Robbins-Monro conditions for persistent exploration learning strategies

TL;DR

This paper establishes conditions under which Q-learning with local and global clock-dependent learning rates converges, confirming a conjecture and ensuring persistent exploration in Markov decision processes.

Contribution

It formulates simple assumptions that imply Robbins-Monro conditions for Q-learning with local and global clocks, extending theoretical understanding of convergence.

Findings

Conditions for convergence of Q-learning with local clock-dependent rates.

Partial confirmation of Bradkte's 1994 conjecture.

Theoretical framework for persistent exploration in MDPs.

Abstract

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).