Adaptive online convex optimization with unknown feedback delay

Ping Wu; Heyan Huang; Haolin Lu; Zhengyang Liu

doi:10.1016/j.eswa.2025.129269

Adaptive online convex optimization with unknown feedback delay

Ping Wu
, Heyan Huang
, Haolin Lu
, Zhengyang Liu^*

^*Corresponding author for this work

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

Online Convex Optimization (OCO) with unknown feedback delay presents a considerable challenge, particularly when the delay period is not available a priori. In this paper, we propose an adaptive delayed mirror descent (ADMD) algorithm to address this issue, which incorporates a virtual iterate sequence and a learning rate based on the cumulative missed feedback instances. This method improves regret bounds and eliminates the need for prior knowledge of the delay period. Furthermore, we transform the ADMD algorithm into adaptive delayed dual averaging (ADDA) using lazy gradient descent, establishing a connection between these two frameworks. To further enhance the algorithm's adaptability, we introduce a novel delayed doubling trick. Through extensive experiments, we demonstrate the efficacy of our approach, showing superior performance compared to existing algorithms.

Original language	English
Article number	129269
Journal	Expert Systems with Applications
Volume	297
DOIs	https://doi.org/10.1016/j.eswa.2025.129269
Publication status	Published - 1 Feb 2026
Externally published	Yes

Keywords

Dual averaging
Learning rate
Mirror descent
Online convex optimization
Unknown feedback delay

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10.1016/j.eswa.2025.129269

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title = "Adaptive online convex optimization with unknown feedback delay",

abstract = "Online Convex Optimization (OCO) with unknown feedback delay presents a considerable challenge, particularly when the delay period is not available a priori. In this paper, we propose an adaptive delayed mirror descent (ADMD) algorithm to address this issue, which incorporates a virtual iterate sequence and a learning rate based on the cumulative missed feedback instances. This method improves regret bounds and eliminates the need for prior knowledge of the delay period. Furthermore, we transform the ADMD algorithm into adaptive delayed dual averaging (ADDA) using lazy gradient descent, establishing a connection between these two frameworks. To further enhance the algorithm's adaptability, we introduce a novel delayed doubling trick. Through extensive experiments, we demonstrate the efficacy of our approach, showing superior performance compared to existing algorithms.",

keywords = "Dual averaging, Learning rate, Mirror descent, Online convex optimization, Unknown feedback delay",

author = "Ping Wu and Heyan Huang and Haolin Lu and Zhengyang Liu",

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T1 - Adaptive online convex optimization with unknown feedback delay

AU - Wu, Ping

AU - Huang, Heyan

AU - Lu, Haolin

AU - Liu, Zhengyang

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N2 - Online Convex Optimization (OCO) with unknown feedback delay presents a considerable challenge, particularly when the delay period is not available a priori. In this paper, we propose an adaptive delayed mirror descent (ADMD) algorithm to address this issue, which incorporates a virtual iterate sequence and a learning rate based on the cumulative missed feedback instances. This method improves regret bounds and eliminates the need for prior knowledge of the delay period. Furthermore, we transform the ADMD algorithm into adaptive delayed dual averaging (ADDA) using lazy gradient descent, establishing a connection between these two frameworks. To further enhance the algorithm's adaptability, we introduce a novel delayed doubling trick. Through extensive experiments, we demonstrate the efficacy of our approach, showing superior performance compared to existing algorithms.

AB - Online Convex Optimization (OCO) with unknown feedback delay presents a considerable challenge, particularly when the delay period is not available a priori. In this paper, we propose an adaptive delayed mirror descent (ADMD) algorithm to address this issue, which incorporates a virtual iterate sequence and a learning rate based on the cumulative missed feedback instances. This method improves regret bounds and eliminates the need for prior knowledge of the delay period. Furthermore, we transform the ADMD algorithm into adaptive delayed dual averaging (ADDA) using lazy gradient descent, establishing a connection between these two frameworks. To further enhance the algorithm's adaptability, we introduce a novel delayed doubling trick. Through extensive experiments, we demonstrate the efficacy of our approach, showing superior performance compared to existing algorithms.

KW - Dual averaging

KW - Learning rate

KW - Mirror descent

KW - Online convex optimization

KW - Unknown feedback delay

UR - https://www.scopus.com/pages/publications/105013521116

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DO - 10.1016/j.eswa.2025.129269

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SN - 0957-4174

VL - 297

JO - Expert Systems with Applications

JF - Expert Systems with Applications

M1 - 129269

ER -

Adaptive online convex optimization with unknown feedback delay

Abstract

Keywords

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