Discrete Variational Calculus for Accelerated Optimization
Authors: Cédric M. Campos, Alejandro Mahillo, David Martín de Diego
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Several experiments exemplify the result. Finally, for Section 8, many methods and numerical simulations have been implemented in Julia v1.8.2. We optimize several test functions with our methodology and other methods that appeared recently in the literature. One of the test functions is reused afterwards for a machine learning example. |
| Researcher Affiliation | Academia | C edric M. Campos EMAIL Departamento de Matem atica Aplicada, Ciencia e Ingenier ıa de los Materiales y Tecnolog ıa Electr onica Universidad Rey Juan Carlos Calle Tulip an s/n, 28933 M ostoles, Spain Alejandro Mahillo EMAIL Departamento de Matem aticas Instituto Universitario de Matem aticas y Aplicaciones Universidad de Zaragoza Calle de Pedro Cerbuna 12, 50009 Zaragoza, Spain David Mart ın de Diego EMAIL Instituto de Ciencias Matem aticas (CSIC-UAM-UC3M-UCM) Calle Nicol as Cabrera 13-15, 28049 Madrid, Spain |
| Pseudocode | No | No explicit pseudocode or algorithm blocks are provided. The methods are described using mathematical equations and textual descriptions, such as equations (2.6a)-(2.6b) for NAG and the 3-phase scheme (8.13a)-(8.13c) for WWJ. |
| Open Source Code | Yes | Methods, functions, and simulations are available online (Campos, 2022a,b). C edric M. Campos. Research repository, 2022b. URL https://github.com/cmcampos-xyz. |
| Open Datasets | Yes | For an actual ANN test, the log-loss function is fed with the widely used Iris dataset (Dua and Graff, 2017; see below for more details). Dheeru Dua and Casey Graff. UCI machine learning repository, 2017. URL http://archive.ics.uci.edu/ml. |
| Dataset Splits | Yes | At each run and for each number of epochs, the samples are randomly split in two: 100 samples for training and 50 samples for testing. |
| Hardware Specification | No | No specific hardware details (such as CPU, GPU, or memory specifications) are provided for running the experiments. The paper only mentions that "The methods have been implemented in Julia v1.8.2 (Bezanson et al., 2017)". |
| Software Dependencies | Yes | The methods have been implemented in Julia v1.8.2 (Bezanson et al., 2017), using solely as nonnative libraries NLsolve.jl (Mogensen et al., 2020) to solve the side problem (8.13c), Plots.jl (Breloff, 2021) and PGFPlots X.jl for plotting, and Pluto.jl for an interactive notebook. The reference for NLsolve.jl specifies 'v4.5.1'. |
| Experiment Setup | Yes | We set Rosenbrock s test function with 30 dimensions and seek for its global minimum at (1, . . . , 1) from (0, . . . , 0) at a pace of h = 0.01 for 20000 epochs. In the case of the YATF, there is a local minimum near (0.32, 1.60) which we seek from ( 0.25, 0.35) with time-step h = 0.01 for 3800 epochs. A random point on a sphere of radius 50 is the initial guess for the 50-dimensional quadratic function, whose global minimum, sought for 10000 epochs with h = 0.1, is clearly at the origin. For the convergence tests, the log-loss function [...] will seek for the infimum for 12000 epochs at a pace of h 0.945 from a random weight distribution with null biases. For an actual ANN test, the log-loss function is fed with the widely used Iris dataset [...]. We train the network (or optimize the objective function) at an increasing number of epochs (from 25 up to 250) for 1000 runs. At the same time, the initial weights of the network are drawn from a normal distribution with null mean and standard deviation σ = 10. |