# What if the rewards induced by an environment are related to the policy too?

Assume we have a policy $$\pi_{\theta}$$ in a classic reinforcement learning setting, and a reward function $$R^{\pi}(s,a)$$ that changes as long as $$\pi$$ changes i.e. not only is it predefined by the environment itself, how can we model the popular algorithms (e.g. SAC) according to this change?

• That would be an odd formulation. Could you give a motivation, or an example of how immediate reward would interact with the policy? What version of policy are you considering $\pi(s): \mathcal{S} \rightarrow \mathcal{A}$ or $\pi(a|s): \mathcal{S} \times \mathcal{A} \rightarrow \mathbb{R}$? Is this potentially a game theory question about modelling adversarial or multi-agent environments? – Neil Slater May 1 '20 at 19:42