Hierarchical Planning and Physical Grounding

• Hierarchical planning and physical grounding are techniques that decompose high-level goals into layered subgoals anchored in sensorimotor experiences.
• They employ model-based reinforcement learning to generate latent abstractions, enhancing knowledge transfer and robust adaptation across varied environments.
• The approach enables rapid planning and decision-making, with applications spanning robotics, adaptive control, and partially observable systems.

Hierarchical planning and physical grounding represent foundational challenges and design paradigms in artificial intelligence, robotics, and cognitive systems research. Hierarchical planning aims to decompose high-level goals into a structured sequence of subgoals and actions across multiple layers of abstraction, while physical grounding ensures that these representations and plans remain anchored in sensorimotor or environmental data, facilitating generalization, efficient knowledge transfer, and robust adaptation to new tasks or contexts. This entry provides a detailed survey and synthesis of core concepts and technical frameworks in hierarchical planning and physical grounding, with a primary focus on model-based reinforcement learning methods that interleave abstraction and interaction, and context from related approaches.

1. Hierarchical Representations in Planning

Hierarchical representations in reinforcement learning are constructed by organizing state spaces and policies at multiple levels of abstraction. The approach proposed by “Grounding Hierarchical Reinforcement Learning Models for Knowledge Transfer” (Wernsdorfer et al., 2014) centers on building latent representations by clustering histories of sensorimotor experiences rather than relying on hand-engineered state decompositions. Formally, given a history of sensory and action data $h \in H$, an abstraction function $A: H \to L$ maps $h$ to a latent state $l \in L$, where $L$ is the set of all latent representations. Each latent state $l$ encapsulates both its identity (“shape”) and a policy $\pi_l = (V_l, M_l)$, with $V_l$ representing the value function and $M_l$ (or equivalently, a model function) predicting abstract state transitions.

This layered structuring enables knowledge transfer by capturing invariances at the abstraction level. When an agent encounters a new environment with similar subjective experience—such as an extended corridor that locally matches the original training environment—the abstract latent state representations persist and can be reused. The system thus achieves generalization such that high-level patterns are robust with respect to variations in the underlying environment.

2. Role of Sensorimotor Interaction in Grounding

Sensorimotor interaction is not only an information source for value estimation but is the substrate for hierarchical abstraction. The model merges perception and actuation into sensorimotor states $x_t = (a_{t-1}, s_t)$, which contain both preceding action and current observation. The abstraction function $A$ maps sequences of these sensorimotor states to latent states. Grounding occurs because these sensorimotor histories reflect the concrete experiences of the agent in its world, providing an empirical foundation for the formation of the latent space.

An illustrative example from (Wernsdorfer et al., 2014) clarifies this: in “subjective” interaction regimes, the agent bases its perception on the configuration of local cues (e.g., neighboring cells in a grid), rather than their global coordinates (“objective” interaction). Even when the environment is modified (e.g., the corridor is lengthened), as long as the local configuration remains unchanged, the abstract representations and their associated policies can be efficiently reapplied, enabling rapid knowledge transfer.

3. Model-Based Versus Model-Free Hierarchical Reinforcement Learning

The framework advanced in (Wernsdorfer et al., 2014) is fundamentally model-based. Classical model-free approaches—such as Q-learning or SARSA—update a value function $V(s, a)$ directly through experience and rewards, with no explicit transition model. In contrast, model-based RL incorporates an explicit model of state transitions. In classical form:

$T: S \times A \rightarrow S$

$$V(s_{t-1}, a_{t-1}) \leftarrow V(s_{t-1}, a_{t-1}) + \alpha \big[ r_t + \gamma V(s_t, a_t) - V(s_{t-1}, a_{t-1}) \big]$$

The hierarchical variant in (Wernsdorfer et al., 2014) replaces concrete state transitions with “queries” in the latent space:

$\mathcal{Q}: L \times L \rightarrow \{\top, \bot\}$

$M: L \times L \rightarrow \{\top, \bot\}$

Here, the model function $M$ predicts the success of transitions between latent states based on previous experience. Planning is carried out by recursively simulating transitions among latent states, combining abstract value estimates with model-predicted feasibility. This permits efficient “what-if” reasoning and enables the agent to plan ahead in latent space without requiring low-level simulation of every physical state transition.

A critical advantage of this approach is the ability to “reuse” policies and representations at the abstract level, streamlining transfer across similar but objectively different environments and supporting robustness in partially observable or ambiguous situations. However, the conjoining of sensor and motor signals (i.e., treating $(a, s)$ as the basic state) increases the number of base-level states, potentially raising computational costs. The hierarchical organization lessens this cost as queries become more abstract and transferable.

4. Technical Foundations: Formulations and Algorithms

The formal structure underpinning hierarchical planning and physical grounding in (Wernsdorfer et al., 2014) comprises several layers:

• Classical observable state value and transition functions:

$$V : S \times A \rightarrow \mathbb{R}, \quad T : S \times A \rightarrow S$$

• Sensorimotor state extension:

$x = (a_{t-1}, s_t) \in SM$

With SARSA-style updates for sensorimotor states:

$$V_l(x_{t-1}) \leftarrow \frac{V_l(x_{t-1}) + \alpha (r_{t-1} + \gamma V_l(x_t))}{1 + \alpha}$$

• Latent-level, query-driven planning:

$$\mathcal{Q} : L \times L \rightarrow \{\top, \bot\}$$

With the query interpreted as: from the latent state $l_{t-n-1}$, can the agent reach $l_q$? The model predicts this via the history $h^{\pi_q}_t = [e_{t-n}, \ldots, e_t]$, the abstraction function $l_t = A(h^{\pi_q}_t)$, and the success condition $$\mathcal{Q}(l_{t-n-1}, l_q) \Leftrightarrow (l_t = l_q)$$.

• Recursive abstract planning: Given these definitions, agent planning involves recursive simulation and evaluation in the latent space, bypassing the need for exhaustive state visitation and thus affording steep computational gains and generalization improvements.

5. Applications: Knowledge Transfer and Robust Decision-Making

The broad applicability of this hierarchical and physically grounded approach extends to any domain requiring transfer of sensorimotor competence between environments—such as autonomous robotics, reinforcement learning for games, and adaptive control in dynamic or partially observable settings. In such domains, agents benefit from the ability to abstract high-level patterns robustly (e.g., navigation strategies or manipulation routines) and instantiate these efficiently in new, sensorimotor realities with minimal re-learning.

Notably, the approach supports planning in partially observable Markov decision processes (POMDPs), where agent perception is inherently ambiguous or incomplete. By tying abstract decision modules to histories of concrete interaction, the model builds representations that are subjective to the agent’s own experience, offering a re-usable substrate for continual, lifelong learning.

6. Broader Implications and Comparisons

The model-based hierarchical RL paradigm outlined in (Wernsdorfer et al., 2014) contrasts starkly with model-free deep RL, which often requires large quantities of experience to achieve similar levels of abstraction or transferability. Model-based hierarchical abstraction accelerates policy adaptation and improves the explanatory control of the agent’s own policy space—since latent state transitions can be queried, visualized, and reasoned about explicitly.

The work also edges artificial learning architectures closer to embodied cognition principles, whereby abstract internal models are grounded directly in the agent’s physical, interactive experience. Agents built along these lines can autonomously develop high-level planning modules whose scope and content are dictated not by designer-imposed abstractions, but by the structure of their own sensorimotor histories—marking a path toward more general and robust artificial intelligence.

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In summary, hierarchical planning and physical grounding, as realized through model-based reinforcement learning frameworks using sensorimotor abstraction, deliver substantial benefits in knowledge transfer, computational efficiency, and robustness to environmental variations. Technical formulations—spanning abstraction functions, sensorimotor concatenation, latent-space transition models, and recursive planning algorithms—enable agents to construct, ground, and leverage multi-level representations directly from their own interaction data. These insights have significant implications for the design of transferable, adaptive, and interpretable decision systems in both theory and application.