How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Robotics](https://mlsanity.com/paper/1710.11040/) (2017)
- [Disciplined Convex-Concave Programming](https://mlsanity.com/paper/1604.02639/) (2016)
- [STEP: Stochastic Traversability Evaluation and Planning for Risk-Aware Off-road Navigation](https://mlsanity.com/paper/2103.02828/) (2021)
- [Policy Gradients for CVaR-Constrained MDPs](https://mlsanity.com/paper/1405.2690/) (2014)
- [A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems](https://mlsanity.com/paper/1902.11277/) (2019)
- [Constrained Risk-Averse Markov Decision Processes](https://mlsanity.com/paper/2012.02423/) (2020)
- [Risk-Averse Planning Under Uncertainty](https://mlsanity.com/paper/1909.12499/) (2019)
- [Stochastic Finite State Control of POMDPs with LTL Specifications](https://mlsanity.com/paper/2001.07679/) (2020)
- [Risk Aversion in Finite Markov Decision Processes Using Total Cost Criteria and Average Value at Risk](https://mlsanity.com/paper/1602.05130/) (2016)
- [Risk-Sensitive Motion Planning using Entropic Value-at-Risk](https://mlsanity.com/paper/2011.11211/) (2020)
- [A Framework for Time-Consistent, Risk-Sensitive Model Predictive Control: Theory and Algorithms](https://mlsanity.com/paper/1703.01029/) (2017)
- [Portfolio Optimization with Entropic Value-at-Risk](https://mlsanity.com/paper/1708.05713/) (2017)

## Built on by (most cited first, 8 of 8)

- [Risk-averse Total-reward MDPs with ERM and EVaR](https://mlsanity.com/paper/2408.17286/) (2024)
- [Sample-Based Bounds for Coherent Risk Measures: Applications to Policy Synthesis and Verification](https://mlsanity.com/paper/2204.09833/) (2022)
- [Risk-Averse Decision Making Under Uncertainty](https://mlsanity.com/paper/2109.04082/) (2021)
- [Risk-Sensitive Agent Compositions](https://mlsanity.com/paper/2506.04632/) (2025)
- [Simplification of Risk Averse POMDPs with Performance Guarantees](https://mlsanity.com/paper/2406.03000/) (2024)
- [Robust Stochastic Shortest-Path Planning via Risk-Sensitive Incremental Sampling](https://mlsanity.com/paper/2408.08668/) (2024)
- [Risk-Averse Total-Reward Reinforcement Learning](https://mlsanity.com/paper/2506.21683/) (2025)
- [Long-Term Sequential Decision Making under Risk](https://mlsanity.com/paper/2607.19914/) (2026)

## Abstract (arXiv)

We consider the stochastic shortest path planning problem in MDPs, i.e., the problem of designing policies that ensure reaching a goal state from a given initial state with minimum accrued cost. In order to account for rare but important realizations of the system, we consider a nested dynamic coherent risk total cost functional rather than the conventional risk-neutral total expected cost. Under some assumptions, we show that optimal, stationary, Markovian policies exist and can be found via a special Bellman's equation. We propose a computational technique based on difference convex programs (DCPs) to find the associated value functions and therefore the risk-averse policies. A rover navigation MDP is used to illustrate the proposed methodology with conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent risk measures.