Differential Equations for Modeling Asynchronous Algorithms

Authors: Li He, Qi Meng, Wei Chen, Zhi-Ming Ma, Tie-Yan Liu

IJCAI 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental In this section, we take F(x) = 1/2(x + 1)^2 + 1/2(x - 1)^2 as a simple example. We compared the discrete optimization algorithms with the Euler-Maruyama schemes of stochastic differential equations. For optimization iteration and Euler-Maruyama scheme, the learning rate is set to be η = 0.005. We run the experiments within 2000 iterations. The figures include ASGD (resp. SGD) path and a sample path for SDDE (resp. SDE) approximation. First, we analyzed SDDE for ASGD algorithm. ... It is observed that the two paths are close. Second, from Fig.1(b) we can see that the SDE approximation and SGD iteration are well matched.
Researcher Affiliation Collaboration Li He1,2 , Qi Meng3 , Wei Chen4, Zhi-Ming Ma1,2 and Tie-Yan Liu4 1 University of Chinese Academy of Sciences 2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences 3 Peking University 4 Microsoft Research
Pseudocode No The paper presents mathematical equations and theoretical proofs but does not include any pseudocode or clearly labeled algorithm blocks.
Open Source Code No The paper does not provide any specific links to source code repositories, nor does it state that the code for the described methodology is publicly released.
Open Datasets No The experiments are conducted using a simple example function F(x) = 1/2(x + 1)^2 + 1/2(x - 1)^2 rather than a named or external dataset, and no access information for any data is provided.
Dataset Splits No The paper uses a simple example function for simulation and theoretical validation, thus traditional dataset splits (training, validation, test) are not applicable and are not mentioned.
Hardware Specification No The paper does not provide any specific details regarding the hardware (e.g., GPU/CPU models, memory specifications) used for running its experiments.
Software Dependencies No The paper does not provide specific software dependencies with version numbers that would be required to replicate the experiment.
Experiment Setup Yes For optimization iteration and Euler-Maruyama scheme, the learning rate is set to be η = 0.005. We run the experiments within 2000 iterations. ... For SDDE, we set the initial function as ξ(θ) = 4 for any θ ∈ [−τ, 0]. For ASGD, we assume a constant delay as l = 10 and let X(0) = 4.