AI RESEARCH
Near-Optimal Regret for the Safe Learning-based Control of the Constrained Linear Quadratic Regulator
arXiv CS.LG
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ArXi:2604.22158v1 Announce Type: cross We study the problem of adaptive control of the stochastic linear quadratic regulator (LQR) with constraints that must be satisfied at every time step. Prior work on the multidimensional problem has shown $\tilde{O}(T^{2/3})$ regret and satisfaction of robust constraints, leaving open the question of whether $\tilde{O}(\sqrt{T})$ regret can be attained in the constrained LQR setting. We contribute to this problem by showing $\tilde{O}(\sqrt{T})$ regret and satisfaction of chance constraints.