Handling Delayed Feedback in Distributed Online Optimization : A Projection-Free Approach

TL;DR

This work tackles online convex optimization under adversarial delayed feedback in both centralized and distributed settings. It introduces two projection-free, Frank-Wolfe–style algorithms (DeLMFW for centralized and De2MFW for distributed) that leverage online linear optimization oracles (e.g., FTPL) to cope with delayed feedback, achieving optimal regret bounds such as $O(\sqrt{B})$ where $B$ is the total delay and $O(\sqrt{dT})$ when delays are bounded by $d$. The distributed variant combines gradient tracking with a consensus matrix to manage asynchrony and delays, with bounds that scale with the spectral gap of the network. Empirical results on MNIST and FashionMNIST demonstrate that the proposed methods outperform existing delayed-feedback projection-free baselines across varying delay regimes and network topologies. Overall, the paper advances edge-friendly online optimization by delivering delay-tolerant, projection-free algorithms suitable for distributed and resource-constrained devices.

Abstract

Learning at the edges has become increasingly important as large quantities of data are continually generated locally. Among others, this paradigm requires algorithms that are simple (so that they can be executed by local devices), robust (again uncertainty as data are continually generated), and reliable in a distributed manner under network issues, especially delays. In this study, we investigate the problem of online convex optimization under adversarial delayed feedback. We propose two projection-free algorithms for centralised and distributed settings in which they are carefully designed to achieve a regret bound of O(\sqrt{B}) where B is the sum of delay, which is optimal for the OCO problem in the delay setting while still being projection-free. We provide an extensive theoretical study and experimentally validate the performance of our algorithms by comparing them with existing ones on real-world problems.

Figures (4)

• Figure 1: Illustration of delayed feedback in distributed system. Given a time $t$, each agent holds a distinct pool of available gradient feedback from $s <t$ that is ready for computation at the current time. The pool can also be empty if no feedback is provided.
• Figure 2: Cumulative Loss Comparison for Different Delays Regimes. Left : Without delay. Middle : Maximal delay 21. Right : Maximal delay 101
• Figure 3: Total loss of BOLD-MFW, DOFW and DeLMFW when varying delay value.
• Figure 4: Total Loss with varying numbers of agents experiencing delayed feedback in the network. $(f=0)$ for no delayed-agents.

Theorems & Definitions (21)

• Lemma 1: Theorem 5.8 Hazanothers16:Introduction-to-online
• Lemma 2
• Theorem 1
• Lemma 3
• Lemma 4
• Theorem 2
• Lemma 2
• proof
• Lemma 5: THANG2022334
• proof