5 ms·

If you apply the cognitive biases model to algorithms which have superhuman performance in various games - like AlphaZero, DeepBlue, Pluribus, and so on - the n

If you apply the cognitive biases model to algorithms which have superhuman performance in various games - like AlphaZero, DeepBlue, Pluribus, and so on - the natural result is to conclude that these models are predictably irrational. The reason you get this conclusion is because it turns out to be necessary to trade off theoretical optimal answers for the sake of speed. The behavioral economic view of human irrationality ought to be considered kind of dumb in view of that result. But it is actually so much worse than that for the field, because the math shows that sacrificing optimality for speed would be something that even an infinitely fast computational intelligence would be forced to do. It isn't irrational; it is a fundamentally necessary tradeoff. In imperfect information games your strategy space is continuous, EV is a function of policy, and many games even have continuous action spaces. If you thought Go was high branching factor you thought wrong; Go is an example of a freakishly low branching factor. It is infinitely smaller than the branching factor in relatively trivial decision problems. If you've never looked at cognitive biases through the lens of performance optimization you should try it. What seems like an arbitrary list from the bias perspective becomes clever approximative techniques in the performance optimization perspective. I often think about why this isn't more commonly known among people who call themselves rationalists and tend to spend a lot of time discussing cognitive bias. They seem to be trending toward a belief that general superintelligence is of infinite power, doubling down on their fallacious and hubristic appreciation for the power of intelligence. I say this, because when you apply the algorithms that don't have these biases - the behavioral economist view wouldn't find them to be irrational since they stick to the math, they follow things like the coherence principles for how we ought to work with probabilities as seen in works by Jayne, Finett, and so on - they either don't terminate, or, if you force them to do so... well... they lose to humans; even humans who aren't very good at the task.

brrrrrm 4y ago
> apply the cognitive biases model to algorithms which have superhuman performance in various games Could you give an example of this?
- JoshCole 4y ago
  - Anthropic bias The algorithms have this tendency. They use counterfactual reasoning to determine that assuming a nash player alike to them is their opponent when making their decisions. Sometimes they don't have a nash opponent, but they persist in this assumption anyway. In the cognitive bias framing this tendency is error. In the game theoretic framing this corresponds with minimizing the degree to which you would be exploited. You can find times where the algorithm plays against something that isn't nash and so it was operating according to a flawed model. You can call it biased for assuming that others operated according to that flawed model. From a complexity perspective this assumption lets you drop an infinite number of continuous strategy distributions from consideration - with strong theoretical backing for why it won't hurt you to do so - since nash is optimal according to some important metrics. - Attentional bias The tendency to pay attention to some things and not other things. Some examples of times where we do that are with alpha beta pruning. You can find moves that involve sacrifice that show the existence of this bias. The conceit in the cognitive bias framing is that it is stupid because some of the things might be important. The justification is that it some things are more promising than others and we have limited computational budget. Better to stop exploring the things which are not promising since they are not promising and direct efforts to where they are promising. Something like an upper confidence bound tree search in the cognitive bias model would turn balancing the explore exploit dynamic as part of approximating the nash equillibrium into erroneous reasoning because it doesn't choose to explore everything is an example of the lesser form of anchoring effects as they relate to attentional bias. It weights the action values according to the promising rollout more highly. - Apophenia Hashing techniques are used to reduce dimensionality. There is an error term here but you gain faster reasoning speed. Seen in blueprint abstraction - the poker example I gave - since we've hashing down using similarity to help bucket similar things. This gives rise to things like selective attention (another bias, and kind of related to this general category of bias). Jumping ahead to something like confirmation bias the heuristic that all these algorithms are using are flawed in various ways. They see that they are flawed after a node expansion and update their beliefs, but they don't update the heuristic. In fact if a flawed heuristic was working well such that it won we would have greater confidence rather than lesser confidence in the bias. --- Putting all that aside I would caution against specifity in understanding my point. I think approaching it in this direction - very specific examples - is horrible because it directs attention to the wrong things; when you look at specific examples you're always in a more specific situation and if you're in a more specific situation it means that your situation is more computationally tractable than the general situation which was being handled by the algorithm. So trying to focus on examples is actually going to give you weird inversions where the rules that applied in general don't apply to the specific situation. You need to come about it from the opposite direction - from the problem descriptions to the necessary constraints on your solution. Then it happens that the error in reasoning is a natural result of trying to do well.
bobthechef 4y ago
It sound like you're talking about, or at least brushing up against, prudential judgement[0]. Sometimes, the optimal move is not to seek the optimum. An obvious class of problems is where determining the optimum takes more time than the lifetime of the problem. Say you need to write an algorithm at work that does X, and you need X by tomorrow. If it would take you a week to find the theoretical optimum, then the optimum in a "global" sense is to deliver the best you can within the constraints, not the abstract theoretical optimum. The time to produce the solution is part of the total cost. An imprudent person would either say it's not possible, or never deliver the solution in time. [0] https://www.newadvent.org/cathen/12517b.htm https://www.newadvent.org/cathen/12517b.htm
- JoshCole 4y ago
  Yeah, that is pretty close to what I'm talking about. Coming at it from a different perspective - learning theory - but it seems to be the same overarching idea. I'm extending it a little though to something similar to anachronistic reasoning being incorrect - you can't divorce prudential decisions from their context. When you do judgement of the decisions is flawed because it doesn't acknowledge the actual constraints the decision was made under.
snovv_crash 4y ago
The thing about continuous space solutions is that they are typically differentiable, which means you can use a gradient descent or LM optimization rather than needing to fully explore the solution space. Typically there are large regions which are heuristically excludable, which is what you are getting at I think, but even an unbiased sampling plus gradient descent often makes problems much more tractable than discrete problems.
- JoshCole 4y ago
  The type of learning problem where I agree with your point is in something like learning how to classify hand written digits. My point about the continuous nature being unsearchable in practice is about recursive forms - if I choose this policy, my opponent will choose to react to the fact that I had that policy. In your learning problem where thing were made tractable by differentiation you have something like an elevation map that you are following, but in the multi-stage decision problem you have something more like a fractal elevation map. When you want to know the value of a particular point on the elevation map you have to look for the highest point or the lowest point on the elevation map you get by zooming in on the area which is the resultant of your having chosen a particular policy. The problem is that since this is a multi-agent environment they can react to your policy choice. So they can for example choose to have you get a high value only if you have the correct password entered on a form. That elevation map is designed to be a plain everywhere and another fractal zoom corresponding with a high utility or a low error term only at the point where you enter the right password. Choose a random point and you aren't going to have any information about what the password was. The optimization process won't help you. So you have to search. One way to do that is to do a random search; if you do that you eventually find a differing elevation - assuming one exists. But what if there were two passwords - one takes you to a low elevation fractal world that corresponds with a low reward because it is a honeypot. The other takes you to the fractal zoom where the elevation map is conditioned on you having root access to the system. This argument shows us that we actually would need to search over every point to get the best answer possible. Yet if we do that we have to search over the entire continuous distribution for our policy. Since by definition there are an infinite number of states a computer with infinite search speed can't enumerate them; there is another infinite fractal under every policy choice that also needs full enumeration. We have non-termination by a diagonalization argument for a computer that has infinite speed. Now observe that in our reality passwords exist. Less extreme - notice that reacting to policy choice in general, for example, moving out of the way of a car that drives toward you but not changing the way you would walk if it doesn't, isn't actually an unusual property in decision problems. It is normal.
Barrin92 4y ago
>why this isn't more commonly known among people who call themselves rationalists because most of these people do nothing else but writing blogs about rationalism. Same reason university tests are sometimes so removed from practicality compared to evaluation criteria in business, the people who make them do nothing else but write these tests. I suspect if you put some rationalists into the trenches in the Donbass for a week they'd quickly have a more balanced view of what's needed to solve a problem besides rational contemplation.

brrrrrm 4y ago

> apply the cognitive biases model to algorithms which have superhuman performance in various games Could you give an example of this?

JoshCole 4y ago
- Anthropic bias The algorithms have this tendency. They use counterfactual reasoning to determine that assuming a nash player alike to them is their opponent when making their decisions. Sometimes they don't have a nash opponent, but they persist in this assumption anyway. In the cognitive bias framing this tendency is error. In the game theoretic framing this corresponds with minimizing the degree to which you would be exploited. You can find times where the algorithm plays against something that isn't nash and so it was operating according to a flawed model. You can call it biased for assuming that others operated according to that flawed model. From a complexity perspective this assumption lets you drop an infinite number of continuous strategy distributions from consideration - with strong theoretical backing for why it won't hurt you to do so - since nash is optimal according to some important metrics. - Attentional bias The tendency to pay attention to some things and not other things. Some examples of times where we do that are with alpha beta pruning. You can find moves that involve sacrifice that show the existence of this bias. The conceit in the cognitive bias framing is that it is stupid because some of the things might be important. The justification is that it some things are more promising than others and we have limited computational budget. Better to stop exploring the things which are not promising since they are not promising and direct efforts to where they are promising. Something like an upper confidence bound tree search in the cognitive bias model would turn balancing the explore exploit dynamic as part of approximating the nash equillibrium into erroneous reasoning because it doesn't choose to explore everything is an example of the lesser form of anchoring effects as they relate to attentional bias. It weights the action values according to the promising rollout more highly. - Apophenia Hashing techniques are used to reduce dimensionality. There is an error term here but you gain faster reasoning speed. Seen in blueprint abstraction - the poker example I gave - since we've hashing down using similarity to help bucket similar things. This gives rise to things like selective attention (another bias, and kind of related to this general category of bias). Jumping ahead to something like confirmation bias the heuristic that all these algorithms are using are flawed in various ways. They see that they are flawed after a node expansion and update their beliefs, but they don't update the heuristic. In fact if a flawed heuristic was working well such that it won we would have greater confidence rather than lesser confidence in the bias. --- Putting all that aside I would caution against specifity in understanding my point. I think approaching it in this direction - very specific examples - is horrible because it directs attention to the wrong things; when you look at specific examples you're always in a more specific situation and if you're in a more specific situation it means that your situation is more computationally tractable than the general situation which was being handled by the algorithm. So trying to focus on examples is actually going to give you weird inversions where the rules that applied in general don't apply to the specific situation. You need to come about it from the opposite direction - from the problem descriptions to the necessary constraints on your solution. Then it happens that the error in reasoning is a natural result of trying to do well.

bobthechef 4y ago

It sound like you're talking about, or at least brushing up against, prudential judgement[0]. Sometimes, the optimal move is not to seek the optimum. An obvious class of problems is where determining the optimum takes more time than the lifetime of the problem. Say you need to write an algorithm at work that does X, and you need X by tomorrow. If it would take you a week to find the theoretical optimum, then the optimum in a "global" sense is to deliver the best you can within the constraints, not the abstract theoretical optimum. The time to produce the solution is part of the total cost. An imprudent person would either say it's not possible, or never deliver the solution in time. [0] https://www.newadvent.org/cathen/12517b.htm https://www.newadvent.org/cathen/12517b.htm

JoshCole 4y ago
Yeah, that is pretty close to what I'm talking about. Coming at it from a different perspective - learning theory - but it seems to be the same overarching idea. I'm extending it a little though to something similar to anachronistic reasoning being incorrect - you can't divorce prudential decisions from their context. When you do judgement of the decisions is flawed because it doesn't acknowledge the actual constraints the decision was made under.

snovv_crash 4y ago

The thing about continuous space solutions is that they are typically differentiable, which means you can use a gradient descent or LM optimization rather than needing to fully explore the solution space. Typically there are large regions which are heuristically excludable, which is what you are getting at I think, but even an unbiased sampling plus gradient descent often makes problems much more tractable than discrete problems.

JoshCole 4y ago
The type of learning problem where I agree with your point is in something like learning how to classify hand written digits. My point about the continuous nature being unsearchable in practice is about recursive forms - if I choose this policy, my opponent will choose to react to the fact that I had that policy. In your learning problem where thing were made tractable by differentiation you have something like an elevation map that you are following, but in the multi-stage decision problem you have something more like a fractal elevation map. When you want to know the value of a particular point on the elevation map you have to look for the highest point or the lowest point on the elevation map you get by zooming in on the area which is the resultant of your having chosen a particular policy. The problem is that since this is a multi-agent environment they can react to your policy choice. So they can for example choose to have you get a high value only if you have the correct password entered on a form. That elevation map is designed to be a plain everywhere and another fractal zoom corresponding with a high utility or a low error term only at the point where you enter the right password. Choose a random point and you aren't going to have any information about what the password was. The optimization process won't help you. So you have to search. One way to do that is to do a random search; if you do that you eventually find a differing elevation - assuming one exists. But what if there were two passwords - one takes you to a low elevation fractal world that corresponds with a low reward because it is a honeypot. The other takes you to the fractal zoom where the elevation map is conditioned on you having root access to the system. This argument shows us that we actually would need to search over every point to get the best answer possible. Yet if we do that we have to search over the entire continuous distribution for our policy. Since by definition there are an infinite number of states a computer with infinite search speed can't enumerate them; there is another infinite fractal under every policy choice that also needs full enumeration. We have non-termination by a diagonalization argument for a computer that has infinite speed. Now observe that in our reality passwords exist. Less extreme - notice that reacting to policy choice in general, for example, moving out of the way of a car that drives toward you but not changing the way you would walk if it doesn't, isn't actually an unusual property in decision problems. It is normal.

Barrin92 4y ago

>why this isn't more commonly known among people who call themselves rationalists because most of these people do nothing else but writing blogs about rationalism. Same reason university tests are sometimes so removed from practicality compared to evaluation criteria in business, the people who make them do nothing else but write these tests. I suspect if you put some rationalists into the trenches in the Donbass for a week they'd quickly have a more balanced view of what's needed to solve a problem besides rational contemplation.