The resource allocation problem consists of the optimal distribution of a budget between agents in a group. We consider such a problem in the context of open systems, where agents can be replaced at some time instances. These replacements lead to variations in both the budget and the total cost function that hinder the overall network's performance. For a simple setting, we analyze the performance of the Random Coordinate Descent algorithm (RCD) using tools similar to those commonly used in online optimization. In particular, we study the accumulated errors that compare solutions issued from the RCD algorithm and the optimal solution or the non-collaborating selfish strategy and we derive some bounds in expectation for these accumulated errors.

翻译：资源分配问题包括在一个集团的代理人之间对预算进行最佳分配。 我们从开放的系统的角度来考虑这个问题,在开放的系统中可以更换代理人,这种更换会导致预算和总成本功能的变化,从而妨碍整个网络的运行。 简单而言,我们使用类似于在网上优化中常用的工具分析随机协调源算法(RCD)的性能。 特别是,我们研究累积的错误,这些错误比较了刚果民盟算法和最佳解决方案或非协调的自私战略所产生的解决办法,我们对这些累积错误的预期有一定的限度。