Disciplined Bilevel Programming
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The paper addresses instability in bilevel optimization solutions when problem data changes. It proposes a lifted formulation for the optimistic setting that remains stable under mild assumptions, without requiring convexity or smoothness. The approach accommodates integer restrictions and disjunctive constraints, relies on pointwise and local calmness of the lower-level problem, and offers computational advantages including an outer approximation algorithm.
arXiv:2512. 02494v2 Announce Type: replace Abstract: Differentiable optimization layers enable learning systems to make decisions by solving embedded optimization problems.
The paper presents a unified taxonomy that classifies machine‑learning and artificial‑intelligence applications according to mathematical programming paradigms such as linear, quadratic, mixed‑integer, conic, bilevel, and others. It standardizes notation, identifies key inputs, decision variables, and principal formulations for each application, and discusses structural properties, solution strategies, and limitations. The authors compare tractability, relaxation quality, decomposition, approximation guarantees, and scalability across paradigms, emphasizing that mathematical programming serves as a disciplined interface between predictions and constrained decisions rather than a universal modeling claim.
arXiv:2609.16350v1 Announce Type: new Abstract: Federated stochastic bilevel optimization has been actively studied in recent years due to its widespread applications in machine learning. However, mo...
arXiv:2608. 15143v1 Announce Type: new Abstract: Constraint solving is a declarative approach for solving combinatorial satisfaction and optimization problems.
The paper presents cvxgenrust, an open‑source tool that generates custom Rust code for solving families of parameterized convex optimization problems defined in CVXPY. It canonicalizes problem families, extracts affine maps to Clarabel cone‑program data, and produces a specialized Rust crate that updates parameters and calls Clarabel natively at runtime. The generated solver can also be exposed to Python and registered as a custom CVXPY solver, supporting a wide range of convex problems up to semidefinite and exponential‑cone programs, and demonstrates reduced runtime compared to direct CVXPY solves and performance comparable to CVXPYgen.