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- W4387389912 abstract "Linear programming has played a crucial role in shaping decision-making, resource allocation, and cost reduction in various domains. In this paper, we investigate the application of overparametrized neural networks and their implicit bias in solving linear programming problems. Specifically, our findings reveal that training diagonal linear networks with gradient descent, while optimizing the squared $L_2$-norm of the slack variable, leads to solutions for entropically regularized linear programming problems. Remarkably, the strength of this regularization depends on the initialization used in the gradient descent process. We analyze the convergence of both discrete-time and continuous-time dynamics and demonstrate that both exhibit a linear rate of convergence, requiring only mild assumptions on the constraint matrix. For the first time, we introduce a comprehensive framework for solving linear programming problems using diagonal neural networks. We underscore the significance of our discoveries by applying them to address challenges in basis pursuit and optimal transport problems." @default.
- W4387389912 created "2023-10-06" @default.
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- W4387389912 date "2023-10-03" @default.
- W4387389912 modified "2023-10-07" @default.
- W4387389912 title "Linear programming using diagonal linear networks" @default.
- W4387389912 doi "https://doi.org/10.48550/arxiv.2310.02535" @default.
- W4387389912 hasPublicationYear "2023" @default.
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