Symbolically-Guided Decision Transformer

• SGDT is a hierarchical neuro-symbolic decision model that uses symbolic subgoals or temporal-logic signals to guide a transformer-based policy.
• It separates high-level symbolic planning from low-level reactive control, thereby enhancing interpretability and long-horizon task decomposition.
• Empirical evaluations in grid-world and multi-robot manipulation tasks demonstrate significant efficiency gains and improved success rates.

Symbolically-Guided Decision Transformer (SGDT) denotes a class of hierarchical neuro-symbolic decision models in which a symbolic planning or specification layer provides structured guidance to a Decision Transformer-style policy, typically through explicit subgoals, prompts, or specification-derived conditioning variables. In the multi-robot formulation that explicitly uses the SGDT name, a neuro-symbolic planner produces a high-level task-oriented plan composed of symbolic subgoals, and a goal-conditioned Decision Transformer (GCDT) performs low-level sequential decision-making conditioned on those subgoals (Rasanji et al., 19 Aug 2025). Closely related formulations include the “Hierarchical Neuro-Symbolic Decision Transformer,” described as a concrete instantiation of the same idea, and temporal-logic Specification-conditioned Decision Transformers that use Signal Temporal Logic (STL) robustness as symbolic guidance rather than planner-generated subgoals (Baheri et al., 10 Mar 2025, Guo et al., 2024).

1. Conceptual scope and defining characteristics

SGDT is defined by the replacement or augmentation of conventional Decision Transformer conditioning with symbolically structured guidance. In a standard DT, conditioning is usually based on return-to-go; in SGDT-style systems, conditioning is instead tied to symbolic subgoals, symbolic operators, or quantitative signals derived from formal specifications. The result is a hierarchical decomposition in which long-horizon task structure is handled by a symbolic mechanism and short-horizon control is handled by an autoregressive sequence model (Rasanji et al., 19 Aug 2025).

The SGDT literature represented here spans at least three distinct but compatible realizations. In the multi-robot manipulation setting, the symbolic layer is a neuro-symbolic planner using PDDL and an LLM to generate a sequence of symbolic subgoals such as PICK Dave bread_slice1 and PUT Chad beef_patty bread_slice1; the low-level layer is a GPT-style GCDT over numerical state, subgoal, and return-to-go (Rasanji et al., 19 Aug 2025). In hierarchical grid-world control, the symbolic layer is a classical planner over propositions $\mathcal{P}$ and operators $\mathcal{O}$, and each operator is mapped by $\psi : \mathcal{O} \to \mathcal{G}$ into a sub-goal token $g_i$ that conditions a Decision Transformer (Baheri et al., 10 Mar 2025). In offline safe RL, the symbolic layer is an STL formula $\phi$, whose quantitative semantics yields prefix and suffix robustness values that are used as transformer conditioning tokens (Guo et al., 2024).

These variants share a common architectural thesis: symbolic guidance is not treated as a post hoc constraint checker alone, but as an explicit conditioning signal that shapes the action distribution. In the hierarchical grid-world formulation, the conditioned policy is

$p_\theta(a_t \mid s_{\le t}, a_{\le t-1}, g_i),$

where $g_i$ encodes the active symbolic operator (Baheri et al., 10 Mar 2025). In the multi-robot formulation, the low-level policy is written as

$$\pi_L(\mathbf{a}_t \mid \mathbf{s}_t, \mathbf{g}_t, \hat{R}_t),$$

with $\mathbf{g}_t$ the numerical encoding of the current symbolic subgoal (Rasanji et al., 19 Aug 2025). The symbolic component therefore governs temporal decomposition, operator ordering, and interpretability, while the transformer handles reactive control and sequence-level dependencies.

2. Architecture and symbolic representations

SGDT architectures are consistently two-level. The high-level component operates in symbolic space and computes a structured plan; the low-level component operates in numerical state space and predicts primitive or joint actions conditioned on the current symbolic instruction. In the multi-robot framework, the planner produces

$$\pi^{*} = \left\{\tilde{\mathbf{g}}_1, \cdots, \tilde{\mathbf{g}}_L \right\},$$

the shortest symbolic plan satisfying PDDL preconditions and effects with uniform cost $\mathcal{O}$0, while the GCDT executes each subgoal through continuous 3D waypoint actions for multiple robot arms (Rasanji et al., 19 Aug 2025).

The symbolic representation depends on domain design. In multi-robot manipulation, symbolic states $\mathcal{O}$1 are PDDL predicate configurations over object types such as robot, food, and location, with predicates including (holding ?r ?f), (on-table ?f), (on ?f1 ?f2), (gripper-free ?r), and (belongs-to ?f ?r). Symbolic high-level actions $\mathcal{O}$2 are grounded PDDL actions such as pick(?r ?f) and put(?r ?f1 ?f2) (Rasanji et al., 19 Aug 2025). In the classical-planner variant, the domain is $\mathcal{O}$3, where $\mathcal{O}$4 is a finite set of propositions and $\mathcal{O}$5 a set of symbolic operators with preconditions and effects, and the abstraction

$\mathcal{O}$6

maps low-level states into symbolic truth assignments (Baheri et al., 10 Mar 2025).

A central representational bridge is the symbolic-to-numeric encoding. In the multi-robot formulation, a mapping $\mathcal{O}$7 converts symbolic states and symbolic subgoals into numerical state and subgoal vectors, with $\mathcal{O}$8 often instantiated as expected 3D coordinates of the participating robots’ arms (Rasanji et al., 19 Aug 2025). In the hierarchical grid-world formulation, the corresponding bridge is $\mathcal{O}$9, which converts symbolic operators such as PickKey1, OpenDoor2, or Move(r,c \to r',c') into sub-goal tokens embedded in the same vector space as state and action tokens (Baheri et al., 10 Mar 2025).

The temporal-logic variant uses a different symbolic interface. Instead of explicit symbolic operators, it computes quantitative semantics $\psi : \mathcal{O} \to \mathcal{G}$0 for an STL formula $\psi : \mathcal{O} \to \mathcal{G}$1, then conditions the model on prefix robustness $\psi : \mathcal{O} \to \mathcal{G}$2 and suffix robustness $\psi : \mathcal{O} \to \mathcal{G}$3. This preserves the symbolic origin of guidance while translating it into real-valued control variables for sequence modeling (Guo et al., 2024).

3. Conditioning mechanisms, execution, and training objectives

SGDT training and inference are organized around subgoal-conditioned or specification-conditioned trajectory segments. In the multi-robot GCDT, the model processes subgoal-conditioned trajectories

$\psi : \mathcal{O} \to \mathcal{G}$4

using linear encoders, embeddings, time embeddings, and a GPT-based causal transformer with a decoder that projects trajectory embeddings to joint multi-robot actions $\psi : \mathcal{O} \to \mathcal{G}$5. Training minimizes

$\psi : \mathcal{O} \to \mathcal{G}$6

and parameters are updated by

$\psi : \mathcal{O} \to \mathcal{G}$7

An external rule-based constraint checker post-processes predicted actions to enforce physical and operational constraints such as collision avoidance (Rasanji et al., 19 Aug 2025).

The runtime control loop is explicitly hierarchical. The high-level policy over subgoals,

$\psi : \mathcal{O} \to \mathcal{G}$8

generates a symbolic plan. The low-level GCDT then predicts $\psi : \mathcal{O} \to \mathcal{G}$9, executes it, updates $g_i$0, checks whether the current subgoal is completed, and advances to the next subgoal or terminates when $g_i$1 (Rasanji et al., 19 Aug 2025). In the classical-planner-conditioned DT, the analogous mechanism is operator-by-operator execution with

$g_i$2

and operator completion occurs when

$g_i$3

If completion fails in time or safety predicates are violated, the symbolic layer can replan (Baheri et al., 10 Mar 2025).

The safe-RL specification-conditioned variant uses a Gaussian policy

$g_i$4

where $g_i$5 contains prefix robustness, suffix robustness, return-to-go, states, and actions. Its objective is

$g_i$6

This formulation shows that symbolic guidance need not be planner output; it can also be derived from the quantitative semantics of temporal logic (Guo et al., 2024).

4. Formal properties and conditioning design

A distinctive aspect of SGDT research is the attempt to separate symbolic planning error from low-level execution error. In the hierarchical neuro-symbolic Decision Transformer, the symbolic planner is assumed to be within $g_i$7 of the optimal symbolic plan, and symbolic cost approximates true MDP costs with per-operator error $g_i$8, yielding $g_i$9. Neural execution incurs per-operator error $\phi$0, with $\phi$1. The resulting bound,

$\phi$2

makes explicit how approximation errors accumulate across hierarchy levels (Baheri et al., 10 Mar 2025). The same work also gives a stochastic accumulation result for random operator-level execution errors $\phi$3, with mean $\phi$4, variance $\phi$5, and bounded deviation $\phi$6, quantifying how local control errors compound along a symbolic plan.

A second formal thread treats symbolic guidance as a quantitative conditioning signal. In STL-conditioned DTs, the robustness semantics

$\phi$7

provide a continuous measure of symbolic satisfaction, with $\phi$8 indicating satisfaction and $\phi$9 indicating violation. Prefix robustness represents achieved satisfaction so far, and suffix robustness represents desired future satisfaction. This makes SGDT compatible with non-Markovian temporal rules such as “always stay within safety bounds” or “return to a safe region within 5 steps,” without collapsing them into a single Markovian cost-to-go (Guo et al., 2024).

Conditioning design has also been analyzed from the perspective of computational efficiency. SlimDT removes return-to-go from the autoregressive token stream and injects conditioning outside the main sequential model, reducing sequence length from $p_\theta(a_t \mid s_{\le t}, a_{\le t-1}, g_i),$0 tokens to $p_\theta(a_t \mid s_{\le t}, a_{\le t-1}, g_i),$1 and the quadratic transformer-side cost from $p_\theta(a_t \mid s_{\le t}, a_{\le t-1}, g_i),$2 to $p_\theta(a_t \mid s_{\le t}, a_{\le t-1}, g_i),$3, or $p_\theta(a_t \mid s_{\le t}, a_{\le t-1}, g_i),$4 with one cross-attention module (Wang et al., 7 May 2026). The paper argues that SGDT “fits naturally” into this design space because symbolic guidance is a conditioning signal rather than part of the environment dynamics. This suggests that SGDT need not always represent symbolic information as full autoregressive tokens; depending on task structure, symbolic guidance may instead be injected by concatenation, adaptive layer normalization, or cross-attention outside the main state-action sequence (Wang et al., 7 May 2026).

5. Empirical results, generalization, and task domains

The empirical literature covers both discrete long-horizon control and continuous multi-robot manipulation. In stochastic grid-worlds, the hierarchical neuro-symbolic Decision Transformer was evaluated in two 5-by-5 domains: a single key-door task and a multi-goal, multi-key, multi-door task. Metrics were success rate, average steps, and average reward across random seeds and multiple fail_prob values. In the single key-door domain, both pure DT and the hybrid method reached moderate-to-high success, but the hybrid consistently used fewer steps and achieved higher rewards. In the multi-goal domain, the hybrid clearly outperformed the pure DT: the pure approach had near 0% success across all tested fail_prob values and often timed out at 300 steps with strongly negative rewards, whereas the hybrid achieved nontrivial success rates, better average steps, and higher rewards (Baheri et al., 10 Mar 2025).

The multi-robot SGDT was evaluated on RoCoBench in Sandwich Making and Grocery Packing. Sandwich Making used a humanoid robot and a UR5e robot, with recipes involving 5, 6, or 8 food items to be picked and stacked in the correct order. Grocery Packing used a Panda robot and a UR5e robot, with six grocery items and a box, and required alternating turns based on distances and symbolic predicates such as closest-to, belongs-to, and in-box ?item (Rasanji et al., 19 Aug 2025).

The neuro-symbolic planner was evaluated by accuracy and average replans. Reported results were 100% accuracy and 0 replans for sandwich making at 5, 6, and 8 items, and 90% accuracy with 0.67 replans for grocery packing (Rasanji et al., 19 Aug 2025). For low-level GCDT evaluation on sandwich tasks, task success rate was defined as the number of subgoals achieved within distance threshold $p_\theta(a_t \mid s_{\le t}, a_{\le t-1}, g_i),$5 divided by the total subgoals in the PDDL plan. The “Without Subgoals” baseline achieved 43.08%, 28.33%, and 29.55% success on 5-item, 6-item, and 8-item tasks, respectively, whereas “With Subgoals” achieved 95.33%, 92.77%, and 80.70%. Average trajectory lengths with subgoals were 54, 66, and 89 steps for the 5-item, 6-item, and 8-item tasks (Rasanji et al., 19 Aug 2025).

Generalization results are central to the SGDT claim. Zero-shot transfer from 5- and 6-item sandwich tasks to unseen 8-item sandwich making yielded 72.35% success. In few-shot adaptation, pretraining on sandwich making and fine-tuning on grocery packing increased success from approximately 52.5% with 1 sample to 92.77% with 100 samples; pretraining on grocery packing and fine-tuning on 5-item sandwich making increased success from approximately 53.33% with 1 sample to 80% with 100 samples. Robustness to changed object sets was also reported: for one changed item, success was 88% on 5-item sandwich making and 88.33% on 6-item sandwich making; for two changed items, 74% and 65%; for three changed items, 52% and 61.67% (Rasanji et al., 19 Aug 2025).

Collectively, these results indicate that symbolic guidance is especially consequential in tasks with long-horizon logical structure. In simpler settings it primarily improves efficiency; in combinatorially structured settings it can separate near-zero success from nontrivial success (Baheri et al., 10 Mar 2025, Rasanji et al., 19 Aug 2025).

6. Relationship to Decision Transformer research, limitations, and future directions

SGDT can be situated within a broader hierarchical reinterpretation of Decision Transformers. A general sequence-modeling framework for RL writes policy factorization as

$p_\theta(a_t \mid s_{\le t}, a_{\le t-1}, g_i),$6

where $p_\theta(a_t \mid s_{\le t}, a_{\le t-1}, g_i),$7 is a prompt generated by a high-level policy and consumed by a low-level policy. In that framework, DT appears as the special case in which the prompt space is scalar return-to-go. Goal-prompted and value-prompted variants show that transformer-based control can be improved when prompts are learned and optimized hierarchically rather than manually chosen (Ma et al., 2023). This places SGDT naturally in the same family, with symbolic prompts replacing or augmenting scalar RTG.

Several limitations recur across SGDT formulations. The symbolic layer requires an accurate domain model: well-defined predicates, operators, preconditions, effects, and abstraction mappings in the classical-planner case, or accurate PDDL modeling in the multi-robot case (Baheri et al., 10 Mar 2025, Rasanji et al., 19 Aug 2025). PDDL-plus-LLM planning may become complex for very large domains with many objects or robots, and the multi-robot formulation assumes shared observation space and centralized control rather than truly decentralized multi-agent execution (Rasanji et al., 19 Aug 2025). The hierarchical grid-world formulation notes that long symbolic plans magnify execution error, and that scaling from low-dimensional discrete worlds to large continuous domains would require more sophisticated $p_\theta(a_t \mid s_{\le t}, a_{\le t-1}, g_i),$8, learned abstractions $p_\theta(a_t \mid s_{\le t}, a_{\le t-1}, g_i),$9, and more powerful planners (Baheri et al., 10 Mar 2025). The multi-robot results are simulation-only, and real robot experiments remain an explicit future direction (Rasanji et al., 19 Aug 2025).

Future work in the cited literature converges on richer abstractions and tighter integration. Proposed directions include deeper hierarchies with more than two levels, richer symbolic languages extending to full PDDL domains and temporal logic constraints, learning $g_i$0 and even $g_i$1 from data, dynamic replanning triggered by execution feedback or confidence estimates, improved LLM prompting, tighter coupling between symbolic planner and transformer, decentralized variants for multi-agent systems, and deployment to industrial domains such as manufacturing, construction, logistics, and healthcare (Baheri et al., 10 Mar 2025, Rasanji et al., 19 Aug 2025). A plausible implication is that SGDT is best understood not as a single architecture but as a design pattern: symbolic structure is used to specify, segment, or constrain long-horizon behavior, while transformer-based sequence models implement the corresponding low-level policy with offline-trained temporal competence.