For online inverse linear optimization, the paper proves a regret bound of O(1/Δ²) that is independent of the time horizon, provided the agent's decision problems satisfy a Δ-gap condition.
We let /u1D6FD/u1D447 +1 = /u1D6FD/u1D447 , which does not affect the analysis (Orabona, 2023, Remark 7.3)
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Revisiting Online Learning Approach to Inverse Linear Optimization: A Fenchel$-$Young Loss Perspective and Gap-Dependent Regret Analysis
For online inverse linear optimization, the paper proves a regret bound of O(1/Δ²) that is independent of the time horizon, provided the agent's decision problems satisfy a Δ-gap condition.