Acorn

10

Sorry for the format here, and I still try to figure out how to use markdown in the comment.

I find difficulty understanding inferences about parameters $ \alpha,\beta,\gamma $ in the "Example:regret" part.

Take the fully rational planner `p`

for example.

Since the human will say `h`

following `s`

, the different between reward functions for `h`

and `-h`

is non-negative, which implies that: $ (\beta R(h)+\gamma R(h|s)) - (\beta R(\sim h)+\gamma R(\sim h|s)) \geq 0 $

Then it is concluded that $ \beta R(h-\sim h)+\gamma R(h-\sim h|s)\geq0$

Similarly, from the human will say $ \sim h$ following `i`

, we have $ \beta R(h-\sim h)+\delta R(h-\sim h|i)\leq0$

It seems that more information about the reward function is need in order to arrive at the final model with $ (p,R(\alpha,\beta,\gamma,\delta)|\gamma\geq-\beta\geq\delta) $

30

Sorry for my vague expressions here. What I try to say is that "I prefer apples to bananas and I prefer apples to peaches". My original thought is that: If this statement is formalized in a single world, since it is not clear that whether I prefer bananas to peaches, it seems that the function l has to map apples to bananas and peaches at the same time, which violates its one-to-one property.

But maybe I also asked a bad question: I mistook the definition of partial preferences for any simple statement about preferences, and tried to apply the model proposed in this post to the "composite" preferences, which actually expressed two preferences.

10

I am studying along your Research Agenda, and I am very excited about your whole plan.

As for this one, I am puzzled that how to formalize preferences like this together, "I prefer apples to both bananas and peaches", since the function l is one-to-one here. In contrast, the model you proposed in the "*Toy model piece #1: Partial preferences revisited*" deals with this quite easily.

It seems on the MacOS Catalina Version 10.15, Safari Version 13.0.2, the Ctrl-Cmd-4 does not work either. I have tried every possible combination (Ctrl,Cmd,4,M) on both Safari and Chrome but none of them works. Do you have any ideas?