Federated Q-Learning Algorithm

• Federated Q-Learning is a distributed reinforcement learning paradigm where agents update local Q-tables and periodically aggregate them without sharing raw data.
• Decentralized mechanisms like mobile-agent ring aggregation using FedAvg and FedMax enable efficient, privacy-preserving policy updates across heterogeneous environments.
• Empirical results indicate accelerated convergence, improved generalization, and enhanced robustness, especially in complex, obstacle-rich multi-agent settings.

Federated Q-Learning is a distributed reinforcement learning paradigm in which multiple agents collaboratively derive optimal control policies for Markov decision processes (MDPs) without sharing raw experiences. Each agent independently updates local value (Q) functions through standard Q-learning, while knowledge sharing is realized via periodic or event-driven aggregation of local Q-estimates. This aggregation can be conducted through centralized servers, decentralized peer-to-peer topologies, or mobile agents, and can utilize various element-wise fusion techniques (e.g., averaging, maximization, or importance weighting). By leveraging experience from multiple agents—often collected in heterogeneous environments—federated Q-learning aims to accelerate convergence, enhance generalization, and preserve privacy, all while mitigating the communication overheads and failure risks of centralized learning. The approach is prominent in multi-robot control, distributed wireless systems, IoT management, and multi-agent simulation, with extensive theoretical analysis characterizing its sample complexity, communication efficiency, and robustness to heterogeneity.

1. Decentralized Federated Q-Learning Mechanisms

Federated Q-learning can be implemented with or without a central aggregator. In decentralized settings, a mobile agent can traverse the network of learners (e.g., robots connected in a logical ring), collecting and aggregating Q-tables during a forward tour and distributing the resulting consensus Q-table on the return path. This was operationalized using the Tartarus platform and the Webots simulator in a multi-robot context, where each robot executes tabular Q-learning in a different obstacle-rich arena and synchronizes via a Prolog-based agent (Nair et al., 2022).

Element-wise Q-table aggregation is performed at each synchronization stage, with two canonical schemes:

• Federated Averaging (FedAvg):

$$Q^{\mathrm{agg}}(s,a) = \frac{1}{N}\sum_{i=1}^N Q^{(i)}(s,a)$$

• Federated Max (FedMax):

$$Q^{\mathrm{agg}}(s,a) = \max_{1\leq i\leq N} Q^{(i)}(s,a)$$

where $N$ is the number of participants.

Pseudocode excerpt for the mobile agent-based protocol:

// Initialization for each robot R_i in {R₁…R_N}: start local Q-learning loop // Mobile agent logic loop forever: wait until R₁ completes m local iterations payload ← Q^(R₁) // Forward pass: collect and aggregate for i ← 2 to N do send payload to host of R_i local_Q ← Q^(R_i) payload ← aggregate(payload, local_Q) end for // Backward pass: distribute aggregate for i ← N down to 1 do send payload to host of R_i Q^(R_i) ← payload end for end loop

Synchronizations occur after a fixed interval of local updates. The mobile agent paradigm completely eliminates single points of failure and minimizes bandwidth use compared to centralized schemes, at the expense of round-trip timing and ring-topology flexibility.

2. Local Q-Learning Dynamics and Aggregation Formulas

Each agent executes classical off-policy Q-learning. At step $t$, after transitioning from state $s$ to $s'$ by taking action $a$ and receiving reward $r$, the update is:

$$Q_{\,\mathrm{new}}(s,a) = Q(s,a) + \alpha \Bigl[ r + \gamma \max_{a'} Q(s',a') - Q(s,a) \Bigr]$$

with learning rate $\alpha$ and discount factor $\gamma$.

Periodically, all agents' Q-tables are merged using either:

• FedAvg (mean across agents): facilitates smooth learning by blending local policies.
• FedMax (element-wise max): may induce abrupt policy shifts if local maxima are misaligned across agents.

Aggregation is implemented in-place: after each synchronization, the local Q-table at each agent is replaced with the global aggregated version, and local learning resumes.

This protocol permits straightforward extensions to heterogeneous learning algorithms (e.g., combining Q-learning and SARSA), as the aggregation operation is performed solely on Q-tables and is agnostic to update specifics.

3. Empirical Results and Performance Analysis

The decentralized federated Q-learning system was deployed on five physically isolated nodes, each simulating a unique arena with differing obstacle densities. Performance was primarily tracked by:

• The sum of Q-table entries over time (proxy for accumulated knowledge).
• Cumulative reward per robot.

Findings include:

• Standalone learners in simple environments initially outpace federated ones but converge to policies tailored to their specific configuration, whereas federated learners—by aggregating across diverse experiences—achieve higher asymptotic Q-sum and reward.
• FedAvg yields steady monotonic improvement; FedMax introduces "dips" when individual maxima from conflicting environments are imposed but converges to high reward eventually.
• Robots in more complex arenas derive pronounced benefit from federated updates, showcasing knowledge transfer from simpler to more difficult tasks.
• Absence of a central server averts catastrophic collapse in the event of a node failure.

Overall, decentralized federated Q-learning demonstrably mitigates overfitting to local environments and accelerates convergence to robust, obstacle-averse policies (Nair et al., 2022).

4. Advantages, Limitations, and Communication Protocols

Advantages:

• Eliminates single-point communication and aggregation failures.
• Fully compatible with privacy requirements: only Q-tables (not raw experience or sensor data) are transferred, and all communication can be encrypted.
• Scales naturally to heterogeneous learning setups and multiple independent learning algorithms coexisting in the same federation.
• Minimal bandwidth: all-to-all, peer-to-peer, or mobile-agent ring communication models inherently reduce network load compared to server-based federated learning.

Limitations:

• Synchronization latency is bounded below by the agent's round-trip cycle, potentially suboptimal for rapidly evolving environments.
• Element-wise aggregations are oblivious to inter-action correlations in Q-space, risking loss of nuanced policy structure.
• Real-world deployments would require robust agent fault-tolerance and dynamic topology management.
• The logical ring is rigid; more general peer-to-peer topologies (gossip, tree, etc.) may further decrease time to consensus.

Table: Summary of Aggregation Methods

Method	Aggregation Formula	Convergence Behavior
FedAvg	$\frac{1}{N} \sum_{i=1}^N Q^{(i)}(s,a)$	Smooth, stable, slow/fair
FedMax	$\max_{i} Q^{(i)}(s,a)$	Fast but potentially unstable

FedAvg is generally preferred when stability and monotonic improvement are desired, while FedMax may accelerate convergence at the cost of transient destabilization.

5. Open Questions and Future Directions

Principal open challenges include:

• Optimizing synchronization intervals (balancing local policy refinement against cross-agent drift).
• Developing aggregation schemes sensitive to environment similarity or agent confidence, possibly utilizing meta-learning or clustering in aggregation space.
• Addressing mobile-agent loss or delay and enabling robust re-routing and backup protocols.
• Extending to asynchronous and dynamically evolving topologies, including gossip-based or tree-based peer-to-peer networks.

There is significant scope for integrating more sophisticated model/parameter fusion mechanisms, real-world robot fleet deployment, and fault-tolerance analysis. The paradigm admits straightforward generalization to deep-Q and policy network representation, though communication and aggregation would then be performed on weight tensors rather than tabular Q-tables (Nair et al., 2022).

6. Theoretical Significance and Application Domains

Decentralized federated Q-learning exemplifies a fully peer-to-peer mode of collaborative policy optimization, removing both data centralization and single-server vulnerabilities. The protocol is broadly applicable to distributed robotics, privacy-preserving multi-agent autonomy, and constrained communication environments.

By leveraging periodic synchronization and mobile agent-based aggregation, the approach preserves the key properties of federated learning—privacy, bandwidth efficiency, robustness—while aligning with the requirements of real-time, distributed, and resource-limited robotic systems. Its demonstrated effectiveness in fusing heterogeneous experience bases to improve reward and generalization validates its potential for large-scale, real-world deployment.

Experimental evidence supports its superiority in collaborative learning for obstacle-rich robot navigation, and methodological innovations—such as mobile agent ring aggregation and aggregation-scheme flexibility—position it as a robust, scalable solution within the federated reinforcement learning landscape (Nair et al., 2022).