Learning Mean-Field Games with Discounted and Average Costs

Authors: Berkay Anahtarci, Can Deha Kariksiz, Naci Saldi

JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental In this section, we present two numerical examples in the case of discounted cost and average cost, respectively, to demonstrate the applicability of our learning algorithm.
Researcher Affiliation Academia Berkay Anahtarci EMAIL Department of Natural and Mathematical Sciences Ozye gin University Istanbul, Turkey Can Deha Kariksiz EMAIL Department of Natural and Mathematical Sciences Ozye gin University Istanbul, Turkey Naci Saldi EMAIL Department of Mathematics Bilkent University Ankara, Turkey
Pseudocode Yes Algorithm 1 Algorithm ˆH1... Algorithm 2 Algorithm ˆH2... Algorithm 3 Learning Algorithm... Algorithm 4 Algorithm ˆHav 1... Algorithm 5 Algorithm ˆHav 2... Algorithm 6 Learning Algorithm
Open Source Code No The text does not contain a clear, affirmative statement about releasing source code for the methodology described, nor does it provide a direct link to a code repository. It mentions using MATLAB's neural network fitting tool, but not their own code.
Open Datasets No The paper defines its own game environments and parameters for numerical examples (e.g., 'We consider the mean-field game that was introduced in Example 1, where we take X = [0, 0.1, 0., 2, . . . , 1], A = [0, 1], c2(a) = ρ a2, and c1(x, µ) = η x (1 ξ µ ) with µ denoting the mean of µ.'). It does not use or provide access information for any publicly available or open dataset.
Dataset Splits No The paper uses generated samples within a simulated environment (e.g., 'Generate i.i.d. samples {(xt, at, ct, yt+1)N t=1}'), rather than pre-existing datasets. Therefore, the concept of specific training/test/validation splits for a dataset is not applicable and not mentioned.
Hardware Specification No The paper mentions using 'neural network fitting tool of MATLAB' for its numerical experiments but does not provide any specific details about the hardware (e.g., CPU, GPU models) used for these computations.
Software Dependencies No The paper states 'We use neural network fitting tool of MATLAB' and specific functions like 'fittnet', 'train', and 'net', but it does not provide version numbers for MATLAB or any other software components used.
Experiment Setup Yes In the numerical experiments, we use the following values for the parameters: η = 2, ξ = 0.4, ρ = 1 κ = 1, γ = 0.4, β = 0.9. We run the learning algorithm using the following parameters: N = 10000, L = 50, M = 1000, K = 50. The output of the learning algorithm contains the average of the state-measure (i.e., mean-field distribution) and mean-field equilibrium policies for states x = 0.1 and x = 0.6. In the fitted Q-iteration algorithm, we pick the function class F as two-layer neural networks with 10 hidden units. We use neural network fitting tool of MATLAB. In particular, we use fittnet , train , and net functions of MATLAB, where Levenberg-Marquardt is picked as the training algorithm and the transfer function is chosen as hyperbolic tangent sigmoid transfer function . The parameters of the neural network fitting tool of MATLAB are set to default values.