I'm trying to understand how Q-learning deals with games where the optimal policy is a mixed strategy. The Bellman equation says that you should choose $max_a(Q(s,a))$ but this implies a single unique action for each $s$. Is Q-learning just not appropriate if you believe that the problem has a mixed strategy?

| improve this question | | | | |
  • $\begingroup$ What is a mixed strategy? Define this concept formally. $\endgroup$ – nbro May 20 '19 at 20:37
  • $\begingroup$ It's a basic concept in game theory. wikiwand.com/en/Strategy_(game_theory)#/… Essentially it's a strategy of sometimes choosing one action and sometimes choosing another in the same situation. $\endgroup$ – Thomas Johnson May 21 '19 at 20:03

One possibility is to use softmax and choose each action a randomly with probabiliy $p = \frac{\exp(Q(s,a))}{\sum_a \exp(Q(s,a))}$. I don't thinks it is still Q-learning though.

| improve this answer | | | | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.