Analysis of Multiscale Reinforcement Q-Learning Algorithms for Mean Field Control Games

• URL: http://arxiv.org/abs/2405.17017v3
• Date: Tue, 4 Jun 2024 02:58:13 GMT
• Title: Analysis of Multiscale Reinforcement Q-Learning Algorithms for Mean Field Control Games
• Authors: Andrea Angiuli, Jean-Pierre Fouque, Mathieu Laurière, Mengrui Zhang,
• Abstract summary: Mean Field Control Games (MFCG) represent competitive games between a large number of large collaborative groups of agents. We prove the convergence of a three-timescale Reinforcement Q-Learning (RL) algorithm to solve MFCG.
• Score: 2.3833208322103605
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Mean Field Control Games (MFCG), introduced in [Angiuli et al., 2022a], represent competitive games between a large number of large collaborative groups of agents in the infinite limit of number and size of groups. In this paper, we prove the convergence of a three-timescale Reinforcement Q-Learning (RL) algorithm to solve MFCG in a model-free approach from the point of view of representative agents. Our analysis uses a Q-table for finite state and action spaces updated at each discrete time-step over an infinite horizon. In [Angiuli et al., 2023], we proved convergence of two-timescale algorithms for MFG and MFC separately highlighting the need to follow multiple population distributions in the MFC case. Here, we integrate this feature for MFCG as well as three rates of update decreasing to zero in the proper ratios. Our technique of proof uses a generalization to three timescales of the two-timescale analysis in [Borkar, 1997]. We give a simple example satisfying the various hypothesis made in the proof of convergence and illustrating the performance of the algorithm.

Related papers

• Last Iterate Convergence in Monotone Mean Field Games [5.407319151576265]
  Mean Field Game (MFG) is a framework utilized to model and approximate the behavior of a large number of agents. We propose the use of a simple, proximal-point-type algorithm to compute equilibria for MFGs. We provide the first last-iterate convergence guarantee under the Lasry--Lions-type monotonicity condition.
  arXiv  Detail & Related papers  (2024-10-07T15:28:18Z)
• Model-Based RL for Mean-Field Games is not Statistically Harder than Single-Agent RL [57.745700271150454]
  We study the sample complexity of reinforcement learning in Mean-Field Games (MFGs) with model-based function approximation. We introduce the Partial Model-Based Eluder Dimension (P-MBED), a more effective notion to characterize the model class complexity.
  arXiv  Detail & Related papers  (2024-02-08T14:54:47Z)
• Deep Reinforcement Learning for Infinite Horizon Mean Field Problems in Continuous Spaces [1.4999444543328293]
  We present a reinforcement learning (RL) algorithm designed to solve mean field games (MFG) and mean field control (MFC) problems in a unified manner. The proposed approach pairs the actor-critic (AC) paradigm with a representation of the mean field distribution via a parameterized score function. A modification of the algorithm allows us to solve mixed mean field control games (MFCGs)
  arXiv  Detail & Related papers  (2023-09-19T22:37:47Z)
• Online Learning with Adversaries: A Differential-Inclusion Analysis [52.43460995467893]
  We introduce an observation-matrix-based framework for fully asynchronous online Federated Learning with adversaries. Our main result is that the proposed algorithm almost surely converges to the desired mean $mu.$ We derive this convergence using a novel differential-inclusion-based two-timescale analysis.
  arXiv  Detail & Related papers  (2023-04-04T04:32:29Z)
• A unified stochastic approximation framework for learning in games [82.74514886461257]
  We develop a flexible approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite) The proposed analysis template incorporates a wide array of popular learning algorithms, including gradient-based methods, exponential/multiplicative weights for learning in finite games, optimistic and bandit variants of the above, etc.
  arXiv  Detail & Related papers  (2022-06-08T14:30:38Z)
• Concave Utility Reinforcement Learning: the Mean-field Game viewpoint [42.403650997341806]
  Concave Utility Reinforcement Learning (CURL) extends RL from linear to concave utilities in the occupancy measure induced by the agent's policy. This more general paradigm invalidates the classical Bellman equations, and calls for new algorithms. We show that CURL is a subclass of Mean-field Games (MFGs)
  arXiv  Detail & Related papers  (2021-06-07T16:51:07Z)
• Scaling up Mean Field Games with Online Mirror Descent [55.36153467919289]
  We address scaling up equilibrium computation in Mean Field Games (MFGs) using Online Mirror Descent (OMD) We show that continuous-time OMD provably converges to a Nash equilibrium under a natural and well-motivated set of monotonicity assumptions. A thorough experimental investigation on various single and multi-population MFGs shows that OMD outperforms traditional algorithms such as Fictitious Play (FP)
  arXiv  Detail & Related papers  (2021-02-28T21:28:36Z)
• Global Convergence of Policy Gradient for Linear-Quadratic Mean-Field Control/Game in Continuous Time [109.06623773924737]
  We study the policy gradient method for the linear-quadratic mean-field control and game. We show that it converges to the optimal solution at a linear rate, which is verified by a synthetic simulation.
  arXiv  Detail & Related papers  (2020-08-16T06:34:11Z)
• Unified Reinforcement Q-Learning for Mean Field Game and Control Problems [0.0]
  We present a Reinforcement Learning (RL) algorithm to solve infinite horizon Mean Field Game (MFG) and Mean Field Control (MFC) problems. Our approach can be described as a unified two-timescale Mean Field Q-learning: The emphsame algorithm can learn either the MFG or the MFC solution by simply tuning the ratio of two learning parameters.
  arXiv  Detail & Related papers  (2020-06-24T17:45:44Z)
• Finite-Time Last-Iterate Convergence for Multi-Agent Learning in Games [116.0771177871705]
  We characterize the finite-time last-iterate convergence rate for joint OGD learning on $lambda$-cocoercive games. We show, via a novel double-stopping time technique, that this adaptive algorithm achieves same finite-time last-iterate convergence rate as non-adaptive counterpart.
  arXiv  Detail & Related papers  (2020-02-23T01:46:34Z)

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.