DR. WELL: Decentralized Neurosymbolic Planning

• DR. WELL is a decentralized neurosymbolic framework that uses symbolic negotiation and planning to coordinate multi-agent tasks in embodied environments.
• It leverages structured communication, role allocation, and self-refinement to improve task efficiency and mitigate synchronization issues.
• Its dynamic symbolic world model aggregates cross-episode statistics to optimize team sizing, guide decision-making, and enhance decentralized execution.

DR. WELL most explicitly denotes Dynamic Reasoning and Learning with Symbolic World Model for Embodied LLM-Based Multi-Agent Collaboration, a decentralized neurosymbolic framework for embodied cooperative multi-agent planning in which agents negotiate task roles through structured communication, independently synthesize and execute symbolic plans, and improve over time using a shared dynamic symbolic world model that stores cross-episode task, plan, and outcome statistics (Nourzad et al., 6 Nov 2025). It is designed for settings with partial coordination, limited communication, asynchronous execution, task interdependence, and decentralized control, and it replaces brittle trajectory-level synchronization with coordination through symbolic abstractions such as task identifiers, roles, and parameterized symbolic actions (Nourzad et al., 6 Nov 2025).

1. Conceptual basis and task model

DR. WELL is formulated for cooperative embodied tasks in which multiple agents must divide labor across interdependent subtasks. At time $t$, the framework defines the set of agents ready to replan as

$$\mathcal{A}_t^{r} = \{\, a_i \in \mathcal{A} \mid a_i \text{ is ready to replan at time } t \,\}, \qquad \mathcal{A}_t^{r} \subseteq \mathcal{A}.$$

If $|\mathcal{A}_t^{r}| > 0$, those agents enter a shared communication room for negotiation (Nourzad et al., 6 Nov 2025).

The main evaluation environment is CUBE (Cooperative Push Block), a grid-world block-pushing task. Blocks have size or weight $w$, and pushing a block of weight $w$ requires $w$ agents to push simultaneously on the same face. Cooperation is therefore explicit in the task mechanics rather than treated as an emergent side effect (Nourzad et al., 6 Nov 2025).

The framework is motivated by the claim that direct trajectory-level coordination is fragile in embodied multi-agent settings. The cited reasons are that small timing errors can cascade into conflicts, raw LLM outputs are prompt-sensitive, decentralized agents cannot reliably align detailed action sequences without central control, and the number of agents and environmental conditions may vary (Nourzad et al., 6 Nov 2025). DR. WELL addresses this by coordinating over symbolic plans rather than raw trajectories. This shifts the unit of synchronization from low-level motion to higher-level commitments that are reusable, synchronizable, and interpretable (Nourzad et al., 6 Nov 2025).

2. Negotiation protocol and role allocation

DR. WELL organizes coordination as a two-phase negotiation protocol: negotiation / task allocation followed by symbolic planning and execution. Negotiation occurs whenever one or more agents become idle and need a new commitment (Nourzad et al., 6 Nov 2025).

The participating agents are ordered in round-robin form,

$\sigma_t = (a_1,\ldots,a_m),$

and communicate through a shared buffer initialized with the current symbolic environment observation and a retrieved task-summary set from the world model (Nourzad et al., 6 Nov 2025). For each task $x$, the world model stores summary statistics

$$r(x) = [\,\hat{\mu}_{x}^{\text{start}}, \hat{p}_{x}^{\text{succ}}, \hat{\mu}_{x}^{\text{duration}}, N_{x}^{\text{attempt}}\,],$$

representing estimated mean start time, empirical success rate, mean duration, and number of attempts (Nourzad et al., 6 Nov 2025).

In the proposal stage, each agent proposes a candidate task and explains why: $$p_{a_j} = f_{\text{propose},a_j}\!\left(\phi_{a_j,t}, B_t^{(j-1)}\right), \qquad B_t^{(j)} = B_t^{(j-1)} \cup \{(a_j, p_{a_j})\}.$$ A proposal includes a task identifier and a natural-language rationale. The rationale may mention spatial proximity, resource requirements, feasible tasks, and expected coordination needs (Nourzad et al., 6 Nov 2025).

After proposals, the system computes candidate tasks and retrieves the historically most effective team size for each: $$\mathcal{A}_t^{r} = \{\, a_i \in \mathcal{A} \mid a_i \text{ is ready to replan at time } t \,\}, \qquad \mathcal{A}_t^{r} \subseteq \mathcal{A}.$$0 Here, $$\mathcal{A}_t^{r} = \{\, a_i \in \mathcal{A} \mid a_i \text{ is ready to replan at time } t \,\}, \qquad \mathcal{A}_t^{r} \subseteq \mathcal{A}.$$1 is the empirical probability that task $$\mathcal{A}_t^{r} = \{\, a_i \in \mathcal{A} \mid a_i \text{ is ready to replan at time } t \,\}, \qquad \mathcal{A}_t^{r} \subseteq \mathcal{A}.$$2 succeeds with team size $$\mathcal{A}_t^{r} = \{\, a_i \in \mathcal{A} \mid a_i \text{ is ready to replan at time } t \,\}, \qquad \mathcal{A}_t^{r} \subseteq \mathcal{A}.$$3, and $$\mathcal{A}_t^{r} = \{\, a_i \in \mathcal{A} \mid a_i \text{ is ready to replan at time } t \,\}, \qquad \mathcal{A}_t^{r} \subseteq \mathcal{A}.$$4 is the estimated optimal number of agents for that task (Nourzad et al., 6 Nov 2025).

In the commitment stage, each agent selects a task to commit to: $$\mathcal{A}_t^{r} = \{\, a_i \in \mathcal{A} \mid a_i \text{ is ready to replan at time } t \,\}, \qquad \mathcal{A}_t^{r} \subseteq \mathcal{A}.$$5 The resulting allocation is

$$\mathcal{A}_t^{r} = \{\, a_i \in \mathcal{A} \mid a_i \text{ is ready to replan at time } t \,\}, \qquad \mathcal{A}_t^{r} \subseteq \mathcal{A}.$$6

Allocations are finalized only if they satisfy consensus and quorum constraints. A task requiring $$\mathcal{A}_t^{r} = \{\, a_i \in \mathcal{A} \mid a_i \text{ is ready to replan at time } t \,\}, \qquad \mathcal{A}_t^{r} \subseteq \mathcal{A}.$$7 agents proceeds only if at least $$\mathcal{A}_t^{r} = \{\, a_i \in \mathcal{A} \mid a_i \text{ is ready to replan at time } t \,\}, \qquad \mathcal{A}_t^{r} \subseteq \mathcal{A}.$$8 agents commit (Nourzad et al., 6 Nov 2025).

A defining design decision is communicative restraint. During negotiation, agents reveal only candidate tasks, reasoning, and final commitments; they do not reveal detailed symbolic plans (Nourzad et al., 6 Nov 2025). This makes coordination depend on compatible commitments rather than on fragile full-plan sharing.

3. Symbolic planning and decentralized execution

After commitment, each agent plans and acts independently. The paper states that there is no further inter-agent communication during planning and execution. Each agent encodes its commitment into the LLM prompt, drafts a plan from scratch, refines that draft using the world model, executes symbolic actions through a controller, and replans when needed (Nourzad et al., 6 Nov 2025).

For agent $$\mathcal{A}_t^{r} = \{\, a_i \in \mathcal{A} \mid a_i \text{ is ready to replan at time } t \,\}, \qquad \mathcal{A}_t^{r} \subseteq \mathcal{A}.$$9, the initial plan draft is

$|\mathcal{A}_t^{r}| > 0$0

This draft is a plan prototype: an argument-free symbolic action sequence that gives a high-level structural outline (Nourzad et al., 6 Nov 2025). The world model then retrieves the top $|\mathcal{A}_t^{r}| > 0$1 historical plan prototypes for the committed task, ranked by success rate, and for each prototype the top $|\mathcal{A}_t^{r}| > 0$2 plan instances, ranked by success rate and then by shorter duration. The refined plan is

$|\mathcal{A}_t^{r}| > 0$3

This self-refinement mechanism reuses successful prototypes, avoids historically poor patterns, and specializes the current plan to the present context (Nourzad et al., 6 Nov 2025).

The symbolic action vocabulary is fixed, compact, and parameterized.

Symbolic action	Parameters	Function
WaitAgents	count = k, timeout = t	Wait until $|\mathcal{A}_t^{r}| > 0$4 agents are idle, or until timeout
Rendezvous	block_id, side, count = k, timeout = t	Wait until $|\mathcal{A}_t^{r}| > 0$5 agents arrive at a specified side of a block, or timeout
MoveToBlock	block_id, side	Move and align to a specific side of the block
Push	block_id, steps = n	Push the block for $|\mathcal{A}_t^{r}| > 0$6 steps if aligned
YieldFace	block_id, steps = n	Move away from the block to free a face for collaborators

Although the vocabulary is small, parameterization by block identifiers, sides, timeouts, and step counts yields a large effective planning space while preserving interpretability and synchronization (Nourzad et al., 6 Nov 2025).

Execution follows a plan $|\mathcal{A}_t^{r}| > 0$7 execute $|\mathcal{A}_t^{r}| > 0$8 re-plan cycle. The controller checks symbolic preconditions locally, translates symbolic actions into primitive moves, and advances execution like a state machine. Preconditions are checked locally by the controller, while postconditions and effects are confirmed by the environment (Nourzad et al., 6 Nov 2025). If a cooperative action requires more aligned agents than are present, the controller places the agent in a waiting state and uses a timeout counter. If quorum is not reached before timeout, the action fails and the plan index advances. If the plan ends, the agent becomes idle and replanning starts (Nourzad et al., 6 Nov 2025). This mechanism is explicitly intended to avoid deadlock while maintaining decentralized execution.

4. Dynamic symbolic world model

The shared world model is the framework’s central memory structure. It is defined as a dynamic symbolic graph

$|\mathcal{A}_t^{r}| > 0$9

with node sets and edges organized as

$w$0

The node types are episodes, tasks or blocks, plan prototypes, and plan instances; the edges connect episode to task, task to prototype, and prototype to instance (Nourzad et al., 6 Nov 2025).

Each instance node $w$1 is grounded to an observed outcome

$w$2

where $w$3 denotes success and $w$4 failure. Upper-level nodes aggregate statistics from their descendants (Nourzad et al., 6 Nov 2025). The world model is updated episodically. At update step $w$5, each episode contributes an additive subgraph

$w$6

and the graph evolves as

$w$7

The graph therefore grows monotonically with experience (Nourzad et al., 6 Nov 2025).

The world model serves two explicit roles. As a negotiation guidebook, it supplies current timestep, number of active agents, historical completion rates, average durations, and estimated optimal team sizes. As a plan library, it supplies historical plan prototypes, detailed plan instances, success rates, average durations, number of attempts, and team-size information (Nourzad et al., 6 Nov 2025). The framework also stores a full world trace including proposed tasks, commitments, symbolic actions executed, communication events, and completion outcomes (Nourzad et al., 6 Nov 2025). This trace links symbolic intentions to concrete outcomes and supports later reasoning about what was attempted, what succeeded, what failed, how long it took, and how agents synchronized.

A plausible implication is that DR. WELL treats cross-episode learning not as end-to-end parameter adaptation alone, but as explicit accumulation of structured execution evidence. In the paper’s presentation, the world model is not an auxiliary explanation layer; it is the operational substrate that informs both allocation and refinement (Nourzad et al., 6 Nov 2025).

5. Empirical behavior in cooperative block-push tasks

The experimental environment is a grid world in which agents must push blocks into a goal zone with minimal steps. Observations are provided in two modalities: a multi-channel tensor and a symbolic state description. Symbolic observations include agent identifier and position, block size, block position, and distance to goal (Nourzad et al., 6 Nov 2025).

The main baseline is a zero-shot symbolic planner with a fixed prompt. It has no negotiation, no task commitments, no communication, no plan revision, and no shared memory. It repeatedly chooses the block closest to the goal and generates short plans independently (Nourzad et al., 6 Nov 2025). The paper identifies a specific failure mode: multiple agents may redundantly work on the same easy block, while heavier blocks requiring cooperation remain unfinished (Nourzad et al., 6 Nov 2025).

Evaluation uses three metrics: block completion outcome, completion time in wall-clock seconds, and completion time in environment steps (Nourzad et al., 6 Nov 2025). The reported findings are primarily qualitative and graphical rather than tabled as a single numeric benchmark. For the baseline, completion is inconsistent, many blocks remain unfinished—especially larger ones—time per episode stays nearly constant, and behavior shows no adaptation across episodes (Nourzad et al., 6 Nov 2025).

For DR. WELL, the reported trends are different. Almost all blocks are completed consistently after the early episodes; completion times decrease over episodes; environment steps also decline; task allocations become more stable after about Episode 5; overlap between agents decreases; and division of labor improves (Nourzad et al., 6 Nov 2025). The framework incurs a trade-off: wall-clock time increases slightly because negotiation and replanning introduce overhead. The paper states that this overhead is offset by fewer wasted actions, better coordination, fewer failed attempts, faster completion in environment steps, and higher success rate (Nourzad et al., 6 Nov 2025).

The ablation-style analysis attributes the improvement to three components. Negotiation avoids all agents choosing the same task, matches task demands to team size, and enables consensus- and quorum-aware allocation. Self-refinement leverages historically successful prototypes, selects effective plan instances, and adapts them to the current context. The dynamic world model stores reusable symbolic patterns, accumulates success statistics, supports cross-episode reasoning, and captures evolving collaboration strategies (Nourzad et al., 6 Nov 2025). The paper therefore argues that DR. WELL improves cooperative efficiency by combining structured communication at synchronization points, symbolic commitments instead of trajectory sharing, independent decentralized planning after role assignment, and execution-grounded shared memory (Nourzad et al., 6 Nov 2025).

6. Scope, limitations, and adjacent uses of the name

The framework is presented in a relatively structured setting. The paper identifies future extensions including reasoning about latent subgoals, partial local observations instead of full observability, interruption and re-negotiation when plans fail, richer in-group communication during sub-tasks, more realistic dynamic task allocation, the ability to redirect or interrupt teammates, and probabilistic symbolic outcomes for uncertainty (Nourzad et al., 6 Nov 2025). A common misconception would be to treat DR. WELL as a general solution to all multi-agent embodiment settings; the stated future directions indicate that the current formulation assumes an environment well suited to explicit symbolic abstractions (Nourzad et al., 6 Nov 2025).

The name also has adjacent meanings in health-oriented AI discourse. One paper states that, in its context, “DR. WELL” refers to the same idea as a Dr. Watson-type AI: not an autonomous oracle, but a supportive, question-asking, contradiction-finding assistant that helps the human expert think better and decide better (Goldberg et al., 2021). In that formulation, a Dr. Watson-type system does not offer a specific solution, but instead analyzes the user’s solution to reveal logical inconsistencies or insufficient data, using game situations, psychological techniques, and visual presentation of information to stimulate the user’s thinking (Goldberg et al., 2021). Another paper on Reddit-based mental health analysis states that its wellness concept extraction framework would be especially valuable for a wellness-oriented assistant like “Dr. Well”, because it moves from generic risk detection toward interpretable, dimension-specific support (Garg, 2023).

These usages do not describe the same technical system. The embodied multi-agent DR. WELL framework concerns decentralized neurosymbolic planning with symbolic commitments and a dynamic world model (Nourzad et al., 6 Nov 2025), whereas the adjacent “Dr. Well” usages concern wellness-oriented or Dr. Watson-type human-support systems (Goldberg et al., 2021, Garg, 2023). The shared motif is not architecture but assistance through structured, interpretable reasoning.