Signatured Deep Fictitious Play for Mean Field Games with Common Noise
Authors: Ming Min, Ruimeng Hu
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The efficiency is supported by three applications, including linear-quadratic MFGs, mean-field portfolio game, and mean-field game of optimal consumption and investment. Overall, we provide a new point of view from the rough path theory to solve MFGs with common noise with significantly improved efficiency and an extensive range of applications. In addition, we report the first deep learning work to deal with extended MFGs (a mean-field interaction via both the states and controls) with common noise. |
| Researcher Affiliation | Academia | 1Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA 2Department of Mathematics, University of California, Santa Barbara, CA 93106-3080, USA. |
| Pseudocode | Yes | Algorithm 1 The Sig-DFP Algorithm |
| Open Source Code | Yes | Implementation codes are available at https: //github.com/mmin0/Sig DFP. |
| Open Datasets | No | The paper describes how the data was *generated* for the experiments (e.g., "Initial states are generated independently by Xi 0 µ0, with µ0 = U(0, 1) as the uniform distribution. The idiosyncratic Brownian motions W and common noises B are generated by antithetic variates for variance reduction"), but it does not specify or provide access to a pre-existing, publicly available dataset used for training. |
| Dataset Splits | Yes | For all three experiments, the size of both training and test data is N = 215, and the size of validation data is N/2. |
| Hardware Specification | Yes | Training processes are done on a server with Intel Core i9-9820X (10 cores, 3.30 GHz) and RTX 2080 Ti GPU |
| Software Dependencies | No | The paper mentions software packages like "Python package Signatory" and "Python package scikit-learn", and provides citations. However, it does not specify the exact version numbers for these software dependencies, which is required for a reproducible description. |
| Experiment Setup | Yes | The truncated signature depth is chosen at M = 2. The model is trained for 500 iterations of fictitious play. The learning rate is set as 0.1 for the first half and 0.01 for the second half of training. αϕ is a feedforward NN with two hidden layers of width 64. |