Actor-Critic Learning for Extended Mean Field Control with Deterministic Policies

2026-07-14 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Reinforcement Learning · Depth: Expert, extended

Summary

The paper introduces a model-free reinforcement learning framework for continuous-time extended mean field control (MFC) problems, where both dynamics and rewards depend on joint state-control distributions. It employs deterministic feedback policies to circumvent limitations of existing stochastic kernel optimization methods. A key contribution is a model-free sensitivity formula for parameterized McKean–Vlasov dynamics, which leads to a deterministic policy gradient (DPG) formula using an advantage-rate function on the Wasserstein space. This is further refined into local value and advantage-rate representations, resulting in a policy gradient that incorporates both action and measure-derivative terms. The framework culminates in a continuous-time deep deterministic policy-gradient algorithm, integrating particle approximations, measure-dependent neural networks, temporal-difference learning, and exploration. Numerical experiments on stochastic Cucker–Smale consensus control and optimal liquidation with trade crowding demonstrate the method's efficiency, stability, and robustness, even for problems with explicit control distribution dependence.

Key takeaway

For Machine Learning Engineers developing continuous-time reinforcement learning solutions for large-scale multi-agent systems, you should consider adopting deterministic policy gradient algorithms with local advantage-rate function decomposition. This approach, demonstrated to be efficient and robust in extended mean field control problems, offers improved stability and faster convergence compared to stochastic policy methods, especially when dynamics depend on joint state-control distributions. Implement measure-dependent neural networks and martingale-based temporal-difference updates for optimal learning signals.

Key insights

A model-free DPG framework for continuous-time extended MFC uses deterministic policies and local advantage-rate functions for efficient learning.

Principles

• Deterministic policies simplify optimization over stochastic kernels.
• Local advantage-rate functions provide informative learning signals.
• Martingale conditions enable efficient temporal-difference updates.

Method

Develops a model-free DPG formula using a sensitivity formula for McKean–Vlasov dynamics, refined with local value/advantage-rate representations, then implements a deep DPG algorithm with neural networks and particle approximations.

In practice

• Use measure-dependent neural networks for value and advantage functions.
• Employ temporal-difference learning with martingale conditions.
• Explore action or parameter space during training.

Topics

• Extended Mean Field Control
• Deterministic Policy Gradient
• Reinforcement Learning
• McKean–Vlasov Dynamics
• Neural Networks
• Actor-Critic Algorithms

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.