MEMOA: Massive Mixtures of Online Agents via Mean-Field Decentralized Nash Equilibria

Federated learning enables collaborative model training across distributed clients without centralising their data, yet privacy remains a persistent concern because the shared model updates can leak information about local datasets. Existing privacy-preserving methods either inject calibrated noise into client updates, limiting their composition guarantees, or formulate client privacy choices as a multi-agent game whose Nash equilibrium becomes intractable as the number of clients grows. We bridge these two lines of work by formulating privacy-preserving federated learning as a mean-field privacy game: each client strategically chooses its own privacy budget while interacting with the population only through a single mean-field statistic. The mean-field limit yields a tractable equilibrium for arbitrarily many clients, accommodates heterogeneous client preferences, and inherits an exponentially decaying privacy guarantee through a log-Sobolev contraction. The framework recovers the entropic privacy baseline as the homogeneous special case and the multi-agent privacy game as the finite-population case. Experiments on quadratic regression, logistic regression, and MNIST demonstrate that the proposed framework attains the privacy-utility trade-off of the entropic baseline while delivering a personalized privacy guarantee that the homogeneous baseline cannot express.

This paper considers reinforcement learning from human feedback in a federated learning setting with resource-constrained agents, such as edge devices. We propose an efficient federated RLHF algorithm, named Partitioned, Sign-based Stochastic Zeroth-order Policy Optimization (Par-S$^2$ZPO). The algorithm is built on zeroth-order optimization with binary perturbation, resulting in low communication, computation, and memory complexity by design. Our theoretical analysis establishes an upper bound on the convergence rate of Par-S$^2$ZPO, revealing that it is as efficient as its centralized counterpart in terms of sample complexity but converges faster in terms of policy update iterations. Our experimental results show that it outperforms a FedAvg-based RLHF on four MuJoCo RL tasks.

Despite the popularity of the actor-critic method and the practical needs of collaborative policy training, existing works typically either overlook environmental heterogeneity or give up personalization altogether by training a single shared policy across all agents. We consider a federated actor-critic framework in which agents share a common linear subspace representation while maintaining personalized local policy components, and agents iteratively estimate the common subspace, local critic heads, and local policies (i.e., actors). Under canonical single-timescale updates with Markovian sampling, we establish finite-time convergence via a novel joint linear approximation framework. Specifically, we show that the critic error converges to zero at the rate of $\tilde{\mathcal{O}}(1/((1-γ)^4\sqrt{TK}))$, and the policy gradient norm converges to zero at the rate of $\tilde{\mathcal{O}}(1/((1-γ)^6\sqrt{TK}))$, where $T$ is the number of rounds, $K$ is the number of agents, and $γ\in (0,1)$ is the discount factor. These results demonstrate linear speedup with respect to the number of agents $K$, despite heterogeneous Markovian trajectories under distinct transition kernels and coupled learning dynamics. To address these challenges, we develop a new perturbation analysis for the projected subspace updates and QR decomposition steps, together with conditional mixing arguments for heterogeneous Markovian noise. Furthermore, to handle the additional complications induced by policy updates and temporal dependence, we establish fine-grained characterizations of the discrepancies between function evaluations under Markovian sampling and under temporally frozen policies. Experiments instantiate the framework within PPO on federated \texttt{Hopper-v5} action-map heterogeneity, showing gains over Single PPO and FedAvg PPO and downstream transfer from the learned shared trunk.