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Nonsmooth Implicit Differentiation

Code for the paper Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).

Getting started

Install the packages in requirements.txt.

Check out elastic_net_toy.ipynb for an illustrative comparison between deterministic AID and ITD derivative approximation methods for (nonsmooth) elastic net.

How to reproduce results

Run one of the following files:

  • elastic_net_deterministic.py for the experiments comparing AID and ITD on computing the derivative with respect to the hyperparameters of elastic net.
  • elastic_net_stochastic.py for the experiments comparing AID-FP and NSID and SID on computing the derivative with respect to the hyperparameters of elastic net.
  • data_poisoning_stochastic.py for the experiments comparing (N)SID with constant and decreasing step-size schedules on computing the derivative with respect to the corruption noise of the data poisoning with elastic net regularization. The MNIST dataset will be automatically downloaded in the data folder when first run.

When the dataset is large (e.g. for data poisoning) using the GPU can speed up the computation. All Experiments artifacts will be saved in the exps folder inside the project directory

How to analyse results

Use the notebooks in the analyse_results folder to generate plots from the data of previously run experiments.

Additional info

See hypertorch for more details on the AID and ITD hypergradient approximation methdos and some examples on how to incorporate them in a project.

nonsmooth_implicit_diff/stoch_hg.py contains the code for the NSID method to approximate the derivaive of a fixed point which is a composition of an outer map and an inner map accessible only through a stochastic unbiased estimator.

Details on the experimental settings can be found in our paper.

Cite us

If you use this code, please cite our paper.

@article{grazzi2024nonsmooth,
title={Nonsmooth implicit differentiation: Deterministic and stochastic convergence rates},
author={Grazzi, Riccardo and Pontil, Massimiliano and Salzo, Saverio},
journal={arXiv preprint arXiv:2403.11687},
year={2024}
}

About

Code for the paper Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).

Topics

bilevelbilevel-optimizationhypergradient

Resources

Readme
MIT license
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})();
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try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '

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Nonsmooth Implicit Differentiation
Code for the paper
Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).
Getting started
Install the packages in requirements.txt.
Check out elastic_net_toy.ipynb for an illustrative comparison between deterministic AID and ITD derivative approximation methods for (nonsmooth) elastic net.
How to reproduce results
Run one of the following files:
  • elastic_net_deterministic.py for the experiments comparing AID and ITD on computing the derivative with respect to the hyperparameters of elastic net.
  • elastic_net_stochastic.py for the experiments comparing AID-FP and NSID and SID on computing the derivative with respect to the hyperparameters of elastic net.
  • data_poisoning_stochastic.py for the experiments comparing (N)SID with constant and decreasing step-size schedules on computing the derivative with respect to the corruption noise of the data poisoning with elastic net regularization. The MNIST dataset will be automatically downloaded in the data folder when first run.
When the dataset is large (e.g. for data poisoning) using the GPU can speed up the computation.
All Experiments artifacts will be saved in the exps folder inside the project directory
How to analyse results
Use the notebooks in the analyse_results folder to generate plots from the data of previously run experiments.
Additional info
See hypertorch for more details on the AID and ITD hypergradient approximation methdos and some examples on how to incorporate them in a project.
nonsmooth_implicit_diff/stoch_hg.py contains the code for the NSID method to approximate the derivaive of a fixed point which is a composition of an outer map and an inner map accessible only through a stochastic unbiased estimator.
Details on the experimental settings can be found in our paper.
Cite us
If you use this code, please cite our paper.
@article{grazzi2024nonsmooth,
title={Nonsmooth implicit differentiation: Deterministic and stochastic convergence rates},
author={Grazzi, Riccardo and Pontil, Massimiliano and Salzo, Saverio},
journal={arXiv preprint arXiv:2403.11687},
year={2024}
}

About
Code for the paper Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).
Topics
bilevelbilevel-optimizationhypergradient
Resources
Readme
MIT license
Activity
Stars
2 stars
Watchers
1 watching
Forks
0 forks
Report repository
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Force GitHub README to respect dark mode\n(function() {\n var style = document.createElement('style');\n style.textContent = '\n .markdown-body {\n color-scheme: dark light;\n }\n .markdown-body pre { background: #161b22 !important; }\n .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }\n .markdown-body table th, .markdown-body table td { border-color: #30363d !important; }\n .markdown-body img { background: #0d1117; }\n .markdown-body blockquote { border-left-color: #8b949e; }\n .markdown-body hr { border-color: #30363d; }\n ';\n document.head.appendChild(style);\n})();", "GitHub Dark Mode README Fix");
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})();
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var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Nonsmooth Implicit Differentiation
Code for the paper
Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).
Getting started
Install the packages in requirements.txt.
Check out elastic_net_toy.ipynb for an illustrative comparison between deterministic AID and ITD derivative approximation methods for (nonsmooth) elastic net.
How to reproduce results
Run one of the following files:
  • elastic_net_deterministic.py for the experiments comparing AID and ITD on computing the derivative with respect to the hyperparameters of elastic net.
  • elastic_net_stochastic.py for the experiments comparing AID-FP and NSID and SID on computing the derivative with respect to the hyperparameters of elastic net.
  • data_poisoning_stochastic.py for the experiments comparing (N)SID with constant and decreasing step-size schedules on computing the derivative with respect to the corruption noise of the data poisoning with elastic net regularization. The MNIST dataset will be automatically downloaded in the data folder when first run.
When the dataset is large (e.g. for data poisoning) using the GPU can speed up the computation.
All Experiments artifacts will be saved in the exps folder inside the project directory
How to analyse results
Use the notebooks in the analyse_results folder to generate plots from the data of previously run experiments.
Additional info
See hypertorch for more details on the AID and ITD hypergradient approximation methdos and some examples on how to incorporate them in a project.
nonsmooth_implicit_diff/stoch_hg.py contains the code for the NSID method to approximate the derivaive of a fixed point which is a composition of an outer map and an inner map accessible only through a stochastic unbiased estimator.
Details on the experimental settings can be found in our paper.
Cite us
If you use this code, please cite our paper.
@article{grazzi2024nonsmooth,
title={Nonsmooth implicit differentiation: Deterministic and stochastic convergence rates},
author={Grazzi, Riccardo and Pontil, Massimiliano and Salzo, Saverio},
journal={arXiv preprint arXiv:2403.11687},
year={2024}
}

About
Code for the paper Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).
Topics
bilevelbilevel-optimizationhypergradient
Resources
Readme
MIT license
Activity
Stars
2 stars
Watchers
1 watching
Forks
0 forks
Report repository
Used by
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Highlight search terms from Google/DuckDuckGo/Bing referrer\n(function() {\n var ref = document.referrer;\n var terms = [];\n \n if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {\n var url = new URL(ref);\n var q = url.searchParams.get('q') || url.searchParams.get('p');\n if (q) {\n terms = q.split(/\\s+/).filter(function(t) { return t.length > 2; });\n }\n }\n \n if (terms.length === 0) return;\n \n var style = document.createElement('style');\n style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';\n document.head.appendChild(style);\n \n function highlight(node) {\n if (node.nodeType === 3) { // text node\n var text = node.textContent;\n var found = false;\n terms.forEach(function(term) {\n var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\\]\\\\]/g, '\\\\') + ')', 'gi');\n if (regex.test(text)) {\n found = true;\n var frag = document.createDocumentFragment();\n var parts = text.split(regex);\n parts.forEach(function(part, i) {\n if (i % 2 === 0) {\n frag.appendChild(document.createTextNode(part));\n } else {\n var span = document.createElement('span');\n span.className = 'userscript-highlight';\n span.textContent = part;\n frag.appendChild(span);\n }\n });\n node.parentNode.replaceChild(frag, node);\n }\n });\n } else if (node.nodeType === 1 && node.childNodes) { // element\n var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];\n if (!skipTags.includes(node.tagName)) {\n Array.from(node.childNodes).forEach(highlight);\n }\n }\n }\n \n highlight(document.body);\n \n // Re-highlight on dynamic content\n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1 || node.nodeType === 3) highlight(node);\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Highlight Search Terms");
}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Nonsmooth Implicit Differentiation
Code for the paper
Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).
Getting started
Install the packages in requirements.txt.
Check out elastic_net_toy.ipynb for an illustrative comparison between deterministic AID and ITD derivative approximation methods for (nonsmooth) elastic net.
How to reproduce results
Run one of the following files:
  • elastic_net_deterministic.py for the experiments comparing AID and ITD on computing the derivative with respect to the hyperparameters of elastic net.
  • elastic_net_stochastic.py for the experiments comparing AID-FP and NSID and SID on computing the derivative with respect to the hyperparameters of elastic net.
  • data_poisoning_stochastic.py for the experiments comparing (N)SID with constant and decreasing step-size schedules on computing the derivative with respect to the corruption noise of the data poisoning with elastic net regularization. The MNIST dataset will be automatically downloaded in the data folder when first run.
When the dataset is large (e.g. for data poisoning) using the GPU can speed up the computation.
All Experiments artifacts will be saved in the exps folder inside the project directory
How to analyse results
Use the notebooks in the analyse_results folder to generate plots from the data of previously run experiments.
Additional info
See hypertorch for more details on the AID and ITD hypergradient approximation methdos and some examples on how to incorporate them in a project.
nonsmooth_implicit_diff/stoch_hg.py contains the code for the NSID method to approximate the derivaive of a fixed point which is a composition of an outer map and an inner map accessible only through a stochastic unbiased estimator.
Details on the experimental settings can be found in our paper.
Cite us
If you use this code, please cite our paper.
@article{grazzi2024nonsmooth,
title={Nonsmooth implicit differentiation: Deterministic and stochastic convergence rates},
author={Grazzi, Riccardo and Pontil, Massimiliano and Salzo, Saverio},
journal={arXiv preprint arXiv:2403.11687},
year={2024}
}

About
Code for the paper Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).
Topics
bilevelbilevel-optimizationhypergradient
Resources
Readme
MIT license
Activity
Stars
2 stars
Watchers
1 watching
Forks
0 forks
Report repository
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Strip utm_, fbclid, gclid, etc. from all links on page\n(function() {\n var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',\n 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',\n 'ref', 'ref_src', 'source', 'medium', 'campaign'];\n \n function cleanUrl(url) {\n try {\n var u = new URL(url, window.location.origin);\n var changed = false;\n trackingParams.forEach(function(p) {\n if (u.searchParams.has(p)) {\n u.searchParams.delete(p);\n changed = true;\n }\n });\n return changed ? u.toString() : url;\n } catch (e) {\n return url;\n }\n }\n \n function cleanLinks() {\n document.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n \n cleanLinks();\n \n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1) {\n if (node.tagName === 'A') cleanLinks();\n node.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Remove Tracking Parameters from Links");
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} catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); }
})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '

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Nonsmooth Implicit Differentiation
Code for the paper
Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).
Getting started
Install the packages in requirements.txt.
Check out elastic_net_toy.ipynb for an illustrative comparison between deterministic AID and ITD derivative approximation methods for (nonsmooth) elastic net.
How to reproduce results
Run one of the following files:
  • elastic_net_deterministic.py for the experiments comparing AID and ITD on computing the derivative with respect to the hyperparameters of elastic net.
  • elastic_net_stochastic.py for the experiments comparing AID-FP and NSID and SID on computing the derivative with respect to the hyperparameters of elastic net.
  • data_poisoning_stochastic.py for the experiments comparing (N)SID with constant and decreasing step-size schedules on computing the derivative with respect to the corruption noise of the data poisoning with elastic net regularization. The MNIST dataset will be automatically downloaded in the data folder when first run.
When the dataset is large (e.g. for data poisoning) using the GPU can speed up the computation.
All Experiments artifacts will be saved in the exps folder inside the project directory
How to analyse results
Use the notebooks in the analyse_results folder to generate plots from the data of previously run experiments.
Additional info
See hypertorch for more details on the AID and ITD hypergradient approximation methdos and some examples on how to incorporate them in a project.
nonsmooth_implicit_diff/stoch_hg.py contains the code for the NSID method to approximate the derivaive of a fixed point which is a composition of an outer map and an inner map accessible only through a stochastic unbiased estimator.
Details on the experimental settings can be found in our paper.
Cite us
If you use this code, please cite our paper.
@article{grazzi2024nonsmooth,
title={Nonsmooth implicit differentiation: Deterministic and stochastic convergence rates},
author={Grazzi, Riccardo and Pontil, Massimiliano and Salzo, Saverio},
journal={arXiv preprint arXiv:2403.11687},
year={2024}
}

About
Code for the paper Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).
Topics
bilevelbilevel-optimizationhypergradient
Resources
Readme
MIT license
Activity
Stars
2 stars
Watchers
1 watching
Forks
0 forks
Report repository
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Auto-enable theater mode on YouTube\n(function() {\n function tryTheater() {\n var btn = document.querySelector('button[aria-label=\"Theater mode\"], ytd-player #player button[title=\"Theater mode\"]');\n if (btn && !btn.classList.contains('activated')) {\n btn.click();\n }\n }\n \n // Try immediately\n tryTheater();\n \n // Try after navigation (SPA)\n var lastUrl = location.href;\n setInterval(function() {\n if (location.href !== lastUrl) {\n lastUrl = location.href;\n setTimeout(tryTheater, 500);\n }\n }, 1000);\n \n // Also try on player load\n var observer = new MutationObserver(tryTheater);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "YouTube Theater Mode Default");
}
} catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Nonsmooth Implicit Differentiation
Code for the paper
Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).
Getting started
Install the packages in requirements.txt.
Check out elastic_net_toy.ipynb for an illustrative comparison between deterministic AID and ITD derivative approximation methods for (nonsmooth) elastic net.
How to reproduce results
Run one of the following files:
  • elastic_net_deterministic.py for the experiments comparing AID and ITD on computing the derivative with respect to the hyperparameters of elastic net.
  • elastic_net_stochastic.py for the experiments comparing AID-FP and NSID and SID on computing the derivative with respect to the hyperparameters of elastic net.
  • data_poisoning_stochastic.py for the experiments comparing (N)SID with constant and decreasing step-size schedules on computing the derivative with respect to the corruption noise of the data poisoning with elastic net regularization. The MNIST dataset will be automatically downloaded in the data folder when first run.
When the dataset is large (e.g. for data poisoning) using the GPU can speed up the computation.
All Experiments artifacts will be saved in the exps folder inside the project directory
How to analyse results
Use the notebooks in the analyse_results folder to generate plots from the data of previously run experiments.
Additional info
See hypertorch for more details on the AID and ITD hypergradient approximation methdos and some examples on how to incorporate them in a project.
nonsmooth_implicit_diff/stoch_hg.py contains the code for the NSID method to approximate the derivaive of a fixed point which is a composition of an outer map and an inner map accessible only through a stochastic unbiased estimator.
Details on the experimental settings can be found in our paper.
Cite us
If you use this code, please cite our paper.
@article{grazzi2024nonsmooth,
title={Nonsmooth implicit differentiation: Deterministic and stochastic convergence rates},
author={Grazzi, Riccardo and Pontil, Massimiliano and Salzo, Saverio},
journal={arXiv preprint arXiv:2403.11687},
year={2024}
}

About
Code for the paper Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).
Topics
bilevelbilevel-optimizationhypergradient
Resources
Readme
MIT license
Activity
Stars
2 stars
Watchers
1 watching
Forks
0 forks
Report repository
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Remove or un-stick sticky/fixed headers that block content\n(function() {\n function unstick() {\n document.querySelectorAll('header, nav, [role=\"banner\"], .header, .navbar, .sticky, .fixed-top, [style*=\"position: fixed\"], [style*=\"position:sticky\"]').forEach(function(el) {\n if (el.style.position === 'fixed' || el.style.position === 'sticky' || \n getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {\n el.style.position = 'static';\n el.style.top = 'auto';\n el.style.zIndex = 'auto';\n }\n });\n }\n \n unstick();\n \n var observer = new MutationObserver(unstick);\n observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });\n})();", "Kill Sticky Headers");
}
} catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Nonsmooth Implicit Differentiation
Code for the paper
Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).
Getting started
Install the packages in requirements.txt.
Check out elastic_net_toy.ipynb for an illustrative comparison between deterministic AID and ITD derivative approximation methods for (nonsmooth) elastic net.
How to reproduce results
Run one of the following files:
  • elastic_net_deterministic.py for the experiments comparing AID and ITD on computing the derivative with respect to the hyperparameters of elastic net.
  • elastic_net_stochastic.py for the experiments comparing AID-FP and NSID and SID on computing the derivative with respect to the hyperparameters of elastic net.
  • data_poisoning_stochastic.py for the experiments comparing (N)SID with constant and decreasing step-size schedules on computing the derivative with respect to the corruption noise of the data poisoning with elastic net regularization. The MNIST dataset will be automatically downloaded in the data folder when first run.
When the dataset is large (e.g. for data poisoning) using the GPU can speed up the computation.
All Experiments artifacts will be saved in the exps folder inside the project directory
How to analyse results
Use the notebooks in the analyse_results folder to generate plots from the data of previously run experiments.
Additional info
See hypertorch for more details on the AID and ITD hypergradient approximation methdos and some examples on how to incorporate them in a project.
nonsmooth_implicit_diff/stoch_hg.py contains the code for the NSID method to approximate the derivaive of a fixed point which is a composition of an outer map and an inner map accessible only through a stochastic unbiased estimator.
Details on the experimental settings can be found in our paper.
Cite us
If you use this code, please cite our paper.
@article{grazzi2024nonsmooth,
title={Nonsmooth implicit differentiation: Deterministic and stochastic convergence rates},
author={Grazzi, Riccardo and Pontil, Massimiliano and Salzo, Saverio},
journal={arXiv preprint arXiv:2403.11687},
year={2024}
}

About
Code for the paper Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).
Topics
bilevelbilevel-optimizationhypergradient
Resources
Readme
MIT license
Activity
Stars
2 stars
Watchers
1 watching
Forks
0 forks
Report repository
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
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Nonsmooth Implicit Differentiation
Code for the paper
Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).
Getting started
Install the packages in requirements.txt.
Check out elastic_net_toy.ipynb for an illustrative comparison between deterministic AID and ITD derivative approximation methods for (nonsmooth) elastic net.
How to reproduce results
Run one of the following files:
  • elastic_net_deterministic.py for the experiments comparing AID and ITD on computing the derivative with respect to the hyperparameters of elastic net.
  • elastic_net_stochastic.py for the experiments comparing AID-FP and NSID and SID on computing the derivative with respect to the hyperparameters of elastic net.
  • data_poisoning_stochastic.py for the experiments comparing (N)SID with constant and decreasing step-size schedules on computing the derivative with respect to the corruption noise of the data poisoning with elastic net regularization. The MNIST dataset will be automatically downloaded in the data folder when first run.
When the dataset is large (e.g. for data poisoning) using the GPU can speed up the computation.
All Experiments artifacts will be saved in the exps folder inside the project directory
How to analyse results
Use the notebooks in the analyse_results folder to generate plots from the data of previously run experiments.
Additional info
See hypertorch for more details on the AID and ITD hypergradient approximation methdos and some examples on how to incorporate them in a project.
nonsmooth_implicit_diff/stoch_hg.py contains the code for the NSID method to approximate the derivaive of a fixed point which is a composition of an outer map and an inner map accessible only through a stochastic unbiased estimator.
Details on the experimental settings can be found in our paper.
Cite us
If you use this code, please cite our paper.
@article{grazzi2024nonsmooth,
title={Nonsmooth implicit differentiation: Deterministic and stochastic convergence rates},
author={Grazzi, Riccardo and Pontil, Massimiliano and Salzo, Saverio},
journal={arXiv preprint arXiv:2403.11687},
year={2024}
}

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Code for the paper Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates by Riccardo Grazzi, Massimiliano Pontil and Saverio Salzo (ICML 2024).
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bilevelbilevel-optimizationhypergradient
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