# Reinforcement learning based Q-learning for wireless routing

In the Q-learning method to get the optimal strategy, the update method is like the following: $$$$Q(S,A) \leftarrow \ Q(S,A) + \alpha [R+\gamma~max_a(Q(s',a)) -Q(S,A)]$$$$

If in Q-learning the state transition probabilities are fixed to 1 then during the policy exploration how do we consider the $$\epsilon$$-greedy algorithm? As $$\epsilon$$ denotes the small probability during exploration and it must not be 1. Are the state transition probabilities and the probability during policy exploration different?

Notice that the environment responds to the agent's action with a reward $$R_{t+1}$$ and a next state $$S_{t+1}$$. Both of these are, in general, random variables with probability distributions conditioned on action $$A_t$$ and current state $$S_t$$.