arXiv subjects

Stefan Clarke

Publications and source records attributed to Stefan Clarke.

5 recordsLinked to original sources

arXiv2026

Conformal Prediction for Early Stopping in Mixed Integer Optimization

Mixed-integer optimization solvers often find optimal solutions early in the search, yet spend the majority of computation time proving optimality. We exploit this by learning when to terminate solvers early on distributions of similar problem instances. Our method trains a neural network to estimate the true optimality gap from the solver state, then uses conformal prediction to calibrate a stopping threshold with rigorous probabilistic guarantees on solution quality. On five problem families from the distributional MIPLIB library, our method reduces solve time by over 60% while guaranteeing 0.1%- optimal solutions with 95% probability

math.OC↗

arXiv2025

Learning-Based Hierarchical Approach for Fast Mixed-Integer Optimization

We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and a lower level problem, both of smaller size. We solve both problems sequentially, where decisions of the higher level problem become parameters of the constraints of the lower level problem. We formulate this learning task as a convex optimization problem using decision-focused learning techniques and solve it by differentiating through the higher and the lower level problems in our architecture. To ensure robustness, we derive out-of-sample performance guarantees using conformal prediction. Numerical experiments in facility location, knapsack problems, and vehicle routing problems demonstrate that our approach significantly reduces computation time while maintaining feasibility and high solution quality compared to state-of-the-art solvers.

math.OC↗

arXiv2024

Maximum Shannon Capacity of Photonic Structures

Information transfer through electromagnetic waves is an important problem that touches a variety of technologically relevant applications, including computing and telecommunications. Prior attempts to establish limits on optical information transfer have treated waves propagating through known photonic structures (including vacuum). In this article, we address fundamental questions concerning optimal information transfer in photonic devices. Combining information theory, wave scattering, and optimization theory, we formulate bounds on the maximum Shannon capacity that may be achieved by structuring senders, receivers, and their environment. Allowing for arbitrary structuring leads to a non-convex problem that is significantly more difficult than its fixed structure counterpart, which is convex and satisfies a known "water-filling" solution. We derive a geometry-agnostic convex relaxation of the problem that elucidates fundamental physics and scaling behavior of Shannon capacity with respect to device parameters and the importance of structuring for enhancing capacity. We also show that in regimes where communication is dominated by power insertion requirements, bounding Shannon capacity maps to a biconvex optimization problem in the basis of singular vectors of the Green's function. This problem admits analytical solutions that give physically intuitive interpretations of channel and power allocation and reveals how Shannon capacity varies with signal-to-noise ratio. Proof of concept numerical examples show that bounds are within an order of magnitude of achievable device performance and successfully predict the scaling of performance with channel noise. The presented methodologies have implications for the optimization of antennas, integrated photonic devices, metasurface kernels, MIMO space-division multiplexers, and waveguides to maximize communication efficiency and bit-rates.

physics.optics↗

arXiv2023

Differentiable Cutting-plane Layers for Mixed-integer Linear Optimization

We consider the problem of solving a family of parametric mixed-integer linear optimization problems where some entries in the input data change. We introduce the concept of cutting-plane layer (CPL), i.e., a differentiable cutting-plane generator mapping the problem data and previous iterates to cutting planes. We propose a CPL implementation to generate split cuts, and by combining several CPLs, we devise a differentiable cutting-plane algorithm that exploits the repeated nature of parametric instances. In an offline phase, we train our algorithm by updating the internal parameters controlling the CPLs, thus altering cut generation. Once trained, our algorithm computes, with predictable execution times and a fixed number of cuts, solutions with low integrality gaps. Preliminary computational tests show that our algorithm generalizes on unseen instances and captures underlying parametric structures.

math.OC↗

arXiv2023

Learning Rationality in Potential Games

We propose a stochastic first-order algorithm to learn the rationality parameters of simultaneous and non-cooperative potential games, i.e., the parameters of the agents' optimization problems. Our technique combines (i.) an active-set step that enforces that the agents play at a Nash equilibrium and (ii.) an implicit-differentiation step to update the estimates of the rationality parameters. We detail the convergence properties of our algorithm and perform numerical experiments on Cournot and congestion games, showing that our algorithm effectively finds high-quality solutions (in terms of out-of-sample loss) and scales to large datasets.

math.OC↗