# On Global Convergence Rates for Federated Softmax Policy Gradient under Heterogeneous Environments

arXiv: https://arxiv.org/abs/2505.23459 · HTML: https://mlsanity.com/paper/2505.23459/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in RL for energy, networks and operations, one of 15 directions in Deep reinforcement learning methods.
- First posted on arXiv 29 May 2025.

## Placed in

- Deep reinforcement learning methods / [RL for energy, networks and operations](https://mlsanity.com/deeprl/rl-for-energy-networks-and-operations/)

## Built on by (most cited first, 3 of 3)

- [Convergence Guarantees for Federated SARSA with Local Training and Heterogeneous Agents](https://mlsanity.com/paper/2512.17688/) (2025)
- [Refined Analysis of Entropy-Regularized Actor-Critic](https://mlsanity.com/paper/2605.24357/) (2026)
- [Personalized Federated Reinforcement Learning via Model-Agnostic Meta-Learning: Convergence of Exact and Hessian-Free Meta-Policy Gradients](https://mlsanity.com/paper/2609.22833/) (2026)

## Abstract (arXiv)

We provide global convergence rates for vanilla and entropy-regularized federated softmax stochastic policy gradient (FedPG) with local training. We show that FedPG converges to a near-optimal policy in terms of the average agent value, with a gap controlled by the level of heterogeneity. Remarkably, we obtain the first convergence rates for entropy-regularized policy gradient with explicit constants, leveraging a projection-like operator. Our results build upon a new analysis of federated averaging for non-convex objectives, based on the observation that the Lojasiewicz-type inequalities from the single-agent setting (Mei et al., 2020) do not hold for the federated objective. This uncovers a fundamental difference between single-agent and federated reinforcement learning: while single-agent optimal policies can be deterministic, federated objectives may inherently require stochastic policies.