Fast Gradient-Based Methods with Exponential Rate: A Hybrid Control Framework
Authors: Arman Sharifi Kolarijani, Peyman Mohajerin Esfahani, Tamas Keviczky
ICML 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In Section 5, a numerical example is given. ... We consider a quadratic objective function f(x1) = x 1 Qx1 where x1 R5 with the matrix Q = diag{0.1, 0.2, , 0.5}. ... Figure 1 reports the performance of NSR for two values kmin {1, 6, 7}. We note that when kmin = 6, 7, NSR is no longer monotone, while it remains monotone for kmin 5. |
| Researcher Affiliation | Academia | Delft Center for Systems and Control, Delft University of Technology, The Netherlands. Correspondence to: Arman Sharifi Kolarijani <a.sharifikolarijani@tudelft.nl>. |
| Pseudocode | Yes | Algorithm 1 Sate Dependent Scheme Input: data x0 1, ℓf, Lf, µf, α R+, kmax N+ Set: c1 = c2 = β 1 = Lfs, x0 2 = β f(x0 1) x0 = (x0 1, x0 2) for k = 1 to kmax do if c1 xk 2 2 f(xk 1) 2 c2 f(xk 1), xk 2 then xk+1 Fd(xk) else xk+1 Gd(xk) end if end for |
| Open Source Code | No | The paper does not provide any concrete access to source code for the methodology described. |
| Open Datasets | No | The paper uses a synthetic quadratic objective function for its numerical example, not a publicly available dataset with concrete access information. |
| Dataset Splits | No | The paper uses a synthetic quadratic objective function for its numerical example, and therefore does not specify train/validation/test dataset splits. |
| Hardware Specification | No | The paper describes a numerical example but does not specify any hardware used for running the experiments. |
| Software Dependencies | No | The paper mentions comparing performance with 'Nesterov’s accelerated method' and 'Algorithm 1', but does not provide specific software versions or dependencies used for implementation. |
| Experiment Setup | Yes | In what follows, we compare the performance of Algorithm 1 (denoted by HD) with that of Nesterov s accelerated method using the speed restarting scheme proposed in (Su et al., 2016) (denoted by NSR). We set s = 1/Lf in Algorithm 1 and the rest of the parameters are computed according to Corollary 3.9. The NSR algorithm requires a tuning parameter kmin that is the minimum number of iterations between two consecutive restart instants. |