The paper proves O(LB√T) regret for Projected Online Gradient Descent in online quantum state learning under bounded Frobenius norm measurements, with dimension-free corollaries for low-rank and sparse effects, and an O(log T) regret bound for Follow-the-Leader under squared L2 loss.
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Improved regret bounds for structured online learning of quantum states
The paper proves O(LB√T) regret for Projected Online Gradient Descent in online quantum state learning under bounded Frobenius norm measurements, with dimension-free corollaries for low-rank and sparse effects, and an O(log T) regret bound for Follow-the-Leader under squared L2 loss.