2013/09/26 by Luis Gustavo Vianna, Luis Gustavo Rocha Vianna, Vianna, Luis Gustavo +4
Computer Science · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Formal Methods in Verification #Machine Learning and Algorithms #Reinforcement Learning in Robotics #cs.AI
paper · pdf · doi:10.48550/arxiv.1309.6871
Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence (UAI2013)
arxiv created 2013/09/26 · openalex publication_date 2013/09/26 · arxiv updated 2013/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recent advances in symbolic dynamic programming (SDP) combined with the extended algebraic decision diagram (XADD) data structure have provided exact solutions for mixed discrete and continuous (hybrid) MDPs with piecewise linear dynamics and continuous actions. Since XADD-based exact solutions may grow intractably large for many problems, we propose a bounded error compression technique for XADDs that involves the solution of a constrained bilinear saddle point problem. Fortuitously, we show that given the special structure of this problem, it can be expressed as a bilevel linear programming problem and solved to optimality in finite time via constraint generation, despite having an infinite set of constraints. This solution permits the use of efficient linear program solvers for XADD compression and enables a novel class of bounded approximate SDP algorithms for hybrid MDPs that empirically offers order-of-magnitude speedups over the exact solution in exchange for a small approximation error.