Adithya Devraj (Stanford)
Sample complexity bounds are a common performance metric in the RL literature. In the discounted cost, infinite horizon setting, all of the known bounds can be arbitrarily large, as the discount factor approaches unity. For a large discount factor, these bounds seem to imply that a very large number of samples is required to achieve an epsilon-optimal policy. In this talk, we will discuss a new class of algorithms that have sample complexity uniformly bounded for all discount factors.
One may argue that this is impossible, due to a recent min-max lower bound. The explanation is that this previous lower bound is for a specific problem, which we modify, without compromising the ultimate objective of obtaining an epsilon-optimal policy.
Specifically, we show that the asymptotic covariance of the Q-learning algorithm with an optimized step-size sequence is a quadratic function of a factor that goes to infinity, as discount factor gets close to 1; an expected, and essentially known result. The new relative Q-learning algorithm proposed here is shown to have asymptotic covariance that is uniformly bounded for all discount factors.