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</div>
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</div>
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Learning to optimize (LearningToOptimize) package that provides basic functionalities to help fit proxy models for optimization.
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Learning to optimize (LearningToOptimize) package that provides basic functionalities to help fit proxy models for parametric optimization problems.
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Have a look at our sister [HugginFace Organization](https://huggingface.co/LearningToOptimize), for datasets, pre-trained models and benchmarks.
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# Background
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Parametric optimization problems arise in scenarios where certain elements (e.g., coefficients, constraints) may vary according to problem parameters. A general form of a parameterized convex optimization problem is
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$$
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\begin{aligned}
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&\min_{x} \quad f(x; \theta) \\
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&\text{subject to} \quad g_i(x; \theta) \leq 0, \quad i = 1,\dots, m \\
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&\quad\quad\quad\quad A(\theta)x = b(\theta)
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\end{aligned}
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$$
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where $ \theta $ is the parameter.
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**Learning to Optimize (L2O)** is an emerging paradigm where machine learning models *learn* to solve optimization problems efficiently. This approach is also known as using **optimization proxies** or **amortized optimization**.
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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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For a broader overview, see the [SIAM News article on trustworthy optimization proxies](https://www.siam.org/publications/siam-news/articles/fusing-artificial-intelligence-and-optimization-with-trustworthy-optimization-proxies/), which highlights the growing synergy between AI and classical optimization.
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# Installation
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```julia
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] add LearningToOptimize
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```
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## Generate Dataset
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This package provides a basic way of generating a dataset of the solutions of an optimization problem by varying the values of the parameters in the problem and recording it.
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ps.: For illustration purpose, I have represented the id's here as integers, but in reality they are generated as UUIDs.
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ps.: For illustration purpose, I have represented the id's here as integers, but in reality they are generated as UUIDs.
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To load the parameter values back:
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```julia
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problem_iterator =load("input_file.csv", CSVFile)
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```
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### Samplers
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Instead of defining parameter instances manually, one may sample parameter values using pre-defined samplers - e.g. `scaled_distribution_sampler`, `box_sampler`- or define their own sampler. Samplers are functions that take a vector of parameter of type `MOI.Parameter` and return a matrix of parameter values.
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The easiest way to go from problem definition, sampling parameter values and saving them is to use the `general_sampler` function:
This function is a general sampler that uses a set of samplers to sample the parameter space.
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It loads the underlying model from a passed `file` that works with JuMP's `read_from_file` (ps.: currently only tested with `MathOptFormat`), samples the parameters and saves the sampled parameters to `save_file`.
Copy file name to clipboardExpand all lines: docs/src/index.md
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| 9 | 9.0 |
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ps.: For illustration purpose, I have represented the id's here as integers, but in reality they are generated as UUIDs.
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ps.: For illustration purpose, I have represented the id's here as integers, but in reality they are generated as UUIDs.
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To load the parameter values back:
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```julia
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problem_iterator =load("input_file.csv", CSVFile)
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```
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### Samplers
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Instead of defining parameter instances manually, one may sample parameter values using pre-defined samplers - e.g. `scaled_distribution_sampler`, `box_sampler`- or define their own sampler. Samplers are functions that take a vector of parameter of type `MOI.Parameter` and return a matrix of parameter values.
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The easiest way to go from problem definition, sampling parameter values and saving them is to use the `general_sampler` function:
This function is a general sampler that uses a set of samplers to sample the parameter space.
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It loads the underlying model from a passed `file` that works with JuMP's `read_from_file` (ps.: currently only tested with `MathOptFormat`), samples the parameters and saves the sampled parameters to `save_file`.
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