[Paper Review] Improved Memory-Bounded Dynamic Programming for Decentralized POMDPs

Sven Seuken, Shlomo Zilberstein|arXiv (Cornell University)|Jun 20, 2012

Optimization and Search Problems14 references99 citations

TL;DR

This paper improves Memory-Bounded Dynamic Programming (MBDP) for decentralized POMDPs by reducing observation complexity from exponential to polynomial, enabling scalable solutions for large-horizon problems. The method introduces a novel approximation with provable error bounds and demonstrates strong performance on a new, larger benchmark, showing MBDP's effectiveness despite the inherent complexity of decentralized POMDPs.

ABSTRACT

Memory-Bounded Dynamic Programming (MBDP) has proved extremely effective in solving decentralized POMDPs with large horizons. We generalize the algorithm and improve its scalability by reducing the complexity with respect to the number of observations from exponential to polynomial. We derive error bounds on solution quality with respect to this new approximation and analyze the convergence behavior. To evaluate the effectiveness of the improvements, we introduce a new, larger benchmark problem. Experimental results show that despite the high complexity of decentralized POMDPs, scalable solution techniques such as MBDP perform surprisingly well.

Motivation & Objective

• To address the scalability limitations of MBDP in decentralized POMDPs due to exponential dependence on the number of observations.
• To develop a more efficient approximation method that reduces computational complexity while maintaining solution quality.
• To provide theoretical error bounds for the new approximation technique.
• To evaluate the method on a newly introduced, larger benchmark problem to demonstrate scalability.
• To analyze the convergence behavior of the improved algorithm.

Proposed method

• The paper generalizes MBDP by introducing a polynomial-time approximation over observations, replacing the original exponential dependency.
• It employs a bounded memory approach that prunes and aggregates belief states efficiently, reducing the state space growth.
• The method uses a novel observation abstraction technique that groups similar observations to limit the number of belief updates.
• Error bounds on solution quality are derived based on the approximation's fidelity to the original problem structure.
• Convergence is analyzed by examining the stability of value function approximations under the new observation handling strategy.
• The algorithm is evaluated using a new, larger benchmark problem designed to stress-test scalability.

Experimental results

Research questions

• RQ1 Can the computational complexity of MBDP with respect to the number of observations be reduced from exponential to polynomial without sacrificing solution quality?
• RQ2 What are the theoretical error bounds of the proposed approximation in terms of solution quality?
• RQ3 How does the improved MBDP perform on a larger, more complex decentralized POMDP benchmark?
• RQ4 Does the new method maintain convergence properties under the approximation?
• RQ5 To what extent does the new approach scale to larger-horizon decentralized POMDPs?

Key findings

• The proposed method reduces the complexity with respect to the number of observations from exponential to polynomial, significantly improving scalability.
• Theoretical error bounds are established, showing that the approximation maintains a controlled deviation from the optimal solution.
• Experimental results demonstrate that the improved MBDP achieves high-quality solutions on a new, larger benchmark problem.
• Despite the high complexity of decentralized POMDPs, the improved MBDP performs surprisingly well in practice, even at large horizons.
• The algorithm shows stable convergence behavior under the new approximation, supporting its practical viability.
• The new benchmark reveals that scalable techniques like MBDP can handle problems previously considered intractable.