Hierarchical Reinforcement Learning Agents

• Hierarchical Reinforcement Learning agents are decision systems that decompose tasks into manageable subproblems using multi-level policy abstraction.
• They utilize temporal abstraction and dynamic message passing to enhance exploration, credit assignment, and coordination in both single and multi-agent environments.
• HRL frameworks employ advantage-based reward propagation to optimize local policies and align subgoal performance with overall task success.

Hierarchical Reinforcement Learning (HRL) agents are a class of decision-making systems that exploit temporal and structural abstraction to solve complex, long-horizon tasks by decomposing them into manageable subproblems. HRL provides a principled framework for representing policies at multiple levels of granularity, handling temporal abstraction, improving exploration, credit assignment, transferability, and coordinated control, especially in the context of multi-agent, partially observable, and non-stationary environments.

1. Foundational Concepts and Formal Structure

The defining principle of HRL is the modularization of decision processes across multiple hierarchical levels. The canonical formalism is the options framework, where each option (temporally extended action) is characterized by a policy $\pi(a|s, o)$, an initiation set $\mathscr{I}(s, o)$, and a termination function $\beta(s, o)$. The decision-making process alternates between a high-level policy $\mu(o|s)$, which selects an option, and low-level policies that execute until option termination. This framework is extended in diverse contexts, including feudal reinforcement learning—where upper layers define and assign subtasks or "goals" for subordinate policies—as well as hierarchical graph structures in multi-agent reinforcement learning (MARL) (Marzi et al., 31 Jul 2025).

HRL is motivated by the need to:

• Efficiently explore large state-action spaces by reusing temporally extended skills or subroutines (option policies),
• Decompose long-term credit assignment, enabling more local learning signals,
• Transfer knowledge across tasks/domains through compositional and re-usable skills,
• Improve sample efficiency and coordination in multi-agent systems, particularly when combined with communication (e.g., message passing).

2. Hierarchical Structures and Architectures

Multi-Level Hierarchy and Temporal Abstraction

HRL agents are commonly arranged in multiple levels of control, ranging from two-level architectures (manager/worker; high/low) to full multi-tiered hierarchies (manager $\to$ sub-manager $\to$ worker). Each level operates at a characteristic timescale and abstraction. High-level policies typically generate goals or subgoals over extended time intervals, while lower levels translate these into more granular actions (Marzi et al., 31 Jul 2025).

Hierarchical graph structures further support flexible grouping and coordination: Managers assign goals to sub-managers, who in turn refine and delegate to workers. Hierarchies can be static or adapt dynamically, e.g., clustering agents by location or task-specific factors.

Hierarchical Message Passing and Coordination

For scalable multi-agent systems, message-passing mechanisms are essential. Message passing in HRL is implemented via Graph Neural Networks over the dynamically constructed hierarchy, where each node (at each hierarchy level) exchanges messages with its neighbors, allowing for aggregation and dissemination of local and global information. Policy outputs at each level are conditioned on both the received subgoal and the information aggregated from message passing (Marzi et al., 31 Jul 2025):

$$^{i,l+1}_{t} = \operatorname{update}^i_l(^{i,l}_{t}, \operatorname{Aggr}_{j \in \mathcal{B}_t(i)} \{ \operatorname{Msg}^i_l (^{i,l}_{t}, ^{j,l}_{t}) \})$$

where $^{i,l}_{t}$ is the latent state of node $i$ at round $l$.

3. Reward Assignment and Credit Propagation

A central challenge in HRL is assigning appropriate intrinsic rewards to lower-level policies such that maximizing these leads to improvement of the overall task return. Feudal and hierarchical MARL methods address this by propagating "advantage"-based signals from the higher to the lower levels (Marzi et al., 31 Jul 2025):

• Manager reward: For each sub-manager, the manager receives the aggregate extrinsic reward from all downstream workers over the goal horizon.
• Sub-manager reward: The sub-manager's reward includes the upper-level (manager) "advantage" for its state/action and any local environment reward.
• Worker reward: Each worker is rewarded by the advantage measured at its supervising sub-manager, which reflects the contribution of its own actions to upper-level task progress.

Formally, worker reward at time $t$ is:

$r_t^{w} = \frac{A^{\pi_s}({_t^{s \to w}, \pi_s({_t^{s \to w}))}}{\alpha}$

with advantage function:

$A^{\pi_i}(o, a) = Q^{\pi_i}(o, a) - V^{\pi_i}(o)$

This mechanism enables decentralized yet globally aligned training, and—under mild technical conditions (discount factor $\gamma$ near 1)—provably aligns sub-policy optimization with the global objective.

4. Policy Optimization, Communication, and Adaptability

Training in hierarchical agents is performed per-hierarchy, simultaneously optimizing policies at all levels using local rewards. Actor-critic or policy-gradient algorithms (e.g., PPO) are applied independently per policy. Communication across agents is realized via message passing, enabling dynamic coordination and planning at all hierarchy layers. Structural adaptability is supported, with hierarchies able to change dynamically based on agent groupings, environment state, or connectivity.

The learning process allows for synchronous or asynchronous updates, sustaining sample efficiency and specialization at each level. Hierarchical structures support both fully cooperative and mixed-scenario multi-agent systems; as shown in HiMPo, deeper hierarchies and state-dependent structures outperform shallow or static configurations (Marzi et al., 31 Jul 2025).

5. Empirical Evaluations and Benchmarks

The effectiveness of hierarchical HRL agents is assessed on challenging multi-agent and long-horizon benchmarks:

Table: Empirical Evaluation Highlights

Environment/task	Hierarchical Benefits	Observed Results
Level-Based Foraging	Temporal, spatial coordination	HiMPPO exceeds all baselines, learns hard survival
VMAS Sampling	Credit assignment, scalable coordination	Hierarchical message-passing outperforms all rivals
SMACv2	Decentralized, partial observability	Similar to flat approaches; hierarchy less critical

Key empirical findings indicate that HRL agents with hierarchical message passing and advantage-based reward assignment attain superior sample efficiency, robust coordination, and generalize better as problem size or complexity increases, particularly in settings with temporally extended dependencies and high-dimensional multi-agent coordination (Marzi et al., 31 Jul 2025). Ablations show hierarchical reward propagation is essential—replacing it with extrinsic rewards at lower levels degrades coordination performance.

6. Theoretical Analysis and Guarantees

The formal analysis demonstrates that, under the proposed reward propagation, optimizing local policy at each hierarchy results in optimization of the global, task-level objective (Marzi et al., 31 Jul 2025). The manager's return aligns with overall task return; sub-manager and worker objectives are tightly controlled by the advantage signal from upper levels, ensuring the entire hierarchy is incentivized to maximize cooperative performance. Theorems formalize this alignment and bound the required assumptions (discount factor, time scales).

7. Implications and Advantages Over Prior Methods

HRL agents configured with principle-based, hierarchy-wide credit assignment offer several advantages:

• Generalization without hand-crafted intrinsic rewards or bespoke shaping,
• Scalability to larger agent populations via distributed, per-level training and dynamic communication structures,
• Deep temporal and spatial credit assignment, outperforming flat/centralized or message-passing-only approaches in coordination-heavy or exploration-demanding tasks,
• Efficient learning and specialization through decentralized optimization, sample efficiency, and flexible hierarchy design,
• Provable alignment of local and global objectives, safeguarding coordination in cooperative/mixed scenarios.

HiMPo establishes the empirical and theoretical grounds making such architectures new benchmarks for MARL under challenging conditions (Marzi et al., 31 Jul 2025).