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### Technical Explanation
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In more technical terms, **amortized optimization** seeks to learn a function \\( f_
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Recent advances also focus on **trustworthy** or **certifiable** proxies, where constraint satisfaction or performance bounds are guaranteed. This is crucial in domains like energy systems or manufacturing, where infeasible solutions can have large penalties or safety concerns. Overall, learning-based optimization frameworks aim to combine the advantages of ML (data-driven generalization) with the rigor of mathematical programming (constraint handling and optimality).
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### Technical Explanation
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In more technical terms, **amortized optimization** seeks to learn a function \\( f_\theta(x) \\) that maps problem parameters \\( x \\) to solutions \\( y \\) that (approximately) minimize a given objective function subject to constraints. Modern methods leverage techniques like **differentiable optimization layers**, **input-convex neural networks**, or constraint-enforcing architectures (e.g., [DC3](https://openreview.net/pdf?id=0Ow8_1kM5Z)) to ensure that the learned proxy solutions are both feasible and performant. By coupling the solver and the model in an **end-to-end** pipeline, these approaches let the training objective directly reflect downstream metrics, improving speed and reliability.
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Recent advances also focus on **trustworthy** or **certifiable** proxies, where constraint satisfaction or performance bounds are guaranteed. This is crucial in domains like energy systems or manufacturing, where infeasible solutions can have large penalties or safety concerns. Overall, learning-based optimization frameworks aim to combine the advantages of ML (data-driven generalization) with the rigor of mathematical programming (constraint handling and optimality).
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