# Online Stackelberg Optimization via Nonlinear Control

arXiv: https://arxiv.org/abs/2406.18805 · HTML: https://mlsanity.com/paper/2406.18805/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 59 references that are in the map.
- First posted on arXiv 27 Jun 2024.

## Builds on (most cited first, 30 of 32)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Stochastic Optimization for Performative Prediction](https://mlsanity.com/paper/2006.06887/) (2020)
- [Online Control with Adversarial Disturbances](https://mlsanity.com/paper/1902.08721/) (2019)
- [Information Theoretic Regret Bounds for Online Nonlinear Control](https://mlsanity.com/paper/2006.12466/) (2020)
- [Improper Learning for Non-Stochastic Control](https://mlsanity.com/paper/2001.09254/) (2020)
- [Corruption-robust exploration in episodic reinforcement learning](https://mlsanity.com/paper/1911.08689/) (2019)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [Who Leads and Who Follows in Strategic Classification?](https://mlsanity.com/paper/2106.12529/) (2021)
- [Strategizing against No-regret Learners](https://mlsanity.com/paper/1909.13861/) (2019)
- [Selling to a No-Regret Buyer](https://mlsanity.com/paper/1711.09176/) (2017)
- [Near-Optimal No-Regret Learning for Correlated Equilibria in Multi-Player General-Sum Games](https://mlsanity.com/paper/2111.06008/) (2021)
- [Regret Minimization with Performative Feedback](https://mlsanity.com/paper/2202.00628/) (2022)
- [Logarithmic Regret for Online Control](https://mlsanity.com/paper/1909.05062/) (2019)
- [Adaptive Regret for Control of Time-Varying Dynamics](https://mlsanity.com/paper/2007.04393/) (2020)
- [Dynamic Incentive-aware Learning: Robust Pricing in Contextual Auctions](https://mlsanity.com/paper/2002.11137/) (2020)
- [Online learning in MDPs with linear function approximation and bandit feedback](https://mlsanity.com/paper/2007.01612/) (2020)
- [Preference Dynamics Under Personalized Recommendations](https://mlsanity.com/paper/2205.13026/) (2022)
- [Learning in Auctions: Regret is Hard, Envy is Easy](https://mlsanity.com/paper/1511.01411/) (2015)
- [Learning Simple Auctions](https://mlsanity.com/paper/1604.03171/) (2016)
- [Watch and Learn: Optimizing from Revealed Preferences Feedback](https://mlsanity.com/paper/1504.01033/) (2015)
- [Polarization in Geometric Opinion Dynamics](https://mlsanity.com/paper/2106.12459/) (2021)
- [On the Convergence of No-Regret Learning Dynamics in Time-Varying Games](https://mlsanity.com/paper/2301.11241/) (2023)
- [Diversified Recommendations for Agents with Adaptive Preferences](https://mlsanity.com/paper/2210.07773/) (2022)
- [A Geometric Model of Opinion Polarization](https://mlsanity.com/paper/1910.05274/) (2019)
- [Online Learning for Measuring Incentive Compatibility in Ad Auctions](https://mlsanity.com/paper/1901.06808/) (2019)
- [Online Convex Optimization Against Adversaries with Memory and Application to Statistical Arbitrage](https://mlsanity.com/paper/1302.6937/) (2013)
- [An online learning approach to dynamic pricing for demand response](https://mlsanity.com/paper/1404.1325/) (2014)
- [Local controllability does imply global controllability](https://mlsanity.com/paper/2110.06631/) (2021)

## Built on by (most cited first, 1 of 1)

- [Learning Local Stackelberg Equilibria from Repeated Interactions with a Learning Agent](https://mlsanity.com/paper/2510.22471/) (2025)

## Abstract (arXiv)

In repeated interaction problems with adaptive agents, our objective often requires anticipating and optimizing over the space of possible agent responses. We show that many problems of this form can be cast as instances of online (nonlinear) control which satisfy textitlocal controllability, with convex losses over a bounded state space which encodes agent behavior, and we introduce a unified algorithmic framework for tractable regret minimization in such cases. When the instance dynamics are known but otherwise arbitrary, we obtain oracle-efficient O(√T) regret by reduction to online convex optimization, which can be made computationally efficient if dynamics are locally textitaction-linear. In the presence of adversarial disturbances to the state, we give tight bounds in terms of either the cumulative or per-round disturbance magnitude (for textitstrongly or textitweakly locally controllable dynamics, respectively). Additionally, we give sublinear regret results for the cases of unknown locally action-linear dynamics as well as for the bandit feedback setting. Finally, we demonstrate applications of our framework to well-studied problems including performative prediction, recommendations for adaptive agents, adaptive pricing of real-valued goods, and repeated gameplay against no-regret learners, directly yielding extensions beyond prior results in each case.