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[2602.16555] Learning Distributed Equilibria in Linear-Quadratic Stochastic Differential Games: An $α$-Potential Approach
Summary
This paper explores independent policy-gradient learning in N-player linear-quadratic stochastic differential games, establishing global convergence to equilibria through an α-potential approach.
Why It Matters
Understanding distributed equilibria in stochastic differential games is crucial for optimizing multi-agent systems in various applications, including economics and AI. This research provides insights into convergence properties and the impact of interaction asymmetry, which can inform future developments in game theory and machine learning.
Key Takeaways
- Independent policy-gradient methods can achieve global convergence in N-player LQ stochastic games.
- The α-potential structure is key to understanding equilibrium dynamics, especially in asymmetric interactions.
- Numerical experiments validate theoretical findings across different interaction networks.
Mathematics > Optimization and Control arXiv:2602.16555 (math) [Submitted on 18 Feb 2026] Title:Learning Distributed Equilibria in Linear-Quadratic Stochastic Differential Games: An $α$-Potential Approach Authors:Philipp Plank, Yufei Zhang View a PDF of the paper titled Learning Distributed Equilibria in Linear-Quadratic Stochastic Differential Games: An $\alpha$-Potential Approach, by Philipp Plank and 1 other authors View PDF HTML (experimental) Abstract:We analyze independent policy-gradient (PG) learning in $N$-player linear-quadratic (LQ) stochastic differential games. Each player employs a distributed policy that depends only on its own state and updates the policy independently using the gradient of its own objective. We establish global linear convergence of these methods to an equilibrium by showing that the LQ game admits an $\alpha$-potential structure, with $\alpha$ determined by the degree of pairwise interaction asymmetry. For pairwise-symmetric interactions, we construct an affine distributed equilibrium by minimizing the potential function and show that independent PG methods converge globally to this equilibrium, with complexity scaling linearly in the population size and logarithmically in the desired accuracy. For asymmetric interactions, we prove that independent projected PG algorithms converge linearly to an approximate equilibrium, with suboptimality proportional to the degree of asymmetry. Numerical experiments confirm the theoretical results across...
