HierAMLSI: Robust HTN Domain Learning

• HierAMLSI is an algorithm that automatically learns HTN planning domains from partial and noisy execution traces by combining grammar induction with STRIPS-style action model extraction.
• It employs RPNI for DFA induction and a polynomial-time set-cover heuristic to derive compact hierarchical decompositions along with accurate action preconditions and effects.
• Empirical evaluations on IPC2020 domains show high accuracy (>90%) even under significant noise and partial observability, underscoring its practical impact in autonomous planning.

HierAMLSI is an algorithm for automatic acquisition of Hierarchical Task Network (HTN) planning domains from partial and noisy execution traces. Its approach combines grammar induction—specifically, regular positive and negative inference (RPNI)—with STRIPS-style action model induction and a polynomial-time set-cover heuristic for compact HTN-method extraction. HierAMLSI enables learning of both primitive action schemas and hierarchical decomposition methods, including their preconditions and effects, directly from observations, offering robustness to substantial noise and partial observability in the input data (Grand et al., 2022).

1. Problem Setting and HTN Formalism

In HTN planning, a domain is defined by the tuple $$P = (L, C, A, S, M, s_0, w_I, g, \delta, \tau, \lambda, \sigma, \zeta)$$:

• $L$: finite set of ground propositions (fluents).
• $S$: finite set of world-state labels, with initial state $s_0$.
• $A$: set of primitive (PDDL) action labels.
• $C$: set of compound (non-primitive) task labels, $C \cap A = \emptyset$.
• $T = A \cup C$: full task alphabet.
• $w_I \in T^*$: initial, totally-ordered task network.
• $M$: set of HTN method labels; each $m\in M$ is defined by $\sigma(m) = (c, \varphi)$, with $c\in C$ and $\varphi \in T^*$.
• $\delta = (\text{prec}, \text{add}, \text{del})$: precondition, add, and delete sets for each $a\in A$.
• $$\tau(a, s) \equiv (\text{prec}(a)\subseteq \lambda(s))$$: applicability of actions.
• $\gamma(a, s)$: resultant state after $a$; $$\lambda(\gamma(a, s)) = (\lambda(s)\setminus \text{del}(a)) \cup \text{add}(a)$$.
• $\zeta(\omega, s)$: decomposition operator for compound tasks, succeeds if method’s precondition holds.
• $g\subseteq S$: set of goal states; $\lambda(s)$ gives the fluents true in $s$.

A plan $\omega\in A^*$ is a solution if:

1. $w_I \rightarrow^* \omega$ via repeated $\zeta$ applications,
2. $\omega$ is executable from $s_0$ ($\tau$ holds at each step),
3. $\gamma(s_0, \omega) \vDash g$.

HierAMLSI assumes input observations via a function $\lambda: S \to 2^L$, which may be partial (some true fluents unobserved) or noisy (random flipping of truth values). Experiments introduce up to 20% noise and up to 75% missing fluents per observed state.

2. Grammar-Induction Approach

HierAMLSI’s central insight is that the set of valid plans, $\mathcal{L}(P)$, for an HTN domain can be decomposed as

$$\mathcal{L}(P) = \mathcal{L}_H(P) \cap \mathcal{L}_C(P)$$

where

• $$\mathcal{L}_H(P) = \{\omega \in A^* : w_I \rightarrow^* \omega \text{ via method decompositions}\}$$,
• $$\mathcal{L}_C(P) = \{\omega \in A^* : \gamma(s_0, \omega)\vDash g\}$$ (the set of action sequences leading to goal states, regular under STRIPS transitions).

HierAMLSI induces a DFA $\Sigma=(Q, T, \delta_\Sigma, q_0, F)$ where:

• $Q\subseteq S$ are “grammar” states, induced via RPNI,
• $T = A\cup C$,
• $\delta_\Sigma(q, t) = q'$ encodes the transition under task $t$,
• $q_0$ mirrors $s_0$ and $F\subseteq Q$ comprises goal states.

Alternatively, the transition grammar can be represented as a context-free grammar, associating productions to method decompositions.

3. Algorithmic Pipeline and Complexity

HierAMLSI comprises four primary steps:

Step 1. Observation Generation

• Random walks are conducted using a black-box HTN solver. At each step, a task $t \in T$ is randomly chosen; if $t$ is compound and decomposable, it is replaced via the black-box decomposition.
• The maximal primitive prefix is added to the positive set $I^+$; the full sequence (possibly failing) to the negative set $I^-$. Complexity: $O(N_\text{walk} \cdot \ell)$ (with $\ell$ the average trace length).

Step 2. DFA Learning

• The “primitive-only” DFA on $A$ is induced with RPNI using $(I^+ \cap A^*, I^- \cap A^*)$.
• Compound-task transitions are subsequently augmented: for each observed $c \in C$ from $q$ to $q'$, $\delta_\Sigma(q, c) = q'$. RPNI is polynomial in dataset and alphabet size; augmentation is $O(|I^+| \cdot |C|)$.

Step 3. HTN Method Extraction

• For each $c\in C$, all pairs $(q \to q')$ labeled by $c$ in $\Sigma$ yield candidate decompositions.
• A greedy set-cover heuristic (Algorithm 1 in the paper) constructs $M[c]$, iterating to allow up to $i$ compound-tasks per method (for $i=1,\dots,|C|$). The smaller cover is kept.
• Overall complexity: $O(|C|^2 \cdot |I^+|^3)$ (Lemma 2).

Step 4. Preconditions for Methods and Actions

• Each method is treated as a “primitive” task: precondition, add, delete sets are learned by intersections over pre- and post-condition sets for DFA transitions.
• A refinement loop (as in AMLSI) adjusts effects and preconditions iteratively until a fixpoint, followed by a Tabu search over operator schemas for noise-robustness and DFA transition coverage. Each refinement pass is $O(|\text{Trans}(\Sigma)|\cdot |L|)$.

4. Theoretical Properties

Lemma 1 establishes that the heuristic method cover guarantees all observed compound tasks in $I^+$ can be decomposed by some $M[c]$. The procedure initializes from direct observations (ensuring non-empty cover) and each greedy step maintains coverage.

Lemma 2 bounds the method extraction process by $O(|C|^2 \cdot |I^+|^3)$ time: $O(|I^+|^2)$ candidate methods, set-cover in $O(|I^+|^3)$, iterated $O(|C|^2)$ times.

No formal convergence or sample-complexity guarantees are given for the RPNI stage, apart from standard RPNI properties.

5. Empirical Evaluation and Accuracy

HierAMLSI was tested on five IPC2020 HTN domains: Blocksworld, Gripper, Zenotravel, Transport, and Childsnack. Each domain’s $(|A|, |C|, |M|, |L|)$ statistics are detailed in the original work.

Experimental scenarios included:

1. Complete observations (100% observable, 0% noise),
2. Complete observations with 20% noise,
3. Partial observations (25% observable, 0% noise),
4. Partial with 20% noise.

Accuracy metric: $$Acc = \frac{\text{number of test problems solved}}{\text{number of test problems}}$$, using TFD planner with VAL validator across 20 problem instances per domain. When learning only methods (given action models), 600 training tasks yielded $Acc \approx 100\%$ even with noise; 100 tasks sufficed for $Acc > 50\%$. Learning both actions and methods led to slightly lower $Acc$ in noisy domains (notably Blocksworld, Transport, Childsnack), but over 90% accuracy was restored by 300-600 training tasks in all tested conditions.

6. Strengths, Limitations, and Open Questions

Strengths

• Full HDDL domain acquisition—including actions, methods, and preconditions—from partially observable and noisy traces.
• Induced DFA grammar via RPNI generalizes well with minimal negative over-generalization.
• Heuristic method cover yields compact, interpretable HTN libraries.
• High empirical accuracy ($>90\%$) achieved even with 20% noise and heavily incomplete observations.

Limitations and Open Directions

• No formal sample-complexity bounds for HTN learning; relies on empirical random-walk coverage.
• Greedy heuristic for method cover may not yield canonical or “intended” hierarchies.
• Restricted to totally ordered task networks; partial orderings or additional constraints (e.g., time, resources) are not addressed.
• Only STRIPS-style preconditions/effects are learned; extension to temporal or numeric domains requires substantial augmentation.

Potential extensions suggested include incorporating ordering/causal constraints beyond regular grammars, developing active sampling to reduce random walk dependence, and supporting temporal/numeric HTNs by extending the fluent vocabulary.

7. Significance in Autonomous Planning

HierAMLSI represents a significant advance in autonomous HTN domain acquisition by enabling robust, high-fidelity learning of both actions and hierarchical methods under challenging observational regimes (Grand et al., 2022). Its integration of grammar induction (via RPNI), STRIPS-style intersection-based action/model learning, and polynomial-time method cover construction sets a new baseline for domain learning accuracy and scalability in the presence of noise or partial observability. Its modular approach, empirical performance, and open methodology position it as a foundational platform for further developments in learning expressive planning formalisms from real-world data traces.