# Why can constant alpha be used for Q-Learning in practice?

The convergence criteria of Q-Learning state that the learning rate parameter $$\alpha$$ must satisfy the conditions: $$\sum_k \alpha_{n^k(s,a)} =\infty \quad \text{and}\quad \sum_k \alpha_{n^k(s,a)}^{2} <\infty \quad \forall s \in \mathcal{S}$$ where $$n_k(s,a)$$ denotes the $$k^\text{th}$$ time $$(s,a)$$ is visited

Why can a constant $$\alpha$$ be used in practice?

• Why wouldn't you be able to? There's nothing in the above two conditions that says $\alpha$ has to change as $n_k(s,a)$ changes. – jbowman Feb 27 at 20:37
• Sorry, I should have also added $0 \leq \alpha_{n_k(s,a)}\leq 1$. If alpha is constant and non-zero then both sums diverge. I may be missing the point of what you are saying though. – KaneM Feb 27 at 20:50