This paper introduces a theoretical framework for online learning within stabilized linear dynamical games, a setting where multiple agents interact within a shared state that evolves based on linear dynamics and is subject to adversarial disturbances. The research extends adversarial online control to multi-agent systems, focusing on agents that minimize their own convex losses. The study analyzes agents employing online gradient descent with memory to adapt their disturbance-action policies, proving sublinear and near-optimal regret bounds. In scenarios where agents share common interests, the paper demonstrates that the problem can be framed as a time-varying potential game, yielding equilibrium tracking guarantees. AI
IMPACT Provides a theoretical framework for adversarial online learning in complex multi-agent systems, potentially influencing future research in game theory and control.
RANK_REASON Academic paper published on arXiv [lever_c_demoted from research: ic=1 ai=1.0]
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