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In this paper, we address the problem of a two-player linear quadratic differential game with incomplete information, a scenario commonly encountered in multi-agent control, human-robot interaction (HRI), and approximation methods to solve general-sum differential games. While solutions to such linear differential games are typically obtained through coupled Riccati equations, the complexity increases when agents have incomplete information, particularly when neither is aware of the other’s cost function. To tackle this challenge, we propose a model-based Peer-Aware Cost Estimation (PACE) framework for learning the cost parameters of the other agent. In PACE, each agent treats its peer as a learning agent rather than a stationary optimal agent, models their learning dynamics, and leverages this dynamic to infer the cost function parameters of the other agent. This approach enables agents to infer each other’s objective function in real time based solely on their previous state observations and dynamically adapt their control policies. Furthermore, we provide a theoretical guarantee for the convergence of parameter estimation and the stability of system states in PACE. Additionally, using numerical studies, we demonstrate how modeling the learning dynamics of the other agent benefits PACE, compared to approaches that approximate the other agent as having complete information, particularly in terms of stability and convergence speed.
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Random feature models for learning interacting dynamical systems
Particle dynamics and multi-agent systems provide accurate dynamical models for studying and forecasting the behaviour of complex interacting systems. They often take the form of a high-dimensional system of differential equations parameterized by an interaction kernel that models the underlying attractive or repulsive forces between agents. We consider the problem of constructing a data-based approximation of the interacting forces directly from noisy observations of the paths of the agents in time. The learned interaction kernels are then used to predict the agents’ behaviour over a longer time interval. The approximation developed in this work uses a randomized feature algorithm and a sparse randomized feature approach. Sparsity-promoting regression provides a mechanism for pruning the randomly generated features which was observed to be beneficial when one has limited data, in particular, leading to less overfitting than other approaches. In addition, imposing sparsity reduces the kernel evaluation cost which significantly lowers the simulation cost for forecasting the multi-agent systems. Our method is applied to various examples, including first-order systems with homogeneous and heterogeneous interactions, second-order homogeneous systems, and a new sheep swarming system.
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- PAR ID:
- 10466693
- Publisher / Repository:
- Royal Society
- Date Published:
- Journal Name:
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 479
- Issue:
- 2275
- ISSN:
- 1364-5021
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rspa.2022.0835
