# Risk-Averse Trajectory Optimization via Sample Average Approximation

arXiv: https://arxiv.org/abs/2307.03167 · HTML: https://mlsanity.com/paper/2307.03167/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2023.

## Built on by (most cited first, 4 of 4)

- [The Role of Predictive Uncertainty and Diversity in Embodied AI and Robot Learning](https://mlsanity.com/paper/2405.03164/) (2024)
- [MMD-OPT : Maximum Mean Discrepancy Based Sample Efficient Collision Risk Minimization for Autonomous Driving](https://mlsanity.com/paper/2412.09121/) (2024)
- [Safely Learning Controlled Stochastic Dynamics](https://mlsanity.com/paper/2506.02754/) (2025)
- [JPPD: Joint Prediction_Planning Diffusion with Differentiable Safety Guidance for Dynamic Obstacle Avoidance in Intelligent Transportation Systems](https://mlsanity.com/paper/2606.20686/) (2026)

## Abstract (arXiv)

Trajectory optimization under uncertainty underpins a wide range of applications in robotics. However, existing methods are limited in terms of reasoning about sources of epistemic and aleatoric uncertainty, space and time correlations, nonlinear dynamics, and non-convex constraints. In this work, we first introduce a continuous-time planning formulation with an average-value-at-risk constraint over the entire planning horizon. Then, we propose a sample-based approximation that unlocks an efficient and general-purpose algorithm for risk-averse trajectory optimization. We prove that the method is asymptotically optimal and derive finite-sample error bounds. Simulations demonstrate the high speed and reliability of the approach on problems with stochasticity in nonlinear dynamics, obstacle fields, interactions, and terrain parameters.