Deep Distributed Optimization for Large-Scale Quadratic Programming
Authors: Augustinos Saravanos, Hunter Kuperman, Alex Oshin, Arshiya Taj Abdul, Vincent Pacelli, Evangelos Theodorou
ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The proposed framework, as well as its centralized version Deep QP, significantly outperform their standard optimization counterparts on a variety of tasks such as randomly generated problems, optimal control, linear regression, transportation networks and others. Notably, Deep Distributed QP demonstrates strong generalization by training on small problems and scaling to solve much larger ones (up to 50K variables and 150K constraints) using the same policy. Moreover, it achieves orders-of-magnitude improvements in wall-clock time compared to OSQP. The certifiable performance guarantees of our approach are also demonstrated, ensuring higher-quality solutions over traditional optimizers. |
| Researcher Affiliation | Academia | Augustinos D. Saravanos, Hunter Kuperman, Alex Oshin, Arshiya Taj Abdul, Vincent Pacelli and Evangelos A. Theodorou Georgia Institute of Technology, USA EMAIL |
| Pseudocode | Yes | The proposed Distributed QP method is summarized below, where k = 0, 1, . . . , denotes iterations: 1. Local updates for xi, zi. For each node i V, solve in parallel: Qi + µk i I A i Ai 1/ρk i I xk+1 i νk+1 i = qi + µk i wi yi zi 1/ρk i λi and then update in parallel: zk+1 i = sk i + 1/ρk i (νk+1 i λk i ). (5) 2. Local updates for si and global update for w. For each node i V, update in parallel: sk+1 i = Πsi bi αkzk+1 i + (1 αk)sk i + λk i /ρk i . (6) In addition, each global variable component wl is updated through: wk+1 l = αk P G(i,j)=l µk i [xi]j P G(i,j)=l µk i + (1 αk)wk l . (7) 3. Local updates for dual variables λi, yi. For each node i V, update in parallel: λk+1 i = λk i + ρk i (αkzk+1 i + (1 αk)sk i sk+1 i ), (8) yk+1 i = yk i + µk i (αkxk+1 i + (1 αk) wk i wk+1 i ). (9) |
| Open Source Code | No | The paper does not contain any explicit statements or links indicating the release of source code for the methodology described. |
| Open Datasets | Yes | Both the double integrator and the mass-spring problem setups are drawn from Chen et al. (2022a). We consider the same portfolio optimization problem setup as in Stellato et al. (2020). We again consider the same problem setup as in Stellato et al. (2020). The network flow problem is adapted from Mota (2013); Mota et al. (2014). Distributed LASSO (Mateos et al., 2010) extends LASSO to situations where the training data are distributed across different agents and agents cannot share training data with each other. |
| Dataset Splits | Yes | The training dimensions for each problem are detailed in Table 1. Both open-loop and closed-loop versions are trained using shared policies on datasets of size H [500, 1000]. We switch from learning deterministic weights to learning stochastic ones and follow the procedure described in Appendix I with H = 15000 training samples, M = 30000 sampled weights for the bounds evaluation, δ = 0.009 and ϵ = 0.001. |
| Hardware Specification | Yes | All experiments were performed on an system with an RTX 4090 GPU 24GB, a 13th Gen Intel(R) Core(TM) i9-13900K and 64GB of RAM. |
| Software Dependencies | No | The paper mentions using OSQP as an algorithm (Stellato et al., 2020) but does not specify version numbers for OSQP's implementation or other software dependencies like Python, PyTorch, or CUDA. |
| Experiment Setup | Yes | In all experiments, Deep QP was trained with a batch size of 50 using the Adam optimizer with learning rate 10^-3. The feedback layers are set as 2x16 MLPs. Deep QP and OSQP always start with zero initializations in all comparisons. The weights of the training loss were set to γk = exp ((k K) /5) in all experiments. |