Reward Diversity Enables Exploration-Free Personalized Federated RL
Summary:A new study in personalized federated reinforcement learning recasts reward heterogeneity as a source of exploration rather than an obstacle to collaboration. PF-UCBVI separates shared dynamics from personalized objectives and achieves optimal linear speedup, while PF-EFVI removes explicit exploration bonuses and uses reward diversity to preserve state-action coverage, yielding logarithmic regret under sufficient diversity. The approach could reduce exploration overhead in multi-agent federated
Core idea: turning disagreement into an exploration resource
A central obstacle in personalized federated reinforcement learning is that agents may share the same environment dynamics while pursuing different objectives. Aggregating their experience as if every agent had the same reward can corrupt the shared policy, whereas fully independent training wastes the sample-efficiency benefit of federation.
This work treats reward heterogeneity as a structural source of exploration. Under shared transition dynamics, different reward functions induce agents toward different states and actions. If those differences are meaningful rather than mere noise, the union of their trajectories can provide state-action coverage without the uncertainty bonuses used by conventional UCB methods.
The paper introduces two algorithms. PF-UCBVI supports explicit exploration and provides optimal linear speedup by separating shared dynamics from personalized objectives. PF-EFVI removes exploration bonuses entirely and uses a purely greedy value-iteration procedure whose coverage guarantee comes from reward diversity.
PF-UCBVI: separating shared dynamics from personalized values
The central model divides the environment into a shared transition kernel and agent-specific reward functions. For agent i, the action value takes the form
[ Q_i(s,a)=r_i(s,a)+\gamma\sum_{s'}P(s'\mid s,a)V_i(s'). ]
Here, (P(s'\mid s,a)) is shared across participants, while (r_i(s,a)) captures individual goals. PF-UCBVI does not average incompatible Q-values into a single scalar objective. Instead, it shares information that improves environment coverage while preserving personalized reward structures and value estimates.
Under the paper's assumptions, the method obtains optimal linear federated speedup: as more agents participate, total sample complexity can be amortized almost linearly with agent count. This should be interpreted as improved sampling efficiency under parallel interaction, not as a guarantee that task performance itself scales linearly with fleet size.
In practice, each client must maintain personalized value information while communicating transition-related statistics or model updates. The realized benefit therefore depends on communication overhead, stale updates, and whether the transition model remains sufficiently homogeneous.
PF-EFVI: coverage without explicit exploration bonuses
Explicit UCB exploration carries a cost: uncertainty bonuses can dominate the true reward, consume samples on uncertain actions, and complicate policy optimization. PF-EFVI removes those bonuses and performs greedy value iteration.
The key mechanism is differential ordering. Even when each agent selects its locally optimal action, personalized rewards can make different actions optimal for different agents. If the induced trajectories are sufficiently diverse, the federation collectively observes regions that would otherwise require repeated exploratory trials from one agent.
The paper proves logarithmic regret for PF-EFVI under sufficient reward diversity. In the standard tabular formulation, cumulative regret grows as (O(\log T)) rather than linearly with the number of rounds. This result nevertheless depends on shared dynamics, a meaningful diversity condition, and sufficiently accurate value learning.
Logarithmic regret in theory does not automatically imply the same empirical sample efficiency. Continuous action spaces, sparse rewards, function approximation, communication delays, and nonstationary environments can all weaken the guarantee. Reward differences caused only by random noise may also fail to generate complementary behavior.
Why not optimize an averaged reward?
Conventional federated RL often learns a common policy that maximizes average cumulative reward. This is natural for homogeneous agents but can substantially harm users, devices, or business units whose rewards legitimately differ.
Personalized federation instead optimizes a collection of constrained individual optima while sharing compatible environmental knowledge. Potential applications include recommendation systems with different user objectives, resource allocation under heterogeneous costs, and distributed scheduling in which agents share state transitions but incur different penalties.
The benefit is reduced duplicate interaction and better aggregate sample efficiency. The cost is more complex state: clients retain personalized values and policies, while servers determine which information can be aggregated without introducing objective bias.
Engineering trade-offs
The main obstacles extend beyond the learning algorithm:
- Communication: Synchronizing full value tables scales poorly with state size, action count, and client count. Aggregating only transition statistics may save bandwidth but can lose information needed for personalization.
- Reward quality: Useful diversity requires different reward structures that induce meaningfully different optimal actions. Noise can create apparent heterogeneity without reliable exploration.
- Non-stationarity: Policy updates change each client's data distribution, making cached models and aggregated estimates stale.
- Dynamics shift: Different software versions, devices, or environments can violate the shared-transition assumption and turn cross-client transfer into model bias.
- Privacy and fairness: Feature-level sharing and policy updates may expose user behavior, while extreme reward heterogeneity can produce poor outcomes for minority clients.
The theoretical analysis also operates under controlled value-learning conditions. Neural approximation, off-policy data, and asynchronous communication introduce errors that the proof does not directly capture.
Deployment guidance and validation checklist
A practical replication should begin with a controlled environment that has identical dynamics but deliberately different reward orderings. Measure final returns, joint state-action coverage, duplicate sampling, cumulative regret, communication volume, and wall-clock time. The comparison should include independent learning, standard federated averaging, PF-UCBVI, and PF-EFVI.
Researchers should then remove assumptions one at a time: reduce reward diversity, introduce mild transition mismatch, add function-approximation error, and finally impose communication delays. This reveals whether gains come from genuine collective coverage or simply from extra interaction volume.
Before deployment, teams should also test whether reward diversity is stable over time, whether the method satisfies fairness requirements, and whether privacy mechanisms degrade the diversity estimate. At present, PF-EFVI is best viewed as a strong theoretical and prototype baseline for shared-dynamics, heterogeneous-objective federated RL rather than a production-ready general solution.
Conclusion
PF-UCBVI and PF-EFVI recast agent disagreement as an exploration asset. By sharing dynamics while preserving personalized rewards, agents can cover complementary regions; PF-EFVI further shows that sufficient reward diversity can support logarithmic regret without explicit exploration bonuses.
The important change is not merely the removal of an exploration term. It is a transfer of exploration responsibility from temporal trial-and-error within one agent to spatial diversity across many agents. Whether that advantage survives continuous control, dynamic environments, and realistic communication remains an empirical question.
— END —Source: ArXiv Machine Learning (cs.LG) (2026-11-11)
Tags: #Personalized Federated RL #Reward Diversity #Exploration-Free RL #Multi-Agent Collaboration #UCB Value Iteration
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