Bounded Approximate Symbolic Dynamic Programming for Hybrid MDPs
This addresses computational bottlenecks for researchers and practitioners working on hybrid MDPs, though it is incremental as it builds on existing SDP and XADD methods.
The paper tackles the problem of intractably large exact solutions for hybrid MDPs with piecewise linear dynamics and continuous actions by proposing a bounded error compression technique for XADDs, which empirically offers order-of-magnitude speedups over exact solutions in exchange for small approximation errors.
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.