It’s occurred to me that there is a framework where we can see all “indifference” results as corrective rewards, both for the utility function change indifference and for the policy change indifference.
Imagine that the agent has reward \(R_0\) and is following policy \(\pi_0\), and we want to change it to having reward \(R_1\) and following policy \(\pi_1\).
Then the corrective reward we need to pay it, so that it doesn’t attempt to resist or cause that change, is simply the difference between the two expected values:
where \(V\) is the agent’s own valuation of the expected reward, conditional on the policy.
This explains why off-policy reward-based agents are already safely interruptible: since we change the policy, not the reward, \(R_0=R_1\). And since off-policy agents have value estimates that are indifferent to the policy followed, \(V(R_0|\pi_0)=V(R_1|\pi_1)\), and the compensatory rewards are zero.