Optimal and Efficient Online Inverse Optimization
A deterministic polynomial-time algorithm achieves optimal O(sqrt d) regret for online inverse linear optimization.
In online inverse linear optimization, a learner recommends an action and observes an expert maximizing a fixed unknown linear objective in d dimensions, without seeing that objective. Sakaue previously achieved optimal O(sqrt d) regret with a randomized algorithm requiring (dT) to the O(d) linear optimizations per round. This paper gives a deterministic variable-metric variant that matches O(sqrt d) regret for every horizon T and runs in time polynomial in d and T, revoking a metric update once the query point moves far from where it was made.
- Deterministic algorithm matches optimal O(sqrt d) regret for every horizon T.
- Runtime is polynomial in dimension d and horizon T.
- Prior optimal method needed super-polynomial linear optimizations per round.
- A metric update is revoked once the query point moves far away.
From the original article
1 min read at arxiv.orgIn 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.
By Anupam Gupta · arxiv.org
A short excerpt; the article and its images belong to the publisher. Summary, key facts and assessment above are AI-written from the article and can be wrong.