Efficient iterative linear-quadratic approximations for nonlinear multi-player general-sum differential games

D Fridovich-Keil, E Ratner, L Peters… - … on robotics and …, 2020 - ieeexplore.ieee.org
Many problems in robotics involve multiple decision making agents. To operate efficiently in
such settings, a robot must reason about the impact of its decisions on the behavior of other …

Convergence of gradient methods on bilinear zero-sum games

G Zhang, Y Yu - arXiv preprint arXiv:1908.05699, 2019 - arxiv.org
Min-max formulations have attracted great attention in the ML community due to the rise of
deep generative models and adversarial methods, while understanding the dynamics of …

Global convergence of policy gradient for sequential zero-sum linear quadratic dynamic games

J Bu, LJ Ratliff, M Mesbahi - arXiv preprint arXiv:1911.04672, 2019 - arxiv.org
We propose projection-free sequential algorithms for linear-quadratic dynamics games.
These policy gradient based algorithms are akin to Stackelberg leadership model and can …

Linear lower bounds and conditioning of differentiable games

A Ibrahim, W Azizian, G Gidel… - … conference on machine …, 2020 - proceedings.mlr.press
Recent successes of game-theoretic formulations in ML have caused a resurgence of
research interest in differentiable games. Overwhelmingly, that research focuses on …

Inference-based strategy alignment for general-sum differential games

L Peters, D Fridovich-Keil, CJ Tomlin… - arXiv preprint arXiv …, 2020 - arxiv.org
In many settings where multiple agents interact, the optimal choices for each agent depend
heavily on the choices of the others. These coupled interactions are well-described by a …

On finding local nash equilibria (and only local nash equilibria) in zero-sum games

EV Mazumdar, MI Jordan, SS Sastry - arXiv preprint arXiv:1901.00838, 2019 - arxiv.org
We propose local symplectic surgery, a two-timescale procedure for finding local Nash
equilibria in two-player zero-sum games. We first show that previous gradient-based …

Matching-based capture strategies for 3D heterogeneous multiplayer reach-avoid differential games

R Yan, X Duan, Z Shi, Y Zhong, F Bullo - Automatica, 2022 - Elsevier
This paper studies a 3D multiplayer reach-avoid differential game with a goal region and a
play region. Multiple pursuers defend the goal region by consecutively capturing multiple …

First-order algorithm with convergence for-equilibrium in two-person zero-sum games

A Gilpin, J Pena, T Sandholm - Mathematical programming, 2012 - Springer
We propose an iterated version of Nesterov's first-order smoothing method for the two-
person zero-sum game equilibrium problem x ∈ Q_1 y ∈ Q_2 x^\rm T Ay= y ∈ Q_2 x ∈ …

Crocoddyl: An efficient and versatile framework for multi-contact optimal control

C Mastalli, R Budhiraja, W Merkt… - … on Robotics and …, 2020 - ieeexplore.ieee.org
We introduce Crocoddyl (Contact RObot COntrol by Differential DYnamic Library), an open-
source framework tailored for efficient multi-contact optimal control. Crocoddyl efficiently …

An introduction to pursuit-evasion differential games

IE Weintraub, M Pachter… - 2020 American Control …, 2020 - ieeexplore.ieee.org
Pursuit and evasion conflicts represent challenging problems with important applications in
aerospace and robotics. In pursuit-evasion problems, synthesis of intelligent actions must …