Optimal and Efficient Online Inverse Optimization

Abstract:In online inverse linear optimization, a learner recommends an action and then observes the choice of an expert who maximizes a fixed, unknown linear objective on $\mathbb{R}^{d}$; the goal is to learn to optimize this objective without observing it. Sakaue recently obtained the optimal regret $O(\sqrt d)$ with a randomized algorithm making $(dT)^{O(d)}$ linear optimizations per round, and asked whether it can be attained in polynomial time. We answer positively: our deterministic algorithm has regret $O(\sqrt d)$ for every horizon $T$ and runs in time polynomial in $d$ and $T$. It is a variant of the variable-metric algorithms of Sakaue et al.\ and Cai et al., in which a metric update is revoked once the query point moves far enough from where the update was made.

Machine Learning (cs.LG); Data Structures and Algorithms (cs.DS)

arXiv:2610.08735 [cs.LG]

(or arXiv:2610.08735v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.08735 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.