Summary: Near-optimal Regret Bounds for Reinforcement Learning
Peter Auer Thomas Jaksch Ronald Ortner
University of Leoben, Franz-Josef-Strasse 18,
8700 Leoben, Austria
December 19, 2007
For undiscounted reinforcement learning we consider the total regret of a learning algorithm
in respect to an optimal policy. We present a reinforcement learning algorithm with total regret
AT after T steps for any unknown Markov decision process (MDP) with S states,
A actions per state, and diameter D. The diameter of an MDP is at most D if for any pair
of states s1, s2 there is a policy which moves from s1 to s2 in at most D steps (on average).
Our upper bound holds with high probability and it can be converted into a logarithmic regret
bound, if a xed dierence between the average reward of the optimal and the second optimal
policy is assumed.
We also present a corresponding lower bound
DSAT on the worst case total regret of