Tight Regret Bound for Online Inverse Linear Optimization via Multiscale Matrix Weights
We study online inverse linear optimization with a fixed unknown linear utility: in each round, an environment presents a compact action set, the learner recommends an action from it, and the environment returns an action that maximizes the utility over the same set. When the utility vector and the actions lie in the $d$-dimensional Euclidean unit ball, we give a randomized algorithm whose regret---the cumulative utility shortfall relative to optimal actions---is $O(\sqrt d)$ in expectation for every time horizon, without knowledge of the horizon. The dependence on $d$ is optimal up to a constant factor by the known $Ω(\sqrt d)$ lower bound for horizons $T\ge d$. Our algorithm maintains m...
| Authors | Shinsaku Sakaue |
|---|---|
| Primary category | stat.ML |
| Published | 22 September 2026 |
| Last updated at source | 22 September 2026 |
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