LIDS REPORT 2871 1 Q - Learning and Policy Iteration Algorithms for Stochastic Shortest Path Problems ∗

We consider the stochastic shortest path problem, a classical finite-state Markovian decision problem with a termination state, and we propose new convergent Q-learning algorithms that combine elements of policy iteration and classical Q-learning/value iteration. These algorithms are related to the ones introduced by the authors for discounted problems in [BY10b]. The main difference from the standard policy iteration approach is in the policy evaluation phase: instead of solving a linear system of equations, our algorithm solves an optimal stopping problem inexactly with a finite number of value iterations. The main advantage over the standard Qlearning approach is lower overhead: most iterations do not require a minimization over all controls, in the spirit of modified policy iteration. We prove the convergence of asynchronous deterministic and stochastic lookup table implementations of our method for undiscounted, total cost stochastic shortest path problems. These implementations overcome some of the traditional convergence difficulties of asynchronous modified policy iteration, and provide policy iterationlike alternative Q-learning schemes with as reliable convergence as classical Q-learning. We also discuss methods that use basis function approximations of Q-factors and we give an associated error bound. Sep 2011; revised Mar 2012 ∗Work supported by the Air Force Grant FA9550-10-1-0412 and by NSF Grant ECCS-0801549. †Huizhen Yu is with the Lab. for Information and Decision Systems, M.I.T., Cambridge, Mass., 02139. janey [email protected] ‡Dimitri Bertsekas is with the Dept. of Electr. Engineering and Comp. Science, and the Lab. for Information and Decision Systems, M.I.T., Cambridge, Mass., 02139. [email protected]