Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2503.10013

Revisiting Multi-Agent Asynchronous Online Optimization with Delays: the Strongly Convex Case

Lingchan Bao·Tong Wei·Yuanyu Wan
View original source ↗Read source document ↗Export metadata ↓

Abstract

We revisit multi-agent asynchronous online optimization with delays, where only one of the agents becomes active for making the decision at each round, and the corresponding feedback is received by all the agents after unknown delays. Although previous studies have established an $O(\sqrt{dT})$ regret bound for this problem, they assume that the maximum delay $d$ is knowable or the arrival order of feedback satisfies a special property, which may not hold in practice. In this paper, we surprisingly find that when the loss functions are strongly convex, these assumptions can be eliminated, and the existing regret bound can be significantly improved to $O(d\log T)$ meanwhile. Specifically, to exploit the strong convexity of functions, we first propose a delayed variant of the classical follow-the-leader algorithm, namely FTDL, which is very simple but requires the full information of functions as feedback. Moreover, to handle the more general case with only the gradient feedback, we develop an approximate variant of FTDL by combining it with surrogate loss functions. Experimental results show that the approximate FTDL outperforms the existing algorithm in the strongly convex case.

Explore related subjects

cs.LGmath.OC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Lingchan Bao, Tong Wei, Yuanyu Wan. 2026-02-04. Revisiting Multi-Agent Asynchronous Online Optimization with Delays: the Strongly Convex Case. https://arxiv.org/abs/2503.10013

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

CTRL: Control-Based Time Series Forecasting with LLM-Guided Residual Learning

Time series forecasting underpins critical decision-making across diverse domains. While large language models (LLMs) offer promising reasoning capabilities, existing LLM-based time series forecasting approaches either reduce them to numerical predictors that bypass their strengths, or allow direct forecast generation that destabilizes predictions in non-stationary settings. We introduce CTRL, a framework that decouples semantic reasoning from quantitative prediction. A frozen backbone generates base forecasts, while specialized LLM agents function as controllers that analyze backbone prediction errors through decomposed trend, seasonal, and irregular components, grounding reasoning in interpretable temporal structure. Each agent outputs compact control signals that a lightweight residual decoder translates into forecast corrections. CTRL incorporates label-free test-time adaptation that detects distribution shift from input statistics alone and readapts control signals with only 3-24 LLM calls via caching. CTRL is explicitly designed to improve robustness under non-stationary temporal dynamics and distribution shift, while remaining competitive on highly stationary time series where adaptive correction provides limited additional benefit.

cs.LG↗
arXiv2026

Why Ghost Outputs Teach: A Kernel-Based Understanding of Subliminal Learning

Subliminal Learning (SL) is a recently identified phenomenon in which a student model acquires downstream task capabilities by matching seemingly unrelated auxiliary outputs from a teacher, despite never observing task labels, task-specific outputs, or the original training data. While recent studies have identified where subliminal signals may reside, the optimization mechanism underlying this phenomenon remains poorly understood. In this work, we provide a mechanistic understanding of SL through the lens of learning dynamics. Specifically, we derive a chained cross-task kernel that explicitly links ghost-output supervision to changes in task predictions through shared backbone representations. Our unified analytical framework provides a rigorous mathematical explanation for three central empirical puzzles in SL: (i) under shared initialization, the transfer operator forms a strictly Positive Semi-Definite (PSD) structure, guaranteeing that ghost-output optimization aligns the student with the teacher's true task objective without explicit label exposure; (ii) the ghost-output dimensionality acts as an explicit rank bottleneck governing the transfer of task-relevant features; and (iii) synthetic, high-entropy inputs function as broadband probes that maximize cross-task kernel overlap, explaining why random noise consistently outperforms structured data for subliminal transfer. Experiments on the canonical ghost-output setting validate all three theoretical predictions, providing the first learning-dynamics-based theoretical explanation of how ghost-output supervision gives rise to subliminal learning.

cs.LG↗
arXiv2026

Optimal No-Regret Learning for Repeated Prophet Inequality

We study repeated prophet inequalities under prefix feedback. In each of $T$ rounds, a learner encounters fresh values drawn independently from $n$ boxes with unknown $[0,1]$-supported distributions in a fixed order and must irrevocably accept one, observing only the prefix up to its stopping box. Regret is measured against the optimal stopping policy that knows the distributions. We give an efficient algorithm achieving $\widetilde O(\sqrt{T})$ expected regret, matching the lower bound up to logarithmic factors. Our algorithm explores directly through near-optimal policies, combining empirical backward induction with box-specific reach bonuses. A relative-drop aggregation rule then exploits the nesting structure of observed prefixes to preserve exploration, thereby removing the polynomial dependence on the box number $n$. This resolves an open question posed by Liu et al. (2025).

cs.LG↗