Solving POMDPs by Searching in Policy Space (1301.7380v1)

Abstract: Most algorithms for solving POMDPs iteratively improve a value function that implicitly represents a policy and are said to search in value function space. This paper presents an approach to solving POMDPs that represents a policy explicitly as a finite-state controller and iteratively improves the controller by search in policy space. Two related algorithms illustrate this approach. The first is a policy iteration algorithm that can outperform value iteration in solving infinitehorizon POMDPs. It provides the foundation for a new heuristic search algorithm that promises further speedup by focusing computational effort on regions of the problem space that are reachable, or likely to be reached, from a start state.

• The paper introduces a novel method that directly searches policy space using finite-state controllers, reducing the complexity of traditional dynamic programming.
• The paper presents two key algorithms: a policy iteration method optimizing controllers via state transformations and a heuristic search focusing on crucial belief states.
• The paper demonstrates through numerical tests that its approach outperforms value iteration with faster convergence and reduced CPU time in complex POMDP scenarios.

Solving POMDPs by Searching in Policy Space: A Deep Dive into Hansen's Approach

This essay provides an expert analysis of Hansen's seminal work on solving Partially Observable Markov Decision Processes (POMDPs) through policy space exploration, focusing on finite-state controllers.

POMDPs pose a persistent challenge in fields requiring decision-making under uncertainty due to the unobservable nature of states. Traditional solutions iteratively improve value functions, inherently performing a search in value function space. However, Hansen proposes an innovative methodology leveraging explicit policy representation via finite-state controllers, which searches the policy space directly.

Methodology and Algorithms

Hansen introduces two principal algorithms for infinite-horizon POMDPs: a policy iteration approach and a heuristic search algorithm. The policy iteration algorithm addresses the limitations of traditional value iteration by explicitly representing policies as finite-state controllers. This shift facilitates straightforward policy evaluation and improvement. The algorithm employs transformations—such as altering, adding, and pruning machine states—to optimize policy, ultimately leading to either an optimal or an ε-optimal finite-state controller as demonstrated by experiments.

The heuristic search algorithm differs significantly in its implementation. Rather than utilizing dynamic programming updates, which are computationally prohibitive for extensive problem spaces, it harnesses heuristic search strategies rooted in belief state exploration. By targeting only the belief states that pragmatically impact a starting belief state, the heuristic approach focuses computational resources more efficiently, thereby enhancing the tractability of solving larger POMDPs.

Numerical Evaluation and Comparative Analysis

The evaluation section is pivotal, underscoring how policy iteration systematically outperforms value iteration in speed of convergence, highlighted in a series of tests from the Cassandra et al. problem set. Notably, policy iteration emerged as the superior method with consistently lower CPU time across multiple convergence thresholds (ε = 10 to ε = 0.01). The heuristic algorithm showed promise in boundary scenarios where dynamic programming becomes untenable, efficiently enhancing the value of initial finite-state controllers with fewer machine states and improved computational focus.

Theoretical Implications and Future Prospects

Hansen's work has significant theoretical implications. By demonstrating that a finite-state policy space exploration avoids the exponential complexities of the dynamic-programming update, it paves the way for more sophisticated POMDP solutions in high-dimensional spaces. This methodology also bridges prior POMDP research on exact algorithms and forward-search approximation methods, offering an integrated framework for future exploration.

Practically, adopting finite-state controllers simplifies policy deployment by obviating the need for ongoing belief state maintenance at runtime. This has vast potential applications in real-world scenarios involving resource-constrained environments or online decision-making settings.

Conclusion

Hansen's approach to solving POMDPs by searching in policy space enhances both theoretical and practical understanding, making notable contributions to AI and decision-making literature. Future research could focus on refining heuristic bounds and integrating memory-bounded search techniques to further extend this method's applicability to progressively larger and more intricate POMDP scenarios.