Robbins-Monro conditions for persistent exploration learning strategies
This provides incremental theoretical support for reinforcement learning algorithms, benefiting researchers in stochastic approximation and control.
The paper tackled the problem of establishing convergence conditions for Q-learning with local learning rates, showing that under persistent exploration and specific clock dependencies, the Robbins-Monro conditions hold, partially confirming a 1994 conjecture.
We formulate simple assumptions, implying the Robbins-Monro conditions for the $Q$-learning algorithm with the local learning rate, depending on the number of visits of a particular state-action pair (local clock) and the number of iteration (global clock). It is assumed that the Markov decision process is communicating and the learning policy ensures the persistent exploration. The restrictions are imposed on the functional dependence of the learning rate on the local and global clocks. The result partially confirms the conjecture of Bradkte (1994).