Distributionally Robust Linear Quadratic Control
Authors: Bahar Taskesen, Dan Iancu, Çağıl Koçyiğit, Daniel Kuhn
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We propose a numerical solution method that efficiently characterizes this optimal control policy. ... Lastly, we implement the algorithm leveraging Py Torch s automatic differentiation module and we find that it yields uniformly lower runtimes than a direct method (based on solving semidefinite programs) across all problem horizons. ... 5. Numerical Experiments All experiments are run on an Intel i7-8700 CPU (3.2 GHz) machine with 16GB RAM. ... Figure 1a illustrates the execution time for both approaches as a function of the planning horizon T; runs where MOSEK exceeds 100s are not reported. Figure 1b visualizes the empirical convergence behavior of the Frank-Wolfe algorithm. |
| Researcher Affiliation | Academia | Bahar Ta skesen EPFL bahar.taskesen@epfl.ch Dan A. Iancu Stanford University daniancu@stanford.edu Ça gıl Koçyi git University of Luxembourg cagil.kocyigit@uni.lu Daniel Kuhn EPFL daniel.kuhn@epfl.ch |
| Pseudocode | Yes | A detailed description of the proposed Frank-Wolfe method is given in Algorithm 1 below. Algorithm 1 Frank-Wolfe algorithm for solving (12) |
| Open Source Code | Yes | The code is publicly available in the Github repository https: //github.com/RAO-EPFL/DR-Control. |
| Open Datasets | No | The paper does not use a pre-existing publicly available or open dataset. Instead, it describes a process for generating random nominal covariance matrices for its experiments: 'The nominal covariance matrices of the exogenous uncertainties are constructed randomly and with eigenvalues in the interval [1, 2] (so as to ensure they are positive definite).' |
| Dataset Splits | No | The paper does not explicitly provide training/test/validation dataset splits. The research is in control theory and optimization, which typically involves system modeling and simulation rather than fixed datasets with predefined splits commonly found in machine learning. |
| Hardware Specification | Yes | All experiments are run on an Intel i7-8700 CPU (3.2 GHz) machine with 16GB RAM. |
| Software Dependencies | No | The paper mentions 'Python 3.8.6', 'CVXPY [1, 14]', 'MOSEK [37]', 'Pymanopt [48]', and 'Py Torch s automated differentiation module [39, 40]'. While Python has a specific version, multiple other key software components are mentioned without explicit version numbers in the text. |
| Experiment Setup | Yes | Consider a class of distributionally robust LQG problems with n = m = p = 10. We set At = 0.1 A to have ones on the main diagonal and the superdiagonal and zeroes everywhere else (Ai,j = 1 if i = j or i = j 1 and Ai,j = 0 otherwise), and the other matrices to Bt = Ct = Qt = Rt = Id. The Wasserstein radii are set to ρx0 = ρwt = ρvt = 10 1. The nominal covariance matrices of the exogenous uncertainties are constructed randomly and with eigenvalues in the interval [1, 2] (so as to ensure they are positive definite). ... we set a stopping criterion corresponding to an optimality gap below 10 3 and we run the Frank-Wolfe method with δ = 0.95. |