Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study fault-tolerant distributed optimization of a sum of convex (cost) functions with real-valued scalar input/output in the presence of crash faults or Byzantine faults. In particular, the goal is to optimize a global cost function $\frac{1}{n}\sum_{i\in \mathcal{V}} h_i(x)$, where $\mathcal{V}=\{1, \ldots, n\}$ is the collection of agents, and $h_i(x)$ is agent $i$'s local cost function, which is initially known only to agent $i$. Since the above global cost function cannot be optimized exactly in presence of crash faults or Byzantine faults,  define two aker versions of the problem for crash faults and Byzantine faults, respectively. #R##N#When some agents may crash, the goal for the aker problem is to generate an output that is an optimum of a function formed as $$C(\sum_{i\in \mathcal{N}} h_i(x)+\sum_{i\in \mathcal{F}} \alpha_i h_i(x)),$$ where $\mathcal{N}$ is the set of non-faulty agents, $\mathcal{F}$ is the set of faulty agents (crashed agents), $0\le \alpha_i\le 1$ for each $i\in \mathcal{F}$ and $C$ is a normalization constant such that $C(|\mathcal{N}|+\sum_{i\in \mathcal{F}} \alpha_i)=1$.  present an iterative algorithm in which each agent only needs to perform local computation, and send one message per iteration. #R##N#When some agents may be Byzantine, the system cannot take full advantage of the data kept by non-faulty agents. The goal for the associated aker problem is to generate an output that is an optimum of a function formed as $$\sum_{i\in \mathcal{N}}\alpha_i h_i(x),$$ such that $\alpha_i\geq 0$ for each $i\in \mathcal{N}$ and $\sum_{i\in \mathcal{N}}\alpha_i=1$.  present an iterative algorithm, where only local computation is needed and only one message per agent is sent in each iteration, that ensures that at least $|\mathcal{N}|-f$ agents have ights ($\alpha_i$'s) that are lor bounded by $\frac{1}{2(|\mathcal{N}|-f)}$.
['Lili Su', 'Nitin H. Vaidya']
I am writing a research paper on a idea Fault-Tolerant Multi-Agent Optimization: Part III
[{"from": "human", "value": "I am writing a research paper on a idea Fault-Tolerant Multi-Agent Optimization: Part III"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study fault-tolerant distributed optimization of a sum of convex (cost) functions with real-valued scalar input/output in the presence of crash faults or Byzantine faults. In particular, the goal is to optimize a global cost function $\\frac{1}{n}\\sum_{i\\in \\mathcal{V}} h_i(x)$, where $\\mathcal{V}=\\{1, \\ldots, n\\}$ is the collection of agents, and $h_i(x)$ is agent $i$'s local cost function, which is initially known only to agent $i$. Since the above global cost function cannot be optimized exactly in presence of crash faults or Byzantine faults,  define two aker versions of the problem for crash faults and Byzantine faults, respectively. #R##N#When some agents may crash, the goal for the aker problem is to generate an output that is an optimum of a function formed as $$C(\\sum_{i\\in \\mathcal{N}} h_i(x)+\\sum_{i\\in \\mathcal{F}} \\alpha_i h_i(x)),$$ where $\\mathcal{N}$ is the set of non-faulty agents, $\\mathcal{F}$ is the set of faulty agents (crashed agents), $0\\le \\alpha_i\\le 1$ for each $i\\in \\mathcal{F}$ and $C$ is a normalization constant such that $C(|\\mathcal{N}|+\\sum_{i\\in \\mathcal{F}} \\alpha_i)=1$.  present an iterative algorithm in which each agent only needs to perform local computation, and send one message per iteration. #R##N#When some agents may be Byzantine, the system cannot take full advantage of the data kept by non-faulty agents. The goal for the associated aker problem is to generate an output that is an optimum of a function formed as $$\\sum_{i\\in \\mathcal{N}}\\alpha_i h_i(x),$$ such that $\\alpha_i\\geq 0$ for each $i\\in \\mathcal{N}$ and $\\sum_{i\\in \\mathcal{N}}\\alpha_i=1$.  present an iterative algorithm, where only local computation is needed and only one message per agent is sent in each iteration, that ensures that at least $|\\mathcal{N}|-f$ agents have ights ($\\alpha_i$'s) that are lor bounded by $\\frac{1}{2(|\\mathcal{N}|-f)}$."}]