Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems
Authors: Juno Kim, Kakei Yamamoto, Kazusato Oko, Zhuoran Yang, Taiji Suzuki
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We test our proposed algorithms and compare against ordinary descent ascent dynamics in a simulated setting. We report the results in Figure 1. Figure 1(a)-(c) show kernel density plots of the evolving min and max policies µXk, νYk for each algorithm per every 100 epochs. MFL-AG and MFL-ABR converge to similar solutions while MFLDA converges to a different distribution much more rapidly. Figure 1(d) plots convergence speed by computing the sum of the empirical Wasserstein distances W1(µXk, µXk+1) + W1(νYk, νYk+1). To compare the optimality of the outputs (X i, Y i) (i = 0, 1, 2) of the three algorithms, we use the 3-point NI error NIi := maxj Lλ(µX i, νY j) minj Lλ(µX j, νY i) which measures relative optimality analogous to a 3 3 payoff matrix. The values are reported in Figure 1(e). |
| Researcher Affiliation | Academia | Juno Kim1,2 Kakei Yamamoto3 Kazusato Oko1,2 Zhuoran Yang4 Taiji Suzuki1,2 1The University of Tokyo, Tokyo, Japan 2Center for Advanced Intelligence Project, RIKEN 3Massachusetts Institute of Technology, Cambridge, MA 4Yale University, New Haven, CT junokim@g.ecc.u-tokyo.ac.jp |
| Pseudocode | Yes | Algorithm 1 Mean-field Langevin Averaged Gradient (Page 5) and Algorithm 2 Mean-field Langevin Anchored Best Response (Page 11). |
| Open Source Code | No | The paper does not contain any explicit statement about releasing code for the described methods nor provides a link to a public code repository. |
| Open Datasets | No | We consider d X = d Y = 1 and optimize the bilinear objective L(µ, ν) = RR Q(x, y)µ(dx)ν(dy), Q(x, y) = (1 + e (x y)2) 1. The sigmoid nonlinearity introduces nontrivial interactions between the min and max policies. We also take regularizers ρµ = ρν = N(0, 1) and λ = 0.01. (Section 6) The experiments use a simulated setting with defined functions and distributions, not an existing public dataset. |
| Dataset Splits | No | The paper states 'Both MFL-AG with r = 1 and MFL-DA are run with 1,000 particles for 1,000 epochs with learning rate η = 0.3. MFL-ABR is run with 1,000 particles for 50 outer loop iterations with 20 inner iterations per loop and η = 0.3, β = 0.15.' (Section 6). This describes simulation parameters, not standard training/validation/test splits of a dataset. |
| Hardware Specification | No | The paper does not mention any specific hardware (e.g., GPU models, CPU types) used for running the experiments. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers. |
| Experiment Setup | Yes | Both MFL-AG with r = 1 and MFL-DA are run with 1,000 particles for 1,000 epochs with learning rate η = 0.3. MFL-ABR is run with 1,000 particles for 50 outer loop iterations with 20 inner iterations per loop and η = 0.3, β = 0.15. |