# Is it correct to define the equation below as q-learning multiple agent reinforcement learning models

I'm trying to define the q-learning multiple agent reinforcement learning models but I'm not sure if it is correct or not. N the number of agents and $$i \in N$$ and the k is the time episode.

$$Q^{i}_{k+1}(s_{k}, a^{i}_{k}) =(1-\alpha_k)Q^{i}_k(s_{k}, a^{i}_{k})+ \alpha_k[{r^i}_k(s_{k},\\ a^{1}_{k},...,a^{N}_{k}) + \beta\max_{b^i}Q^{i}_k(s_{k+1},b^i)]$$

Any help will be appreciated.

• What makes you think that Q-learning can be "naturally" generalised to the context of multiple agents? Have you read about it somewhere? If yes, it may be opportune to cite it in your question. I know there are multi-agent algorithms which are based on the "temporal difference" idea. You may want to look at these algorithms. Some of them may be the generalization you're looking for. – nbro Feb 11 at 11:23
• @nbro see this mdpi.com/1424-8220/18/2/375/htm – i_th Feb 12 at 11:13