Fast semidefinite programming with feedforward neural networks
arXiv:2011.05785 · doi:10.1088/1367-2630/ac2d72
Abstract
Semidefinite programming is an important optimization task, often used in time-sensitive applications. Though they are solvable in polynomial time, in practice they can be too slow to be used in online, i.e. real-time applications. Here we propose to solve feasibility semidefinite programs using artificial neural networks. Given the optimization constraints as an input, a neural network outputs values for the optimization parameters such that the constraints are satisfied, both for the primal and the dual formulations of the task. We train the network without having to exactly solve the semidefinite program even once, thus avoiding the possibly time-consuming task of having to generate many training samples with conventional solvers. The neural network method is only inconclusive if both the primal and dual models fail to provide feasible solutions. Otherwise we always obtain a certificate, which guarantees false positives to be excluded. We examine the performance of the method on a hierarchy of quantum information tasks, the Navascués-Pironio-Acín hierarchy applied to the Bell scenario. We demonstrate that the trained neural network gives decent accuracy, while showing orders of magnitude increase in speed compared to a traditional solver.
References in corpus (19)
- Bell nonlocality
- Random Numbers Certified by Bell's Theorem
- A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
- Non-local correlations as an information theoretic resource
- Bounding the set of quantum correlations
- Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals
- More Randomness from the Same Data
- MHz-rate semi-device-independent quantum random number generators based on unambiguous state discrimination
- Using complete measurement statistics for optimal device-independent randomness evaluation
- Algorithm 950: Ncpol2sdpa---Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables
- Machine learning non-local correlations
- A neural network oracle for quantum nonlocality problems in networks
- Quantum Inflation: A General Approach to Quantum Causal Compatibility
- Bounding the sets of classical and quantum correlations in networks
- Setting up experimental Bell test with reinforcement learning
- Bounding sets of sequential quantum correlations and device-independent randomness certification
- Approximation algorithms for quantum many-body problems
- A paradox in bosonic energy computations via semidefinite programming relaxations
- How to Teach AI to Play Bell Non-Local Games: Reinforcement Learning