Stochastic Semi-Gradient Descent for Learning Mean Field Games with Population-Aware Function Approximation

• URL: http://arxiv.org/abs/2408.08192v1
• Date: Thu, 15 Aug 2024 14:51:50 GMT
• Title: Stochastic Semi-Gradient Descent for Learning Mean Field Games with Population-Aware Function Approximation
• Authors: Chenyu Zhang, Xu Chen, Xuan Di,
• Abstract summary: Mean field games (MFGs) model the interactions within a large-population multi-agent system using the population distribution. This paper considers an online learning method for MFGs, where an agent updates its policy and population estimates simultaneously and fully asynchronously. We develop a linear function approximation (LFA) for both the value function and the population distribution, resulting in the first population-aware LFA for MFGs on continuous state-action space.
• Score: 16.00164239349632
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Mean field games (MFGs) model the interactions within a large-population multi-agent system using the population distribution. Traditional learning methods for MFGs are based on fixed-point iteration (FPI), which calculates best responses and induced population distribution separately and sequentially. However, FPI-type methods suffer from inefficiency and instability, due to oscillations caused by the forward-backward procedure. This paper considers an online learning method for MFGs, where an agent updates its policy and population estimates simultaneously and fully asynchronously, resulting in a simple stochastic gradient descent (SGD) type method called SemiSGD. Not only does SemiSGD exhibit numerical stability and efficiency, but it also provides a novel perspective by treating the value function and population distribution as a unified parameter. We theoretically show that SemiSGD directs this unified parameter along a descent direction to the mean field equilibrium. Motivated by this perspective, we develop a linear function approximation (LFA) for both the value function and the population distribution, resulting in the first population-aware LFA for MFGs on continuous state-action space. Finite-time convergence and approximation error analysis are provided for SemiSGD equipped with population-aware LFA.

Related papers

• Bellman Diffusion: Generative Modeling as Learning a Linear Operator in the Distribution Space [72.52365911990935]
  We introduce Bellman Diffusion, a novel DGM framework that maintains linearity in MDPs through gradient and scalar field modeling. Our results show that Bellman Diffusion achieves accurate field estimations and is a capable image generator, converging 1.5x faster than the traditional histogram-based baseline in distributional RL tasks.
  arXiv  Detail & Related papers  (2024-10-02T17:53:23Z)
• Stable Heterogeneous Treatment Effect Estimation across Out-of-Distribution Populations [27.163528362979594]
  Heterogeneous treatment effect (HTE) estimation is vital for understanding the change of treatment effect across individuals or groups. Most existing HTE estimation methods focus on addressing selection bias induced by imbalanced distributions of confounders between treated and control units. In real-world applications, where population distributions are subject to continuous changes, there is an urgent need for stable HTE estimation across out-of-distribution populations.
  arXiv  Detail & Related papers  (2024-07-03T13:03:51Z)
• A Single Online Agent Can Efficiently Learn Mean Field Games [16.00164239349632]
  Mean field games (MFGs) are a promising framework for modeling the behavior of large-population systems. This paper introduces a novel online single-agent model-free learning scheme, which enables a single agent to learn MFNE using online samples.
  arXiv  Detail & Related papers  (2024-05-05T16:38:04Z)
• Collaborative Heterogeneous Causal Inference Beyond Meta-analysis [68.4474531911361]
  We propose a collaborative inverse propensity score estimator for causal inference with heterogeneous data. Our method shows significant improvements over the methods based on meta-analysis when heterogeneity increases.
  arXiv  Detail & Related papers  (2024-04-24T09:04:36Z)
• Score-Aware Policy-Gradient Methods and Performance Guarantees using Local Lyapunov Conditions: Applications to Product-Form Stochastic Networks and Queueing Systems [1.747623282473278]
  We introduce a policygradient method for model reinforcement learning (RL) that exploits a type of stationary distributions commonly obtained from decision processes (MDPs) in networks. Specifically, when the stationary distribution of the MDP is parametrized by policy parameters, we can improve existing policy methods for average-reward estimation.
  arXiv  Detail & Related papers  (2023-12-05T14:44:58Z)
• Depersonalized Federated Learning: Tackling Statistical Heterogeneity by Alternating Stochastic Gradient Descent [6.394263208820851]
  Federated learning (FL) enables devices to train a common machine learning (ML) model for intelligent inference without data sharing. Raw data held by various cooperativelyicipators are always non-identically distributedly. We propose a new FL that can significantly statistical optimize by the de-speed of this process.
  arXiv  Detail & Related papers  (2022-10-07T10:30:39Z)
• Domain Adaptation meets Individual Fairness. And they get along [48.95808607591299]
  We show that algorithmic fairness interventions can help machine learning models overcome distribution shifts. In particular, we show that enforcing suitable notions of individual fairness (IF) can improve the out-of-distribution accuracy of ML models.
  arXiv  Detail & Related papers  (2022-05-01T16:19:55Z)
• A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions [3.198144010381572]
  Gradient descent (GD) type optimization methods are the standard instrument to train artificial neural networks (ANNs) with rectified linear unit (ReLU) activation.
  arXiv  Detail & Related papers  (2021-08-10T12:01:37Z)
• Loss function based second-order Jensen inequality and its application to particle variational inference [112.58907653042317]
  Particle variational inference (PVI) uses an ensemble of models as an empirical approximation for the posterior distribution. PVI iteratively updates each model with a repulsion force to ensure the diversity of the optimized models. We derive a novel generalization error bound and show that it can be reduced by enhancing the diversity of models.
  arXiv  Detail & Related papers  (2021-06-09T12:13:51Z)
• Learning Invariant Representations and Risks for Semi-supervised Domain Adaptation [109.73983088432364]
  We propose the first method that aims to simultaneously learn invariant representations and risks under the setting of semi-supervised domain adaptation (Semi-DA) We introduce the LIRR algorithm for jointly textbfLearning textbfInvariant textbfRepresentations and textbfRisks.
  arXiv  Detail & Related papers  (2020-10-09T15:42:35Z)
• A maximum-entropy approach to off-policy evaluation in average-reward MDPs [54.967872716145656]
  This work focuses on off-policy evaluation (OPE) with function approximation in infinite-horizon undiscounted Markov decision processes (MDPs) We provide the first finite-sample OPE error bound, extending existing results beyond the episodic and discounted cases. We show that this results in an exponential-family distribution whose sufficient statistics are the features, paralleling maximum-entropy approaches in supervised learning.
  arXiv  Detail & Related papers  (2020-06-17T18:13:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.