74 3 18 69 4 32 78 1c:T568,## Contributions - **FrODO provides a new framework for distributed optimization** that incorporates fractional-order memory terms to enhance convergence properties. - The approach achieves **provable linear convergence** for all strongly connected networks. - **Empirical results** demonstrate a convergence speedup of up to 4× on ill-conditioned problems and 2-3× in federated neural network training. ## Previous Methods and Their Limitations - Traditional methods often struggle with **ill-conditioned problems**, leading to poor convergence rates and instability. - Existing techniques **lack stability or speed** depending on optimization landscapes. ## Our Theory and Methods - **FrODO operates in three stages**: 1. Calculation of descent directions using both gradient and memory terms. 2. Local updates for each agent based on computed directions. 3. Consensus-driven alignment across neighboring agents. - **Convergence and complexity analyses** confirm linear convergence under appropriate parameter choices. ## Experiments Settings & Results - **Experiment 1**: Tests on a quadratic function with an ill-conditioned Hessian showed FrODO outperforms traditional methods in convergence iterations. - **Experiment 2**: Evaluated FrODO on a federated learning setup, demonstrating faster convergence while achi

ID	age	weight
1	15	65
2	24	74
3	18	69
4	32	78

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Fractional Order Distributed Optimization