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?
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2$\begingroup$ 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? $\endgroup$ – Neil Slater May 1 '20 at 19:42
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