  We discuss the relative merits of optimistic and randomized approaches to
exploration in reinforcement learning. Optimistic approaches presented in the
literature apply an optimistic boost to the value estimate at each state-action
pair and select actions that are greedy with respect to the resulting
optimistic value function. Randomized approaches sample from among
statistically plausible value functions and select actions that are greedy with
respect to the random sample. Prior computational experience suggests that
randomized approaches can lead to far more statistically efficient learning. We
present two simple analytic examples that elucidate why this is the case. In
principle, there should be optimistic approaches that fare well relative to
randomized approaches, but that would require intractable computation.
Optimistic approaches that have been proposed in the literature sacrifice
statistical efficiency for the sake of computational efficiency. Randomized
approaches, on the other hand, may enable simultaneous statistical and
computational efficiency.
