Aggregation-Aware Reinforcement Learning

• Aggregation-aware RL is a framework that compresses and fuses states, actions, and policies to create surrogate models while preserving key decision-making information.
• It enables robust transfer, adaptive exploration, and safety by integrating multiple policy estimates and managing distributed or partially observable environments.
• The approach is supported by theoretical bounds on error and regret, with empirical success in scalable, multi-agent, and communication-constrained RL systems.

Aggregation-aware reinforcement learning encompasses a spectrum of techniques centered on compressing, integrating, or fusing states, value functions, actions, or policy outputs in order to manage complexity, facilitate transfer, improve exploration, enforce safety, handle distributed settings, or adapt to non-Markov, partially observable, or aggregation-constrained feedback. At its core, aggregation-aware RL recognizes that learning and control can often proceed efficiently and robustly using groupings, surrogates, or combinations that operate at a granularity coarser than individual states or trajectories, provided that the crucial information for optimal (or near-optimal) decision-making is preserved or can be approximately reconstructed. This approach underpins advances from history and feature aggregation in environments without Markov assumptions (Hutter, 2014), to multiplicity of advisory Q-functions (Laroche et al., 2017), to state-of-the-art scalable, distributed, or meta-learning RL architectures.

1. State Aggregation: Histories, Features, and Surrogate MDPs

State (or more generally, feature or history) aggregation provides a mapping $\varphi:\mathcal{H} \rightarrow \mathcal{S}$ from histories or raw states to a reduced space, as in

$s = \varphi(h)$

where $h\in\mathcal{H}$ (the space of histories) and $s\in\mathcal{S}$ (the aggregated space), as detailed in (Hutter, 2014). This framework does not require standard Markov or MDP assumptions. The critical result is that if the optimal value functions or policies of the original process can be (approximately) represented as functions of the aggregates (i.e., are “$\varphi$-uniform”), then the solution to an associated finite surrogate MDP, constructed via an “averaged” or “dispersed” transition kernel

$$p(s', r' | s, a) = \sum_{h: \varphi(h) = s} B(h | s, a) P_\varphi(s', r' | h, a)$$

(for a suitable dispersion probability $B$), yields approximate value functions $q^*, v^*$ and policies that solve the original non-Markov RL problem, up to $\mathcal{O}(\epsilon)$ error, where $\epsilon$ is the maximum discrepancy across $Q^*$ within each aggregate.

In feature-based aggregation for MDPs, feature extraction $F(i)$ is followed by partitioning of the state space into “disaggregation sets” $I_\ell$ defined by feature similarity, from which a lower-dimensional aggregate DP, with contraction and provable error bounds

$$\| J^* - J \|_\infty \leq \frac{\epsilon}{1 - \alpha}$$

(where $\epsilon$ quantifies within-group variation), can be directly solved (Bertsekas, 2018). Integration with deep RL is natural, using neural feature encoders to form non-linear, piecewise approximators for the cost function.

2. Aggregation for Transfer, Robustness, and Exploration

Adaptive and multi-source policy aggregation leverages ensembles of source policies. In MULTIPOLAR (Barekatain et al., 2019), the target policy is parameterized as

$$F(s_t; L, \theta_{\text{agg}}, \theta_{\text{aux}}) = F_{\text{agg}}(s_t; L, \theta_{\text{agg}}) + F_{\text{aux}}(s_t; \theta_{\text{aux}})$$

where $F_{\text{agg}}$ adaptively aggregates deterministic actions from $K$ source policies, and $F_{\text{aux}}$ supplies a learned, state-dependent residual. This allows the agent to exploit transferable knowledge from previous tasks and maintain expressivity, improving sample efficiency and resilience to poorly-performing sources. Relatedly, the adaptive aggregation framework for safety-critical control (Zhang et al., 2023) uses an attention network to state-dependently weight source policies and an auxiliary network, with a safeguard module to enforce constraint satisfaction.

In advisory systems, multiple “advisors” specializing in distinct subtasks provide local Q-functions, and a linear aggregator synthesizes these into the global action-value function (Laroche et al., 2017). Theoretical and empirical results demonstrate the critical role of aggregation strategy—egocentric, agnostic, or empathic planning—in balancing overestimation, exploration, and coordination.

Aggregation can also encode resource constraints or partial observability. In multi-channel spectrum aggregation (Li et al., 2020), partial observations and a DQN aggregate across possible channel segments, learning policies robust to unknown, correlated dynamics and action-constrained aggregation requirements.

3. Learning and Regret with Aggregated Representations

Aggregation-aware RL supports principled algorithms with regret bounds and scalability guarantees. In fixed-horizon episodic MDPs with aggregated states, if the mapping $\phi_h: S \times A \to [M]$ induces $\varepsilon$-error aggregation, an optimistic Q-learning variant achieves

$$\widetilde{\mathcal{O}}\left( \sqrt{H^5 M K} + \varepsilon H K \right)$$

regret, independent of the number of atomic states or actions (Dong et al., 2019). The aggregation error $\varepsilon$ directly controls the per-period regret floor.

In RL with aggregate bandit feedback (RL-ABF) (Cassel et al., 13 May 2024), reward is revealed only as the episode sum. Ensemble-based value and policy optimization algorithms (RE-LSVI and REPO) with linear function approximation exploit randomization and hedging schemes to enable near-optimal exploration and low regret in $\tilde{\mathcal{O}}(\sqrt{d^5 H^7 K})$, $d$ being the feature dimension. The core technical advance is maintaining optimistic backups by constructing multiple Q-functions with independent perturbations, and aggregating their value estimates for exploration and learning under maximal reward compression.

Biased aggregation further incorporates prior knowledge via a bias function $V$ added to the aggregate DP, yielding

$$J(i) + V(i) = \min_{u\in U(i)} \sum_{j} P_{ij}(u) \left( g(i, u, j) + \alpha \left[ J(j) + V(j) \right] \right)$$

and relates single-state aggregate DP to rollout algorithms, providing a bridge between aggregation and policy improvement (Bertsekas, 2019).

4. Aggregation in Distributed, Multi-Agent, and Communication-Constrained RL

In distributed RL, aggregation-aware algorithms efficiently combine gradients, policies, or value estimates in parallel and asynchronous computation environments. Asynchronous policy gradient aggregation methods, such as Rennala NIGT and Malenia NIGT (Tyurin et al., 29 Sep 2025), employ normalized gradient tracking with momentum and aggregation subroutines (using AllReduce or local averaging) that provably improve wall-clock and communication complexity by exploiting agent computation time diversity and local aggregation. Heterogeneous computation and environment distributions are handled by unweighted cross-agent averaging, enabling robustness to both straggler effects and environment non-i.i.d.ness.

In decentralized multi-agent RL, efficient information aggregation enables scaling and privacy preservation. TD error aggregation techniques allow agents to cooperate without exposing local state, reward, or value functions, exchanging only summary statistics such as error estimates (Figura et al., 2022). These methods provide convergence guarantees to local optima of team-average objective functions, with communication cost scaling quadratically with network size in the general setting.

Graph-based aggregation via GNNs (InforMARL (Nayak et al., 2022)) or permutation-invariant message encoders (MASIA (Guan et al., 2023)) allows agents to integrate neighbors’ local state and relational information efficiently, supporting scalable MARL and robust performance under variable group size or communication regimes, including online and offline learning.

5. Recursive and Directional Aggregation: Generalizing Objectives and Ensemble Fusion

Aggregation-aware RL supports both the extension of cumulative objectives and the dynamic fusion of ensemble estimates. The recursive reward aggregation perspective (Tang et al., 11 Jul 2025) frames the value function as a fold (catamorphism) over the sequence of generated rewards, allowing for alternative objectives—discounted max, min, log-sum-exp, or Sharpe ratio—to be specified by the choice of aggregation operator and post-processing. For instance,

$\dmax([r_1, r_2, \dots]) = \max\{ r_1,\, \gamma\, \dmax([r_2, r_3, \dots]) \}$

and the corresponding BeLLMan equations emerge naturally from this algebraic construction, integrating seamlessly with both value-based and actor-critic algorithms without modifying the per-step reward.

Directional Ensemble Aggregation (DEA) (Werge et al., 31 Jul 2025) advances ensemble-based off-policy actor-critic methods by learning scalar aggregation parameters for the critic and the actor sides, modulating the aggregation of ensemble Q-values adaptively based on ensemble disagreement. Specifically, the critic-side target is

$$\bar{Q}_{\bar\kappa}(s,a) = \frac{1}{N} \sum_{i=1}^N \bar{Q}_i(s,a) + \bar\kappa \delta_{\text{bar}}(s,a)$$

with analogous actor-side aggregation. The aggregation weights are adjusted by disagreement-weighted BeLLMan errors, enabling adaptive conservatism or optimism aligned with training phase and estimate uncertainty.

6. Applications, Extensions, and Empirical Validation

Aggregation-aware methods have demonstrated robust empirical performance:

• Transfer and multi-policy fusion: Adaptive aggregation frameworks such as MULTIPOLAR and its safety-critical variant enable fast adaptation and safety transfer in domains with diverse dynamics and constraints (Barekatain et al., 2019, Zhang et al., 2023).
• Distributed RL: Rennala/Malenia NIGT methods yield order-of-magnitude improvements in training time and communication over prior distributed policy gradient methods, handling both synchronization and heterogeneity (Tyurin et al., 29 Sep 2025).
• Meta-RL and sequence models: Split aggregation approaches like SplAgger (Beck et al., 5 Mar 2024) combine invariant and variant representations to achieve rapid learning in new tasks, outperforming pure RNN or invariant models, particularly in memory- or order-sensitive environments.
• Efficient communication and coordination: InforMARL and MASIA architectures enable scalable multi-agent systems via graph or permutation-invariant message aggregation, yielding improved sample efficiency and robustness across team sizes (Nayak et al., 2022, Guan et al., 2023).
• Combinatorial optimization and domain-specific tasks: State aggregation coupled with deep RL (e.g., in the knapsack problem) leads to both superior solution quality and faster convergence (Afshar et al., 2020).

7. Broader Implications and Theoretical Foundations

Aggregation-aware reinforcement learning reflects a convergence of ideas in function approximation, state abstraction, transfer and multi-agent learning, safety, distributed optimization, and objective flexibility. Key theoretical advances include error bounds relating aggregation granularity to suboptimality, regret guarantees decoupled from atomic state/action space size, and contraction properties for aggregate BeLLMan operators under diverse objectives. Practical successes suggest that aggregation—carefully tuned or learned—can be a powerful means for scaling RL, aligning agent behavior with complex or non-standard objectives, and enabling robust adaptation or coordination in demanding real-world settings.

This aggregation-centered perspective also explains why RL algorithms designed for strict MDP settings occasionally perform well even in environments that are non-Markovian, partially observed, or where only coarse aggregated data is accessible (Hutter, 2014). As research progresses, aggregation-aware learning frameworks are poised to play an increasingly central role in the development of adaptive, scalable, and versatile RL systems.