POMDP Vector Pruning.pdf

Improved vector pruning enhances exact algorithms for solving partially observable Markov decision processes (POMDPs) by reducing the size of linear programs in the pruning subroutine. The approach limits both the number of constraints and variables, improving performance and scalability, especially for problems with larger state spaces.

Key aspects include:
- POMDPs model single-agent planning problems in stochastic domains with imperfect state information.
- Exact algorithms for POMDPs rely on dynamic programming and a pruning subroutine to remove dominated vectors from piecewise-linear and convex value functions.
- The pruning subroutine solves linear programs, with the traditional approach having a large number of variables and constraints, limiting scalability.
- Recent work improved performance by incrementally generating relevant constraints, but did not reduce the number of variables.
- The new approach enhances this by also incrementally generating variables, further reducing the size of linear programs and improving performance.

The algorithm PR(W) prunes a vector set W by iteratively removing dominated vectors, using a linear program LP(w, D, ε) to test for domination. The approach ensures that the resulting pruned vector set D represents the same value function as the original set W, but with a minimal number of vectors.

The improvements enable exact algorithms to solve larger POMDPs, providing optimal solutions and a benchmark for approximation algorithms. The work contributes to the development of more scalable and efficient algorithms for solving POMDPs, which is crucial for applications in stochastic domains with imperfect state information.