Goal Decomposition: Principles & Applications

• Goal decomposition is a strategy that breaks down complex, long-horizon objectives into clear hierarchical subgoals to improve planning efficiency and interpretability.
• Methodologies include hierarchical reinforcement learning, symbolic task planning, and visual phase detection, enabling automated subgoal generation and modular policy integration.
• Empirical results show that goal decomposition boosts sample efficiency, success rates, and scalability while mitigating computational complexity in diverse applications.

Goal decomposition refers to the partitioning of a complex, long-horizon objective into a sequence or hierarchy of subgoals or subtasks. This principle underlies much of modern AI planning, reinforcement learning (RL), hierarchical control, task planning in robotics, and human cognitive problem-solving. Goal decomposition schemes seek to enhance sample efficiency, modularity, interpretability, transfer, and scalability by structuring search or policy learning around intermediate milestones.

1. Formalizations of Goal Decomposition

Goal decomposition has been instantiated across several formal frameworks, reflecting the structural diversity of long-horizon problems.

• Hierarchical RL: The core motif is to factor policy π into a high-level meta-controller that selects subgoals (sometimes in a latent space) and a low-level controller that realizes these subgoals, as in

$$P(a_t|s_t) = \sum_{\ell^g} P(\ell^g|I, O_0)\cdot P(a_t|\ell^g, O_{1:t})$$

where $\ell^g$ is a predicted goal location and $O_{1:t}$ are the observations to time $t$ (Misra et al., 2018, Sukhbaatar et al., 2018, Park et al., 2023, Giammarino et al., 12 Dec 2025).

• Task planning: The problem is posed as splitting a planning tuple $$P \equiv \langle \mathcal{S}, \mathcal{A}, \mathcal{T}, s_0, S^{*} \rangle$$ into subproblems $$P_i = \langle \mathcal{S}, \mathcal{A}, \mathcal{T}, s_i, S^*_{i+1} \rangle$$, with an LLM or rule-based agent partitioning $S^*$ into intermediate $S^*_i$ subgoal sets (Kwon et al., 2024).
• Multi-agent settings: Temporal logic specifications or centralized goals $\varphi$ are decomposed into syntax subtrees, each assigned to a subteam, through Satisfiability Modulo Theories (SMT)-driven syntax transformations and agent assignment functions (Leahy et al., 2020).
• Sketch decompositions in planning: A mapping $G: S(P) \rightarrow 2^{S(P)}$ ascribes to every state $s$ a set of subgoals $G(s)$, ensuring that subproblems $P[s,G(s)]$ have bounded width $k$ (i.e., solvable by IW$(k)$) (Aichmüller et al., 2024).
• Graph-theoretic models: Subgoal sets $\mathcal{Z} \subseteq \mathcal{S}$ in state graphs enable agents to chain plans $(s_0 \to z_1 \to \cdots \to g)$, where selecting $\mathcal{Z}$ optimizes for a computational cost–utility tradeoff (Correa et al., 2022).

The formal decomposition operator thus varies: from explicit subgoal state sets, to temporal logic formulae, to continuous or discrete subgoal embeddings.

2. Algorithmic Approaches and Subgoal Generation

Approaches to goal decomposition span learning-based, symbolic, and hybrid paradigms:

• Unsupervised/self-play discovery: Asymmetric self-play between “Alice” and “Bob” policies fosters continuous goal-set coverage, leveraging entropy bonuses to diversify subgoals and imitation losses to induce consistent goal-conditioned skills (Sukhbaatar et al., 2018).
• Predefined or model-based: In task planning, LLMs are prompted with the domain signature and in-context examples to elicit an ordered sequence of intermediate subgoals. For highly structured environments, symbolic rules or temporal logic formulae (e.g., CaTL) are decomposed via syntax-tree transformations and SMT-based assignments (Kwon et al., 2024, Leahy et al., 2020).
• Attention and sequential windowing: Meta-controller architectures employ recurrent attention to select state-space regions for subgoal creation, as in recurrent-attention deep RL (Sahni et al., 2017).
• Visual decomposition: In long-horizon visuomotor tasks, phase shifts in a pretrained visual embedding space identify subgoal boundaries, enabling fully-visual subgoal extraction without further training (Zhang et al., 2023).
• DRL-based sketch learning: Relational GNN policies select successor states (subgoals) reachable by bounded-width novelty-based search (IW$(k)$), with actor–critic reinforcement learning in the induced MDP (states as nodes, actions as subgoal transitions) (Aichmüller et al., 2024).
• Human task decomposition: Behavioral experiments show that optimal subgoal selection by humans can be rationalized as a cost–utility trade-off, often well-approximated by betweenness centrality or resource-rational search metrics (Correa et al., 2022).

The table below summarizes representative approaches:

Approach	Subgoal Representation	Generation/Assignment Mechanism
Unsupervised self-play	Continuous state embedding	Entropy-regularized self-play loop
LLM task planning	Ordered state sets	Prompted LLM with domain/task priors
Temporal logic planning	Syntax subtrees / formulas	SMT over assignments, logic rewrites
Visual phase detection	Visual embedding frames	Embedding-distance curve maxima
DRL policy sketches	Successors by IW$(k)$	Greedy GNN actor–critic policy
Human cognitive planning	Subgoal set in state graph	Implicit resource-rational optimization

3. Theoretical Foundations and Complexity

A unifying rationale for goal decomposition is to mitigate the curse of dimensionality and search depth in complex problems:

• Search space reduction: Decomposition transforms $O(b^d)$ search into subproblems of complexity $\sum_i O(b^{d_i})$, with $d = \sum_i d_i$ and $d_i \ll d$ in practice (Kwon et al., 2024).
• Width in planning: When sketch decompositions yield subproblems of width $k$ scalable by IW$(k)$, entire classes of long-horizon problems become solvable in polynomial time (Aichmüller et al., 2024).
• Independence and optimality: Under joint-state factorizations and additive cost/transition independence, decomposed MDP policies are provably optimal for the global objective (Quamar et al., 30 Nov 2025).
• Robustness to value noise: Hierarchical approaches (e.g., two-level policies) tolerate greater error in value function approximation for distant goals, as error compounds only over short sub-intervals (Park et al., 2023).

The DRL sketch decomposition and UAV mission planning frameworks both demonstrate that appropriate decomposition can confer low-overhead computational complexity and policy-optimality guarantees under suitable independence or width assumptions (Aichmüller et al., 2024, Quamar et al., 30 Nov 2025).

4. Integration, Modularity, and Learning Pipelines

Most systems instantiate goal decomposition in a modular, multi-phase pipeline:

1. Subgoal identification:
   • LLM- or vision-based extraction of intermediate states or specifications.
   • Logic-based decomposition using temporal formulae or planning sketches.
2. Subproblem planning/learning:
   • Solving each subproblem either via symbolic planning (e.g., Fast-Downward), model-based methods, or RL (policy gradient, actor–critic, BC with relabeled subgoals).
   • Selection of solver based on subproblem complexity (e.g., minimum description length) (Kwon et al., 2024).
3. Policy integration:
   • Hierarchical controllers dispatch subgoals and orchestrate lower-level controllers or agents (Misra et al., 2018, Park et al., 2023, Giammarino et al., 12 Dec 2025).
   • In multi-agent or mission settings, local solutions are assigned to subteams and recombined into globally feasible plans, possibly with meta-policies for conflict arbitration (Leahy et al., 2020, Quamar et al., 30 Nov 2025).
4. Evaluation and ablation:
   • Quantitative metrics: success rate, task completion, final distance to goal, coverage, robustness.
   • Qualitative ablations: effect of subgoal quality, modular policy freezing, complexity thresholding, and subgoal assignment strategy (Kwon et al., 2024, Zhang et al., 2023, Li et al., 2023).

5. Empirical Results and Benchmarking

Key empirical findings include:

• Sample efficiency: Hierarchical and modular decompositions yield substantial gains in sample efficiency, especially in multi-agent and sparse-reward settings (Sukhbaatar et al., 2018, Li et al., 2023, Kwon et al., 2024).
• Success rates and generalization: Subgoal decomposition enables near-perfect navigation/task success in simpler domains and significant improvements in compositional generalization for unseen subtask orders (Misra et al., 2018, Zhang et al., 2023).
• Scalability: Decomposed approaches scale to exponentially larger state spaces and larger agent or goal counts (e.g., up to 50-agent temporal logic planning, multi-goal UAV missions) (Leahy et al., 2020, Quamar et al., 30 Nov 2025).
• Robustness and error tolerance: Hierarchical policies demonstrate resilience to noisy value function learning and better out-of-distribution generalization (Park et al., 2023, Giammarino et al., 12 Dec 2025).
• Ablation studies: Disabling subgoal detection, reward shaping, or language alignment leads to considerable performance drops, underscoring the necessity of principled decomposition (Zhang et al., 2023, Li et al., 2023).

6. Limitations, Open Problems, and Human Grounding

Despite the broad utility of goal decomposition, important limitations persist:

• Subgoal selection criteria: In many neuro-symbolic or LLM-based frameworks, the number and selection of subgoals lack an automatic, theoretically justified criterion—current thresholds (e.g., by empirically measured complexity or phase change) are heuristic (Kwon et al., 2024, Zhang et al., 2023).
• Quality and alignment of subgoals: LLMs or attention-based generators may propose spurious or irrelevant subgoals absent semantic constraint mechanisms (Li et al., 2023).
• Integration with continuous and motion-planning domains: Full integration with task-and-motion planning and hybrid continuous/discrete spaces is often pending (Kwon et al., 2024).
• Human-comparable decompositions: Human task decomposition appears to reflect resource-rational optimization, balancing path efficiency and planning cost. Heuristics such as betweenness centrality approximate human subgoal selection but can diverge in graphs without bottlenecks or with asymmetric structure (Correa et al., 2022).

Table: Points of Contact Between Human and Automated Goal Decomposition

Human Cost–Utility Framework (Correa et al., 2022)	Automated/Algorithmic Analogs
Subgoal sets in state space	Subgoal states, syntax nodes, embeddings
Utility–cost tradeoff	Sample complexity, search/plan time
Bottleneck identification	Centrality-based or width-minimizing
Sequential or parallel subtask assembly	Hierarchical/MARL, SMT-based partition

7. Applications Across Domains

Goal decomposition is foundational across a range of application domains:

• Instruction following and embodied agents: Mapping natural language instructions to visual goals, with subsequent goal-conditioned action generation (Misra et al., 2018).
• Robotics and manipulation: Automated segmentation of demonstration videos into phase-aligned subgoals for imitation and RL, yielding improved generalization and sample-use (Zhang et al., 2023).
• Classical and neuro-symbolic planning: Multi-level decomposition pipelines integrate LLM-based common sense with symbolic planners and MCTS rollouts for long-horizon robotic tasks (Kwon et al., 2024).
• Multi-agent coordination and logic synthesis: Decomposition of global temporal logic specs for heterogeneous teams, with correctness-preserving reconciliation of agent/subplan assignments (Leahy et al., 2020).
• Hierarchical reinforcement learning: Continuous/latent subgoals discovered via self-play or advantage-weighted regression enhance robustness and action-free policy learning (Sukhbaatar et al., 2018, Park et al., 2023, Giammarino et al., 12 Dec 2025).
• Scalable mission planning: Factor-based partitioning of large MDPs in UAV settings supports real-time recombination with provable policy equivalence (Quamar et al., 30 Nov 2025).

These instantiations demonstrate the pervasive and flexible utility of goal decomposition as a core architectural and algorithmic strategy.