Optimal Regularized Online Allocation by Adaptive Re-Solving

Author:

Ma Wanteng1ORCID,Cao Ying2ORCID,Tsang Danny H. K.2ORCID,Xia Dong1ORCID

Affiliation:

1. Department of Mathematics, The Hong Kong University of Science and Technology, Clearwater Bay, Kowloon, Hong Kong;

2. Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Clearwater Bay, Kowloon, Hong Kong

Abstract

Online resource allocation is challenging when the decision maker aims to achieve fairness, load balancing, diversity, and so on. In “Optimal Regularized Online Allocation by Adaptive Re-Solving,” Ma, Cao, Tsang, and Xia examine the online allocation problem equipped with a nonseparable regularizer, which is commonly adopted to promote fairness and beyond. Under certain regularity, smoothness, and nondegeneracy assumptions of the dual problem, the authors show that a dual-based optimization strategy with adaptively updated resource constraints and history-based re-solving can achieve optimal logarithmic regret, even without the notorious log-log factor. The authors also demonstrate that an optimal regret upper bound can be achieved using infrequent re-solving and that an even faster algorithm is available if nearly optimal regret performance is acceptable. Their results demonstrate that optimal logarithmic regret is achievable under the max-min fairness or load-balancing constraints.

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

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