This post considers “distributed decisions” and thinks about a few conceptual implications of thinking about that.
Roughly, distributed decisions are decisions that are not made by “one rational Bayesian agent”, but by a collective of nodes that together “share a goal”. Thus, this post is about the “width” of actions instead of the “depth” (the distance to “the thing impacted”).
Together, the nodes ideally form a “distributed Bayesian agent”, which by definition acts so as to rationally use the locally available information:
Each node has the goal to maximize E[u(X)] over some shared outcome variable X and shared utility function u.
Each node does that by trying to steer the probability distribution p_A(X, Y, Z, …) over world states by choosing the optimal action A.
Side remark: the world state (X, Y, Z) can also contain variables encoding information from the past, like Y = “is the movie on Netflix?”.
If one makes an observation (e.g., Y = y), then what’s steered is the conditional probability distribution p_A(X, Z, … | Y = y) instead, where Y = y is information that may only be accessible to one of the nodes. So this node acts locally rationally, even if other nodes have maybe more useful information.
Sometimes, information is so useful that it is worth it to invest to pass a summary of that information around to cause others to make more overall useful decisions.
This seems to suggest that summaries of local information are a resource in the sense of the measuring stick of utility problem.
Overall, this tentatively suggests that natural abstraction summaries are a “resource”. However, this would require showing that they are additive across decisions, which is an open problem in itself.
Confusions/Questions:
The telephone theorem seems to say (according to the “optimization at a distance” post) that the low-dimensional abstract summary is “arbitrarily well-preserved” at a distance. If it is, then It doesn’t seem like a “resource”? The following are highly confused elaborations on this:
I consider a “resource” something that can be “used up” and then isn’t there anymore. If it’s arbitrarily well-preserved, then it isn’t used up.
On the other hand, I also disagree that what I intuitively consider “actions” are arbitrarily well-preserved: If I do an action, and this changes the world, then the action will only be accessible to “what’s changed”, but not further along. E.g., if I build a house, then sufficiently far in the future, people will not see anymore what actions built that house, they just see the house.
Maybe the house could be considered an “even lower-dimensional summary”, but it seems to me that this is also not arbitrarily well-preserved. At some point, the house will be destroyed, eventually removing all traces of it ever having existed.
This suggests I should understand the telephone theorem better.
Rebuttal to my claim that resources should be used up: if I use money to buy something, then money is used up for me, but the person whom I gave the money can use it for something else.
Fundamentally, resources were more like… “traded” in this case. How should I think about that?
Okay, let’s assume that “summary information is the fundamental notion of a resource”. Does this explain all types of resources in our world?
If I want a house, I need money, so to a first approximation, “money” seems like a relevant resource.
But then the question is “how do I get money”?
The relevant answer to that question may be pieces of low-dimensional information that tell me how I can best use the configuration of my physical body to make money.
So in that sense, information is the more fundamental resource.
Wikipedia: “Knowledge here consists of information with a good explanatory function that has proven resistant to falsification. Any real process is physically possible to perform provided the knowledge to do so has been acquired.”
I currently share most of these confusions. It seems to me like “resources” have to be more than just well-conserved summaries; there should be some additional condition having to do with controllability/”ownership” and additivity.
Similarly, there’s probably additional conditions for conserved summaries to be “actions”—none of these posts have really established a causal direction distinguishing “action” from “observation”, for instance, which could be a hairy issue insofar as some summary dimensions are jointly determined.
And finally, there’s the question of “conserved over what?”. Summaries can be conserved over multiple length/time-scales, or over more abstract notions of “distance”, and these posts haven’t carefully stated the relevant conditions because I don’t yet have a very precise idea of what the relevant conditions are.
Summary
This post considers “distributed decisions” and thinks about a few conceptual implications of thinking about that.
Roughly, distributed decisions are decisions that are not made by “one rational Bayesian agent”, but by a collective of nodes that together “share a goal”. Thus, this post is about the “width” of actions instead of the “depth” (the distance to “the thing impacted”).
Together, the nodes ideally form a “distributed Bayesian agent”, which by definition acts so as to rationally use the locally available information:
Each node has the goal to maximize E[u(X)] over some shared outcome variable X and shared utility function u.
Each node does that by trying to steer the probability distribution p_A(X, Y, Z, …) over world states by choosing the optimal action A.
Side remark: the world state (X, Y, Z) can also contain variables encoding information from the past, like Y = “is the movie on Netflix?”.
If one makes an observation (e.g., Y = y), then what’s steered is the conditional probability distribution p_A(X, Z, … | Y = y) instead, where Y = y is information that may only be accessible to one of the nodes. So this node acts locally rationally, even if other nodes have maybe more useful information.
Sometimes, information is so useful that it is worth it to invest to pass a summary of that information around to cause others to make more overall useful decisions.
This seems to suggest that summaries of local information are a resource in the sense of the measuring stick of utility problem.
Overall, this tentatively suggests that natural abstraction summaries are a “resource”. However, this would require showing that they are additive across decisions, which is an open problem in itself.
Confusions/Questions:
The telephone theorem seems to say (according to the “optimization at a distance” post) that the low-dimensional abstract summary is “arbitrarily well-preserved” at a distance. If it is, then It doesn’t seem like a “resource”? The following are highly confused elaborations on this:
I consider a “resource” something that can be “used up” and then isn’t there anymore. If it’s arbitrarily well-preserved, then it isn’t used up.
On the other hand, I also disagree that what I intuitively consider “actions” are arbitrarily well-preserved: If I do an action, and this changes the world, then the action will only be accessible to “what’s changed”, but not further along. E.g., if I build a house, then sufficiently far in the future, people will not see anymore what actions built that house, they just see the house.
Maybe the house could be considered an “even lower-dimensional summary”, but it seems to me that this is also not arbitrarily well-preserved. At some point, the house will be destroyed, eventually removing all traces of it ever having existed.
This suggests I should understand the telephone theorem better.
Rebuttal to my claim that resources should be used up: if I use money to buy something, then money is used up for me, but the person whom I gave the money can use it for something else.
Fundamentally, resources were more like… “traded” in this case. How should I think about that?
Okay, let’s assume that “summary information is the fundamental notion of a resource”. Does this explain all types of resources in our world?
If I want a house, I need money, so to a first approximation, “money” seems like a relevant resource.
But then the question is “how do I get money”?
The relevant answer to that question may be pieces of low-dimensional information that tell me how I can best use the configuration of my physical body to make money.
So in that sense, information is the more fundamental resource.
Is this related to David Deutsch’s The Beginning of Infinity?
Wikipedia: “Knowledge here consists of information with a good explanatory function that has proven resistant to falsification. Any real process is physically possible to perform provided the knowledge to do so has been acquired.”
I currently share most of these confusions. It seems to me like “resources” have to be more than just well-conserved summaries; there should be some additional condition having to do with controllability/”ownership” and additivity.
Similarly, there’s probably additional conditions for conserved summaries to be “actions”—none of these posts have really established a causal direction distinguishing “action” from “observation”, for instance, which could be a hairy issue insofar as some summary dimensions are jointly determined.
And finally, there’s the question of “conserved over what?”. Summaries can be conserved over multiple length/time-scales, or over more abstract notions of “distance”, and these posts haven’t carefully stated the relevant conditions because I don’t yet have a very precise idea of what the relevant conditions are.