# Learning responsibility allocations for multi-agent interactions: A differentiable optimization approach with control barrier functions

arXiv: https://arxiv.org/abs/2410.07409 · HTML: https://mlsanity.com/paper/2410.07409/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 9 Oct 2024.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Wayformer: Motion Forecasting via Simple & Efficient Attention Networks](https://mlsanity.com/paper/2207.05844/) (2022)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Multimodal Probabilistic Model-Based Planning for Human-Robot Interaction](https://mlsanity.com/paper/1710.09483/) (2017)
- [Multimodal Deep Generative Models for Trajectory Prediction: A Conditional Variational Autoencoder Approach](https://mlsanity.com/paper/2008.03880/) (2020)
- [PORCA: Modeling and Planning for Autonomous Driving among Many Pedestrians](https://mlsanity.com/paper/1805.11833/) (2018)
- [CoBL-Diffusion: Diffusion-Based Conditional Robot Planning in Dynamic Environments Using Control Barrier and Lyapunov Functions](https://mlsanity.com/paper/2406.05309/) (2024)
- [Learning Convex Optimization Control Policies](https://mlsanity.com/paper/1912.09529/) (2019)
- [Social Coordination and Altruism in Autonomous Driving](https://mlsanity.com/paper/2107.00200/) (2021)
- [Cooperative Autonomous Vehicles that Sympathize with Human Drivers](https://mlsanity.com/paper/2107.00898/) (2021)
- [Learning Convex Optimization Models](https://mlsanity.com/paper/2006.04248/) (2020)
- [Courteous Autonomous Cars](https://mlsanity.com/paper/1808.02633/) (2018)
- [Learning Responsibility Allocations for Safe Human-Robot Interaction with Applications to Autonomous Driving](https://mlsanity.com/paper/2303.03504/) (2023)
- [On the Differentiability of the Primal-Dual Interior-Point Method](https://mlsanity.com/paper/2406.11749/) (2024)

## Built on by (most cited first, 3 of 3)

- [Modular Speaker Architecture: A Framework for Sustaining Responsibility and Contextual Integrity in Multi-Agent AI Communication](https://mlsanity.com/paper/2506.01095/) (2025)
- [Learning Probabilistic Responsibility Allocations for Multi-Agent Interactions](https://mlsanity.com/paper/2604.13128/) (2026)
- [Who Bears the Burden? Learning Responsibility for Shared Constraints in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2610.07491/) (2026)

## Abstract (arXiv)

From autonomous driving to package delivery, ensuring safe yet efficient multi-agent interaction is challenging as the interaction dynamics are influenced by hard-to-model factors such as social norms and contextual cues. Understanding these influences can aid in the design and evaluation of socially-aware autonomous agents whose behaviors are aligned with human values. In this work, we seek to codify factors governing safe multi-agent interactions via the lens of responsibility, i.e., an agent's willingness to deviate from their desired control to accommodate safe interaction with others. Specifically, we propose a data-driven modeling approach based on control barrier functions and differentiable optimization that efficiently learns agents' responsibility allocation from data. We demonstrate on synthetic and real-world datasets that we can obtain an interpretable and quantitative understanding of how much agents adjust their behavior to ensure the safety of others given their current environment.