1 research outputs found
Q-learning with Nearest Neighbors
We consider model-free reinforcement learning for infinite-horizon discounted
Markov Decision Processes (MDPs) with a continuous state space and unknown
transition kernel, when only a single sample path under an arbitrary policy of
the system is available. We consider the Nearest Neighbor Q-Learning (NNQL)
algorithm to learn the optimal Q function using nearest neighbor regression
method. As the main contribution, we provide tight finite sample analysis of
the convergence rate. In particular, for MDPs with a -dimensional state
space and the discounted factor , given an arbitrary sample
path with "covering time" , we establish that the algorithm is guaranteed
to output an -accurate estimate of the optimal Q-function using
samples. For instance, for a
well-behaved MDP, the covering time of the sample path under the purely random
policy scales as so the sample
complexity scales as Indeed, we
establish a lower bound that argues that the dependence of is necessary.Comment: Accepted to NIPS 201