2022/09/01 by Wanteng Ma, Ying Cao, Ma, Wanteng +5 · 1 citation
Computer Science · Decision Sciences · Engineering · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2209.00399
openalex publication_date 2022/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper introduces a dual-based algorithm framework for solving the regularized online resource allocation problems, which have potentially non-concave cumulative rewards, hard resource constraints, and a non-separable regularizer. Under a strategy of adaptively updating the resource constraints, the proposed framework only requests approximate solutions to the empirical dual problems up to a certain accuracy and yet delivers an optimal logarithmic regret under a locally second-order growth condition. Surprisingly, a delicate analysis of the dual objective function enables us to eliminate the notorious log-log factor in regret bound. The flexible framework renders renowned and computationally fast algorithms immediately applicable, e.g., dual stochastic gradient descent. Additionally, an infrequent re-solving scheme is proposed, which significantly reduces computational demands without compromising the optimal regret performance. A worst-case square-root regret lower bound is established if the resource constraints are not adaptively updated during dual optimization, which underscores the critical role of adaptive dual variable update. Comprehensive numerical experiments demonstrate the merits of the proposed algorithm framework.