提出首个真正去中心化的多智能体优化算法,实现渐近最优且计算高效。
Optimal Decentralized Smoothed Online Convex Optimization
- 各智能体仅用邻居信息本地决策,无需全局协调。
- 竞争比随时间缩短,计算复杂度仅对数依赖于智能体数量。
- 适用于动态网络,比现有最优算法更快更省算力。
研究多智能体平滑在线凸优化(SOCO)问题,$N$ 个智能体通过通信图交互。每轮中,每个智能体 $i$ 在线接收强凸损失函数 $f^i_t$,选择动作 $x^i_t \in \mathbb{R}^d$。目标是最小化全局累计成本,包括个体损失 $f^i_t(x^i_t)$、时间切换成本和邻域间决策差异的相似性惩罚。本文提出首个真正去中心化的算法 ACORD,可证明具有渐近最优性。每个智能体仅需利用图中邻近节点的局部信息。对于有限时间性能,我们证明竞争比随时间 $T$ 减小,且可依据每轮可用计算量灵活调节。算法具备可证明的可扩展复杂度:仅对数依赖于智能体数,几乎线性依赖于其度数。结果在通信图任意自适应变化下依然成立。此外,由于渐近最优性,ACORD 被证明优于现有最优的 LPC 算法,同时计算开销更低。多种网络拓扑上的大量数值实验验证了理论结论。
原文摘要 · Abstract (English)
We study the multi-agent Smoothed Online Convex Optimization (SOCO) problem, where $N$ agents interact through a communication graph. In each round, each agent $i$ receives a strongly convex hitting cost function $f^i_t$ in an online fashion and selects an action $x^i_t \in \mathbb{R}^d$. The objective is to minimize the global cumulative cost, which includes the sum of individual hitting costs $f^i_t(x^i_t)$, a temporal "switching cost" for changing decisions, and a spatial "dissimilarity cost" that penalizes deviations in decisions among neighboring agents. We propose the first truly decentralized algorithm ACORD for multi-agent SOCO that provably exhibits asymptotic optimality. Our approach allows each agent to operate using only local information from its immediate neighbors in the graph. For finite-time performance, we establish that the optimality gap in the competitive ratio decreases with time horizon $T$ and can be conveniently tuned based on the per-round computation available to each agent. Our algorithm benefits from a provably scalable computational complexity that depends only logarithmically on the number of agents and almost linearly on their degree within the graph. Moreover, our results hold even when the communication graph changes arbitrarily and adaptively over time. Finally, ACORD, by virtue of its asymptotic-optimality, is shown to be provably superior to the state-of-the-art LPC algorithm, while exhibiting much lower computational complexity. Extensive numerical experiments across various network topologies further corroborate our theoretical claims.
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