Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
756363 | Systems & Control Letters | 2012 | 6 Pages |
We provide a bound on the first moment of the error in the QQ-function estimate resulting from fixed step-size algorithms applied to finite state-space, discounted reward Markov decision problems. Motivated by Tsitsiklis’ proof for the decreasing step-size case, we decompose the QQ-learning update equations into a dynamical system driven by a noise sequence and another dynamical system whose state variable is the QQ-learning error, i.e., the difference between the true QQ-function and the estimate. A natural persistence of excitation condition allows us to sample the system periodically and derive a simple scalar difference equation from which the convergence properties and bounds on the error of the QQ-learning algorithm can be derived.