I am a beginner and it is my first question.
I know that Q-learning update equation is:
$Q(s_t, a_t) = Q(s_t, a_t)+α(r_{t+1} +γ·max_AQ(s_{t+1}, a_t)−Q(s_t, a_t))$
But in some of the researches it is changed as a slightly different version which will be called the Q-learning function from this point.
$Q(s_t, a_t) = r_{t+1} + γ · max_AQ′(s_{t+1}, a_{t+1})$

For example in a traffic control paper, which used deep Q-learning, it is used that different version.
I see also it, in other papers. Why it changed the Q-learning function?
Where is it useful to change?
Thank you

I am a beginner and it is my first question.
I know that Q-learning update equation is:
$Q(s_t, a_t) = Q(s_t, a_t)+α(r_{t+1} +γ·max_AQ(s_{t+1}, a_t)−Q(s_t, a_t))$
But in some of the researches it is changed as a slightly different version which will be called the Q-learning function from this point.
$Q(s_t, a_t) = r_{t+1} + γ · max_AQ′(s_{t+1}, a_{t+1})$

For example in a traffic control paper, which used deep Q-learning, it is used that different version.
I see also it, in other papers. Why it changed the Q-learning function?
Where is it useful to change?
Is it for the reason of never be negative?
Thank you