# Collaborative Value Function Estimation Under Model Mismatch: A Federated Temporal Difference Analysis

arXiv: https://arxiv.org/abs/2503.17454 · HTML: https://mlsanity.com/paper/2503.17454/

## Key facts

- Cited by 2 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.
- Builds on 31 of its 56 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## Placed in

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

## Builds on (most cited first, 30 of 31)

- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [Sim-to-Real Transfer in Deep Reinforcement Learning for Robotics: a Survey](https://mlsanity.com/paper/2009.13303/) (2020)
- [A Finite Time Analysis of Temporal Difference Learning With Linear Function Approximation](https://mlsanity.com/paper/1806.02450/) (2018)
- [Finite-Time Error Bounds For Linear Stochastic Approximation and TD Learning](https://mlsanity.com/paper/1902.00923/) (2019)
- [Federated Reinforcement Learning: Techniques, Applications, and Open Challenges](https://mlsanity.com/paper/2108.11887/) (2021)
- [Robust Reinforcement Learning for Continuous Control with Model Misspecification](https://mlsanity.com/paper/1906.07516/) (2019)
- [Sub-sampled Cubic Regularization for Non-convex Optimization](https://mlsanity.com/paper/1705.05933/) (2017)
- [Federated Reinforcement Learning with Environment Heterogeneity](https://mlsanity.com/paper/2204.02634/) (2022)
- [A Lyapunov Theory for Finite-Sample Guarantees of Asynchronous Q-Learning and TD-Learning Variants](https://mlsanity.com/paper/2102.01567/) (2021)
- [Fault-Tolerant Federated Reinforcement Learning with Theoretical Guarantee](https://mlsanity.com/paper/2110.14074/) (2021)
- [Adapting to Mixing Time in Stochastic Optimization with Markovian Data](https://mlsanity.com/paper/2202.04428/) (2022)
- [The Blessing of Heterogeneity in Federated Q-Learning: Linear Speedup and Beyond](https://mlsanity.com/paper/2305.10697/) (2023)
- [Federated Deep Reinforcement Learning](https://mlsanity.com/paper/1901.08277/) (2019)
- [Finite-Time Analysis of On-Policy Heterogeneous Federated Reinforcement Learning](https://mlsanity.com/paper/2401.15273/) (2024)
- [FedKL: Tackling Data Heterogeneity in Federated Reinforcement Learning by Penalizing KL Divergence](https://mlsanity.com/paper/2204.08125/) (2022)
- [Sample and Communication-Efficient Decentralized Actor-Critic Algorithms with Finite-Time Analysis](https://mlsanity.com/paper/2109.03699/) (2021)
- [Towards Understanding Asynchronous Advantage Actor-critic: Convergence and Linear Speedup](https://mlsanity.com/paper/2012.15511/) (2020)
- [Improved High-Probability Bounds for the Temporal Difference Learning Algorithm via Exponential Stability](https://mlsanity.com/paper/2310.14286/) (2023)
- [Federated Q-Learning: Linear Regret Speedup with Low Communication Cost](https://mlsanity.com/paper/2312.15023/) (2023)
- [Characterizing the Exact Behaviors of Temporal Difference Learning Algorithms Using Markov Jump Linear System Theory](https://mlsanity.com/paper/1906.06781/) (2019)
- [Gossip-based Actor-Learner Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1906.04585/) (2019)
- [A Simple Finite-Time Analysis of TD Learning with Linear Function Approximation](https://mlsanity.com/paper/2403.02476/) (2024)
- [Federated TD Learning over Finite-Rate Erasure Channels: Linear Speedup under Markovian Sampling](https://mlsanity.com/paper/2305.08104/) (2023)
- [Distributed TD(0) with Almost No Communication](https://mlsanity.com/paper/2305.16246/) (2023)
- [Convergent Actor-Critic Algorithms Under Off-Policy Training and Function Approximation](https://mlsanity.com/paper/1802.07842/) (2018)
- [Temporal Difference Learning with Compressed Updates: Error-Feedback meets Reinforcement Learning](https://mlsanity.com/paper/2301.00944/) (2023)
- [On the Convergence of Consensus Algorithms with Markovian Noise and Gradient Bias](https://mlsanity.com/paper/2008.07841/) (2020)
- [Compressed Federated Reinforcement Learning with a Generative Model](https://mlsanity.com/paper/2404.10635/) (2024)

## Built on by (most cited first, 2 of 2)

- [Convergence Guarantees for Federated SARSA with Local Training and Heterogeneous Agents](https://mlsanity.com/paper/2512.17688/) (2025)
- [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)

Federated reinforcement learning (FedRL) enables collaborative learning while preserving data privacy by preventing direct data exchange between agents. However, many existing FedRL algorithms assume that all agents operate in identical environments, which is often unrealistic. In real-world applications, such as multi-robot teams, crowdsourced systems, and large-scale sensor networks, each agent may experience slightly different transition dynamics, leading to inherent model mismatches. In this paper, we first establish linear convergence guarantees for single-agent temporal difference learning (TD(0)) in policy evaluation and demonstrate that under a perturbed environment, the agent suffers a systematic bias that prevents accurate estimation of the true value function. This result holds under both i.i.d. and Markovian sampling regimes. We then extend our analysis to the federated TD(0) (FedTD(0)) setting, where multiple agents, each interacting with its own perturbed environment, periodically share value estimates to collaboratively approximate the true value function of a common underlying model. Our theoretical results indicate the impact of model mismatch, network connectivity, and mixing behavior on the convergence of FedTD(0). Empirical experiments corroborate our theoretical gains, highlighting that even moderate levels of information sharing significantly mitigate environment-specific errors.