# Uncoupled Learning of Differential Stackelberg Equilibria with Commitments

arXiv: https://arxiv.org/abs/2302.03438 · HTML: https://mlsanity.com/paper/2302.03438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 56 references that are in the map.
- First posted on arXiv 7 Feb 2023.

## Builds on (most cited first, 24 of 24)

- [Learning with Opponent-Learning Awareness](https://mlsanity.com/paper/1709.04326/) (2017)
- [Bilevel Optimization: Convergence Analysis and Enhanced Design](https://mlsanity.com/paper/2010.07962/) (2020)
- [Unrolled Generative Adversarial Networks](https://mlsanity.com/paper/1611.02163/) (2016)
- [On the Iteration Complexity of Hypergradient Computation](https://mlsanity.com/paper/2006.16218/) (2020)
- [Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods](https://mlsanity.com/paper/1902.08297/) (2019)
- [Cycles in adversarial regularized learning](https://mlsanity.com/paper/1709.02738/) (2017)
- [The Mechanics of n-Player Differentiable Games](https://mlsanity.com/paper/1802.05642/) (2018)
- [The Numerics of GANs](https://mlsanity.com/paper/1705.10461/) (2017)
- [BOME! Bilevel Optimization Made Easy: A Simple First-Order Approach](https://mlsanity.com/paper/2209.08709/) (2022)
- [Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyond](https://mlsanity.com/paper/2110.00455/) (2021)
- [Who Leads and Who Follows in Strategic Classification?](https://mlsanity.com/paper/2106.12529/) (2021)
- [Social diversity and social preferences in mixed-motive reinforcement learning](https://mlsanity.com/paper/2002.02325/) (2020)
- [Hierarchical Game-Theoretic Planning for Autonomous Vehicles](https://mlsanity.com/paper/1810.05766/) (2018)
- [Model-Free Opponent Shaping](https://mlsanity.com/paper/2205.01447/) (2022)
- [Differentiable Game Mechanics](https://mlsanity.com/paper/1905.04926/) (2019)
- [Sample-Efficient Learning of Stackelberg Equilibria in General-Sum Games](https://mlsanity.com/paper/2102.11494/) (2021)
- [COLA: Consistent Learning with Opponent-Learning Awareness](https://mlsanity.com/paper/2203.04098/) (2022)
- [On Finding Local Nash Equilibria (and Only Local Nash Equilibria) in Zero-Sum Games](https://mlsanity.com/paper/1901.00838/) (2019)
- [Competitive Gradient Descent](https://mlsanity.com/paper/1905.12103/) (2019)
- [Convergence of Learning Dynamics in Stackelberg Games](https://mlsanity.com/paper/1906.01217/) (2019)
- [On the Characterization of Local Nash Equilibria in Continuous Games](https://mlsanity.com/paper/1411.2168/) (2014)
- [Game-Theoretic Modeling of Human Adaptation in Human-Robot Collaboration](https://mlsanity.com/paper/1701.07790/) (2017)
- [Stackelberg Actor-Critic: Game-Theoretic Reinforcement Learning Algorithms](https://mlsanity.com/paper/2109.12286/) (2021)
- [Best-Response Bayesian Reinforcement Learning with Bayes-adaptive POMDPs for Centaurs](https://mlsanity.com/paper/2204.01160/) (2022)

## Abstract (arXiv)

In multi-agent problems requiring a high degree of cooperation, success often depends on the ability of the agents to adapt to each other's behavior. A natural solution concept in such settings is the Stackelberg equilibrium, in which the ``leader'' agent selects the strategy that maximizes its own payoff given that the ``follower'' agent will choose their best response to this strategy. Recent work has extended this solution concept to two-player differentiable games, such as those arising from multi-agent deep reinforcement learning, in the form of the textitdifferential Stackelberg equilibrium. While this previous work has presented learning dynamics which converge to such equilibria, these dynamics are ``coupled'' in the sense that the learning updates for the leader's strategy require some information about the follower's payoff function. As such, these methods cannot be applied to truly decentralised multi-agent settings, particularly ad hoc cooperation, where each agent only has access to its own payoff function. In this work we present ``uncoupled'' learning dynamics based on zeroth-order gradient estimators, in which each agent's strategy update depends only on their observations of the other's behavior. We analyze the convergence of these dynamics in general-sum games, and prove that they converge to differential Stackelberg equilibria under the same conditions as previous coupled methods. Furthermore, we present an online mechanism by which symmetric learners can negotiate leader-follower roles. We conclude with a discussion of the implications of our work for multi-agent reinforcement learning and ad hoc collaboration more generally.