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Title: Combining Regularization with Look-Ahead for Competitive Online Convex Optimization
There has been significant interest in leveraging limited look-ahead to achieve low competitive ratios for online convex optimization (OCO). However, existing online algorithms (such as Averaging Fixed Horizon Control (AFHC)) that can leverage look-ahead to reduce the competitive ratios still produce competitive ratios that grow unbounded as the coefficient ratio (i.e., the maximum ratio of the switching-cost coefficient and the service-cost coefficient) increases. On the other hand, the regularization method can attain a competitive ratio that remains bounded when the coefficient ratio is large, but it does not benefit from look-ahead. In this paper, we propose a new algorithm, called Regularization with Look-Ahead (RLA), that can get the best of both AFHC and the regularization method, i.e., its competitive ratio decreases with the look-ahead window size when the coefficient ratio is small, and remains bounded when the coefficient ratio is large. We also provide a matching lower bound for the competitive ratios of all online algorithms with look-ahead, which differs from the achievable competitive ratio of RLA by a factor that only depends on the problem size. The competitive analysis of RLA involves a non-trivial generalization of online primal-dual analysis to the case with look-ahead.  more » « less
Award ID(s):
1717493 1703014
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Page Range / eLocation ID:
1 to 10
Medium: X
Sponsoring Org:
National Science Foundation
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