Finding Approximate POMDP solutions Through Belief Compression (1107.0053v2)

Abstract: Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are generally considered to be intractable for large models. The intractability of these algorithms is to a large extent a consequence of computing an exact, optimal policy over the entire belief space. However, in real-world POMDP problems, computing the optimal policy for the full belief space is often unnecessary for good control even for problems with complicated policy classes. The beliefs experienced by the controller often lie near a structured, low-dimensional subspace embedded in the high-dimensional belief space. Finding a good approximation to the optimal value function for only this subspace can be much easier than computing the full value function. We introduce a new method for solving large-scale POMDPs by reducing the dimensionality of the belief space. We use Exponential family Principal Components Analysis (Collins, Dasgupta and Schapire, 2002) to represent sparse, high-dimensional belief spaces using small sets of learned features of the belief state. We then plan only in terms of the low-dimensional belief features. By planning in this low-dimensional space, we can find policies for POMDP models that are orders of magnitude larger than models that can be handled by conventional techniques. We demonstrate the use of this algorithm on a synthetic problem and on mobile robot navigation tasks.

• The paper introduces E-PCA to compress belief spaces, enabling efficient planning in large POMDPs.
• It reduces the dimensionality of complex belief distributions to a manageable subspace, lowering computational costs.
• Experimental results on synthetic and robotic tasks demonstrate scalable and robust performance compared to traditional methods.

Overview of the Paper "Finding Approximate POMDP Solutions Through Belief Compression"

The paper "Finding Approximate POMDP Solutions Through Belief Compression," authored by Nicholas Roy, Geoffrey Gordon, and Sebastian Thrun, presents a novel approach to solving large Partially Observable Markov Decision Processes (POMDPs) by leveraging a dimensionality reduction technique specifically developed for belief space compression. Traditional methods for POMDP solutions are computationally intractable for large models due to the high-dimensional belief spaces that need to be navigated. This paper proposes an innovative method to address this challenge by reducing the dimensionality of the belief space using Exponential-family Principal Component Analysis (E-PCA).

The prevailing value function methods for POMDPs are constrained by the necessity to calculate an exact, optimal policy across an expansive belief space, which is prohibitive for real-world problems. The authors argue that in practice, the beliefs an agent encounters typically reside in a structured, low-dimensional subspace embedded within the larger belief space. They propose to focus computational resources on this subspace, thereby simplifying the solution process without significantly compromising control quality.

Methodology and Contributions

The core contribution of the paper is the introduction of E-PCA into the POMDP framework. E-PCA is employed to distill the high-dimensional belief space into a compact form using a small set of learned belief features, allowing for efficient planning in the reduced space. This process is computationally manageable for much larger models than those feasible with traditional POMDP algorithms. The method comprises several key steps:

• Dimension Reduction: Applying E-PCA, the belief space is represented in terms of sparse, high-dimensional data, which is then compressed into a low-dimensional surface by minimizing a specific loss function. This loss function more accurately represents the properties of belief distributions compared to traditional PCA.
• Belief Feature Planning: The planning is conducted within the low-dimensional space, facilitating the derivation of policies for significantly larger POMDP models. This approach alleviates the curse of dimensionality that plagues conventional POMDP solutions.
• Experimental Validation: The authors demonstrate their algorithm on synthetic datasets and mobile robot navigation tasks, showcasing the ability to handle problems with intricate state spaces and numerous possible observations and actions.

Experimental Results and Implications

The authors provide robust experimental results which validate the efficacy of their approach. They apply their methodology to scenarios including a simplified synthetic problem and real-world navigation problems, effectively handling thousands of states. The results indicate that E-PCA can reduce the computational burden significantly while maintaining solution quality. Importantly, solutions are found to perform well when compared to existing heuristic methods and previous POMDP algorithms, offering a more scalable solution without sacrificing robustness in handling uncertainties inherent in real-world environments.

Implications and Future Directions

This research has substantial implications for fields requiring decision-making under uncertainty, such as robotics and autonomous systems. By removing the computational bottleneck associated with solving large POMDPs, this approach opens the door for more complex and sophisticated applications which require real-time control and decision-making capabilities.

Moving forward, the framework suggested by this paper could be expanded by investigating alternative dimensionality reduction techniques, potentially incorporating non-linear mappings more strongly into the compression phase, enhancing representation quality even further. Additionally, the refinement of policies that optimize for control accuracy rather than solely reconstruction accuracy represents a promising direction. This could involve incorporating more sophisticated function approximators or exploring hybrid approaches combining policy learning and belief compression.

In conclusion, this work by Roy, Gordon, and Thrun advances the capability to address large-scale POMDP problems efficiently, redefining the feasible bounds of automated planning and control in complex, partially observable environments.