# What should be the policy for online reinforcement learning with intrinsic reward

An agent receives an extrinsic reward $$r_{ext}$$ and an intrinsic reward $$r_{int}$$ and a Q-function approximation is trained using TD learning such that $$Q(s,a)$$ approximates the expected return of $$r_{ext} + \beta r_{int}$$ where $$\beta$$ is a coefficient less than 1.

In online reinforcement learning, what is a good policy to use when there is intrinsic rewards? For example, if $$\epsilon$$-greedy is used, then there is a probability of $$\epsilon$$ that a random action is selected (i.e., undirected exploration). This ignores the intrinsic reward which is a form of directed exploration. If a greedy policy is used, then this risks myopic exploration within a subset of the state space and the agent might never experience certain intrinsic rewards that guides it to meaningful states. It seems then that $$\epsilon$$ needs to be tune correctly: too high and it ignores intrinsic rewards, too low and it is myopic.

On the other hand, are there other policies that can be used? Even if $$\epsilon$$ is small, say $$0.2$$, the agent still ignores directed exploration 2 out of 10 times.