协同优化中的弹性：冗余和独立成本函数
Resilience in Collaborative Optimization: Redundant and Independent Cost Functions
摘要：
本文研究了多智能体协同优化中的拜占庭容错问题。在这个问题中，每个代理都有一个局部成本函数。协同优化算法的目标是计算代理成本函数的最小值。我们考虑的情况下，一定数量的代理可能是拜占庭式的故障。这种错误的代理可能不遵循规定的算法，并且它们可能发送关于其本地成本函数的任意或不正确的信息。一个合理的目标，在存在这样的故障代理是最小化的总成本的非故障代理。在这份报告中，我们表明，这一目标可以实现，当且仅当成本函数的非故障代理有一个最小的冗余属性。我们提出了不同的算法，实现这种宽容对故障代理，并证明了算法的复杂性和代理的成本函数的属性之间的权衡。此外，我们还考虑的情况下，成本函数是独立的或不满足最小冗余属性。在这种情况下，我们通过引入一个称为弱弹性的度量来量化对错误代理的容忍度。我们提出了一个算法，达到弱弹性时，有故障的代理人是少数和成本函数是非负的。
英文摘要：
This report considers the problem of Byzantine fault-tolerance in multi-agent collaborative optimization. In this problem, each agent has a local cost function. The goal of a collaborative optimization algorithm is to compute a minimum of the aggregate of the agents' cost functions. We consider the case when a certain number of agents may be Byzantine faulty. Such faulty agents may not follow a prescribed algorithm, and they may send arbitrary or incorrect information regarding their local cost functions. A reasonable goal in presence of such faulty agents is to minimize the aggregate cost of the non-faulty agents. In this report, we show that this goal can be achieved if and only if the cost functions of the non-faulty agents have a minimal redundancy property. We present different algorithms that achieve such tolerance against faulty agents, and demonstrate a trade-off between the complexity of an algorithm and the properties of the agents' cost functions. Further, we also consider the case when the cost functions are independent or do not satisfy the minimal redundancy property. In that case, we quantify the tolerance against faulty agents by introducing a metric called weak resilience. We present an algorithm that attains weak resilience when the faulty agents are in the minority and the cost functions are non-negative.
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。
