An Efficient Interior-Point Method for Online Convex Optimization

• URL: http://arxiv.org/abs/2307.11668v1
• Date: Fri, 21 Jul 2023 16:12:46 GMT
• Title: An Efficient Interior-Point Method for Online Convex Optimization
• Authors: Elad Hazan and Nimrod Megiddo
• Abstract summary: The algorithm is adaptive, in the sense that the regret bounds hold not only for the time periods $1,ldots,T$ but also for every sub-interval $s,s+1,ldots,t$. The running time of the algorithm matches that of newly introduced interior point algorithms for regret minimization.
• Score: 31.771131314017385
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A new algorithm for regret minimization in online convex optimization is described. The regret of the algorithm after $T$ time periods is $O(\sqrt{T \log T})$ - which is the minimum possible up to a logarithmic term. In addition, the new algorithm is adaptive, in the sense that the regret bounds hold not only for the time periods $1,\ldots,T$ but also for every sub-interval $s,s+1,\ldots,t$. The running time of the algorithm matches that of newly introduced interior point algorithms for regret minimization: in $n$-dimensional space, during each iteration the new algorithm essentially solves a system of linear equations of order $n$, rather than solving some constrained convex optimization problem in $n$ dimensions and possibly many constraints.

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