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"schema_version": 1,
"title": "Reproduction: A Fully First-Order Layer for Differentiable Optimization",
"emoji": "📊",
"space_id": "snaykey/repro-first-order-diffopt",
"paper": {
"openreview_id": "jJur8Fq7IK"
},
"tags": [
"icml2026-repro",
"paper-jJur8Fq7IK"
],
"updated_at": "2026-08-01T00:00:00Z",
"root": {
"slug": "index",
"title": "Reproduction: A Fully First-Order Layer for Differentiable Optimization",
"file": "pages/index.md",
"children": [
{
"slug": "executive-summary",
"title": "Executive summary",
"file": "pages/executive-summary/page.md",
"children": []
},
{
"slug": "claim-1-sec42-alg1-firstorder-oracle",
"title": "FFOLayer computes an ε-approximate hypergradient using an active-set Lagrangian oracle that requires no Hessian evaluations, achieving Õ(1) first-order oracle calls per hypergradient estimate (Section 4.2, Algorithm 1).",
"file": "pages/claim-1-sec42-alg1-firstorder-oracle/page.md",
"children": []
},
{
"slug": "claim-2-thm41-ghost-reformulation-preserves-hypergradient",
"title": "Theorem 4.1 proves that the 'ghost bilevel optimization' reformulation, which treats active constraints as equalities, preserves the accuracy of the hypergradient computed at the original constrained-optimization solution (Section 4.1, Theorem 4.1).",
"file": "pages/claim-2-thm41-ghost-reformulation-preserves-hypergradient/page.md",
"children": []
},
{
"slug": "claim-3-sec4-oracle-complexity",
"title": "For constrained bilevel optimization, the method achieves an oracle complexity of Õ(δ⁻¹ε⁻³), matching best-known rates for non-smooth non-convex optimization, while extending prior guarantees from linear to general convex constraints (Section 4, complexity analysis).",
"file": "pages/claim-3-sec4-oracle-complexity/page.md",
"children": []
},
{
"slug": "claim-4-dfl-qp-sudoku-convergence-faster-backward",
"title": "On synthetic decision-focused-learning QP tasks and 9×9 Sudoku constraint-learning tasks formulated as linear programs, FFOLayer matches the convergence of exact differentiable-optimization solvers CvxpyLayer and qpth while using a substantially faster backward pass (Experiments section, synthetic QP and Sudoku benchmarks).",
"file": "pages/claim-4-dfl-qp-sudoku-convergence-faster-backward/page.md",
"children": []
},
{
"slug": "claim-5-objective-agnostic-detach-coefficient",
"title": "FFOLayer's PyTorch implementation is objective-agnostic, exposing task-loss influence via a single detached gradient coefficient c := detach(dF/dy*), allowing users to substitute it for CvxpyLayer with minimal code changes (Section on practical implementation).",
"file": "pages/claim-5-objective-agnostic-detach-coefficient/page.md",
"children": []
},
{
"slug": "claim-6-outperforms-lpgd-no-hessian-inversion",
"title": "FFOLayer outperforms the gradient-unrolling baseline LPGD in the reported experiments while eliminating the cubic-complexity Hessian inversion required by standard implicit differentiation (Experiments section, comparison with LPGD).",
"file": "pages/claim-6-outperforms-lpgd-no-hessian-inversion/page.md",
"children": []
},
{
"slug": "conclusion",
"title": "Conclusion",
"file": "pages/conclusion/page.md",
"children": []
}
]
}
} |