CBBA-PR: Decentralized Partial Replanning

• The paper's main contribution is the introduction of CBBA-PR, which extends the original CBBA by using controlled partial resets to balance rapid response with coordination quality.
• CBBA-PR employs a controlled partial bundle reset where low-bid tasks are released for rebidding, minimizing communication overhead while preserving existing consensus.
• The algorithm leverages fixed-parameter tractability and integrates classical and data-driven planning techniques to maintain efficient real-time multi-agent task allocation under dynamic conditions.

The Partial Replanning Extension (CBBA-PR) is a decentralized mechanism for dynamic task allocation in multi-agent systems, particularly designed to accommodate online arrival of tasks and changing mission objectives. CBBA-PR extends the Consensus-Based Bundle Algorithm (CBBA) by enabling agents to revise only a portion of their current task assignments (“bundle reset”), thus trading off between rapid response to new information and coordination quality without the prohibitive communication and computational overhead of full replanning. This approach leverages parameterized complexity results for tractable plan reuse and incorporates techniques from classical and data-driven planning to efficiently update existing allocations under real-world constraints.

1. Foundations in Decentralized Task Allocation

CBBA-PR builds upon the theoretical framework of the Consensus-Based Bundle Algorithm (CBBA), a decentralized task allocation strategy that assigns tasks to agents via distributed bidding and consensus phases. In CBBA, agents construct task bundles by greedily selecting tasks based on marginal gain, communicate bid and winner information, and resolve assignment conflicts to ensure a globally conflict-free solution, typically converging to a near-optimal allocation under diminishing marginal gain reward functions.

The innovation in CBBA-PR addresses limitations of the original algorithm in dynamic environments, where new tasks can appear during execution and full bundle resets impose excessive communication and convergence delays. By resetting only a subset of tasks—typically those with the lowest bid values—CBBA-PR maintains most of the prior allocation, allowing quick integration of new tasks and localized reallocation, thereby preserving bounded response times and improved solution quality (Buckman et al., 2018).

2. Controlled Partial Replanning Mechanism

The operational core of CBBA-PR is the controlled “partial bundle reset” prior to initiating a new bidding cycle for emerging tasks. Each agent identifies the lowest $n_{i,\mathrm{reset}}$ tasks in its bundle—those most recently assigned or with minimal marginal gain—and releases them for rebidding. Tasks with higher bid values remain fixed, preserving earlier consensus and minimizing disruption. The algorithm allows for flexibility: fewer reset tasks yield faster convergence and lower communication, while larger resets increase coordination and solution optimality but at the expense of more negotiation rounds.

The method generalizes to subteam coordination, where only a subset of agents or tasks participates in the reset, further reducing the network footprint. The partial reset is mathematically formalized by resetting the bid and winner values for selected tasks: $$y_{i, b_{i}(m)} = -\infty, \quad z_{i, b_{i}(m)} = -1 \quad \forall m \geq \bar{n}$$ where $\bar{n}$ is the index of first conflicting or released task (Buckman et al., 2018).

3. Fixed-Parameter Tractability in Plan Adaptation

CBBA-PR exploits parameterized complexity results to ensure tractable plan reuse and modification. In plan adaptation, the insertion of additional (“glue”) actions to a stored plan is computationally demanding in the general case; however, fixed-parameter tractability (FPT) can be achieved by restricting the number and character of modifications:

• Limiting glue steps ($L$): Bounding the number of extra planning steps alone does not guarantee tractability ({L}-CASEMOD is W[2]-complete).
• Restricting modifying actions ($A'$): Tractability is realized when the glue steps are drawn from a small, contextually pruned action set. When $|A'| = k$, the plan reuse problem has complexity $T(n, k) = O(f(k) \cdot n^c)$ for computable $f$ and constant $c$—i.e., FPT (Haan et al., 2013).
• Structural restrictions ($V, D$): If actions reference at most $k$ variables and $m$ values, the total number of possible actions remains bounded by $(m + 1)^{2k}$, further controlling the replanning search space.

Efficient implementation of CBBA-PR leverages these results by (i) strictly limiting the glue step count, (ii) pruning the modifying action space via domain heuristics, and (iii) parameterizing replanning by the structural properties of the tasks/variables involved, thus ensuring scalability for large agent populations and complex assignments (Haan et al., 2013).

4. Consensus Enforcement and Team Coordination

The consensus phase in CBBA-PR utilizes the well-ordered structure of bid arrays to resolve conflicts after partial resets. If two agents disagree over a task’s assignment, all tasks inserted after that point in the bundle are reset and rebid, maintaining that only descending bid values persist. This mechanism guarantees that the team converges to a globally conflict-free solution—meaning no task is doubly allocated—even when partial resets cause temporary coordination ambiguities.

CBBA-PR’s effectiveness is appreciably enhanced by subteam-focused replanning, where only a fraction of agents participates in reallocating the lowest scoring tasks. The number of communication rounds required to reach consensus is upper bounded by $O(n_{\mathrm{reset}} \cdot D)$, with $D$ as the network diameter (Buckman et al., 2018). This selective protocol ensures rapid response in time-critical scenarios and explicit scalability for large teams.

5. Integration with Classical and Data-Driven Replanning

CBBA-PR is conceptually compatible with advanced replanning strategies, including those based on classical planning reductions and data-driven models:

• Classical planning with partial observability: Sampling and determinization techniques, as in SDR (“Sample, Determinize, Replan”) (Brafman et al., 2014), can be adapted. Agents represent uncertain states via sampled hypotheses, plan accordingly, and trigger replanning when executed actions invalidate the assumptions. Lazy regression-based belief state queries facilitate on-demand safety checks, enabling decentralized planning with partial resets in uncertain or sensing-rich environments.
• Data-driven replanning with diffusion models: Adaptive online partial replanning is achievable using diffusion-based trajectory models (Zhou et al., 2023). The likelihood of the existing plan is continuously monitored via internal KL divergence statistics. If deviations are detected, only the problematic trajectory segment is regenerated, preserving forward progress and minimizing computational cost. Empirical results in Maze2D and RLBench domains demonstrate 38%–63% improvement over standard planners, suggesting CBBA-PR could integrate such signal-driven partial replanning for robust real-time multi-agent operation.

6. Empirical Validation and Theoretical Guarantees

Multi-UAV simulation experiments with CBBA-PR confirm the tradeoff between convergence speed and solution quality. No-reset strategies offer the fastest adaptation to new tasks but yield lower allocation utility. Full resets maximize solution quality but suffer from protracted convergence. Partial replanning approaches, both local and team-based, achieve rapid integration of new tasks and solution scores nearly matching the global optimum, with substantially reduced communication and runtime (Buckman et al., 2018).

Mathematical formulations underpin these outcomes:

• Task allocation optimization:

$$\max \sum_{i=1}^{n_r} \left[ \sum_{j=1}^{n_t} c_{ij}(x_i,p_i)x_{ij} \right]$$

Subject to bundle size and allocation uniqueness constraints.

• Team score in time-discounted missions:

$$S(p_i) = \sum_{j \in p_i} \lambda_{ij}^{\tau_j^{p_i}} R_{ij}$$

The team-wide replan sets $$n_{\mathrm{reset}} = \frac{t_{\mathrm{response}}}{d\cdot\Delta_{\mathrm{comm}}}$$, where $d$ is the effective diameter and $\Delta_{\mathrm{comm}}$ is the communication delay.

Consensus and performance bounds, as inherited from CBBA, remain applicable in CBBA-PR due to the algorithm’s maintenance of the diminishing marginal gain structure and conflict resolution rules.

7. Design Implications and Practical Considerations

The design and deployment of CBBA-PR in real-world applications require careful heuristics for action set pruning (to maintain problem tractability), configuration of reset sizes (balancing coordination against responsiveness), and adoption of sampling or likelihood-monitoring methods for robust behavior in stochastic environments. Empirical and theoretical findings support usage in large-scale multi-agent scenarios—including surveillance, disaster response, and warehouse logistics—where tasks and environmental states evolve online and rapid restoration of conflict-free coordination is essential.

A plausible implication is that future research directions may focus on integrating event-driven communication mechanisms (e.g., ED-CBBA (Sao et al., 8 Sep 2025)) with partial replanning logic in CBBA-PR to further minimize network load and resource consumption during frequent plan adaptations. Additionally, rigorous complexity analysis and formal guarantees for hybrid classical/data-driven replanning modules in CBBA-PR remain open areas for investigation.

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CBBA-PR exemplifies principled, tractable partial replanning in decentralized multi-agent task allocation, empirically tested and theoretically supported, with direct connections to parameterized planning complexity, sampling-based belief revision, and adaptive trajectory optimization. The method delivers a tunable balance between communication efficiency, solution quality, and rapid response, suitable for deployment in dynamic, time-sensitive autonomous systems.