An algorithm for constrained stochastic LQR achieves tilde O of square root T regret and chance constraint satisfaction via SDP-based optimistic policies scaled for safety.
The proof is in Section B.6.4
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Rate-Optimal Regret for the Safe Learning-based Control of the Constrained Linear Quadratic Regulator
An algorithm for constrained stochastic LQR achieves tilde O of square root T regret and chance constraint satisfaction via SDP-based optimistic policies scaled for safety.