拥堵博弈中强盗式无遗憾动态的多项式收敛性
Polynomial Convergence of Bandit No-Regret Dynamics in Congestion Games
AI总结：
本文提出一种强盗反馈下的在线学习算法，使拥堵博弈动态在多项式轮数内收敛到ε-近似纳什均衡，并保证次线性遗憾，同时为DAG网络拥堵博弈给出多项式时间实现。
摘要：
我们提出了一种在强盗反馈模型下的在线学习算法，一旦拥堵博弈中的所有智能体都采用该算法，博弈动态将在关于 $1/ε$、玩家数量和可用资源数量的多项式轮数内收敛到 $ε$-近似纳什均衡。所提出的算法还保证任何采用它的智能体获得次线性遗憾。因此，我们的工作回答了 arXiv:2206.01880 中的一个开放问题，并将 arXiv:2306.15543 的近期结果扩展到了强盗反馈模型。我们还进一步证明，通过为有向无环图（DAG）构造精确的 $1$-重心稀疏器，我们的在线学习算法可以在网络拥堵博弈于有向无环图（DAG）这一重要特殊情形下以多项式时间实现。
英文摘要：
We introduce an online learning algorithm in the bandit feedback model that, once adopted by all agents of a congestion game, results in game-dynamics that converge to an $ε$-approximate Nash Equilibrium in a polynomial number of rounds with respect to $1/ε$, the number of players and the number of available resources. The proposed algorithm also guarantees sublinear regret to any agent adopting it. As a result, our work answers an open question from arXiv:2206.01880 and extends the recent results of arXiv:2306.15543 to the bandit feedback model. We additionally establish that our online learning algorithm can be implemented in polynomial time for the important special case of Network Congestion Games on Directed Acyclic Graphs (DAG) by constructing an exact $1$-barycentric spanner for DAGs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
