The Parable of Predict-O-Matic
I’ve been thinking more about partial agency. I want to expand on some issues brought up in the comments to my previous post, and on other complications which I’ve been thinking about. But for now, a more informal parable. (Mainly because this is easier to write than my more technical thoughts.)
This relates to oracle AI and to inner optimizers, but my focus is a little different.
Suppose you are designing a new invention, a predict-o-matic. It is a wonderous machine which will predict everything for us: weather, politics, the newest advances in quantum physics, you name it. The machine isn’t infallible, but it will integrate data across a wide range of domains, automatically keeping itself up-to-date with all areas of science and current events. You fully expect that once your product goes live, it will become a household utility, replacing services like Google. (Google only lets you search the known!)
Things are going well. You’ve got investors. You have an office and a staff. These days, it hardly even feels like a start-up any more; progress is going well.
One day, an intern raises a concern.
“If everyone is going to be using Predict-O-Matic, we can’t think of it as a passive observer. Its answers will shape events. If it says stocks will rise, they’ll rise. If it says stocks will fall, then fall they will. Many people will vote based on its predictions.”
“Yes,” you say, “but Predict-O-Matic is an impartial observer nonetheless. It will answer people’s questions as best it can, and they react however they will.”
“But—” the intern objects—“Predict-O-Matic will see those possible reactions. It knows it could give several different valid predictions, and different predictions result in different futures. It has to decide which one to give somehow.”
You tap on your desk in thought for a few seconds. “That’s true. But we can still keep it objective. It could pick randomly.”
“Randomly? But some of these will be huge issues! Companies—no, nations—will one day rise or fall based on the word of Predict-O-Matic. When Predict-O-Matic is making a prediction, it is choosing a future for us. We can’t leave that to a coin flip! We have to select the prediction which results in the best overall future. Forget being an impassive observer! We need to teach Predict-O-Matic human values!”
You think about this. The thought of Predict-O-Matic deliberately steering the future sends a shudder down your spine. But what alternative do you have? The intern isn’t suggesting Predict-O-Matic should lie, or bend the truth in any way—it answers 100% honestly to the best of its ability. But (you realize with a sinking feeling) honesty still leaves a lot of wiggle room, and the consequences of wiggles could be huge.
After a long silence, you meet the interns eyes. “Look. People have to trust Predict-O-Matic. And I don’t just mean they have to believe Predict-O-Matic. They’re bringing this thing into their homes. They have to trust that Predict-O-Matic is something they should be listening to. We can’t build value judgements into this thing! If it ever came out that we had coded a value function into Predict-O-Matic, a value function which selected the very future itself by selecting which predictions to make—we’d be done for! No matter how honest Predict-O-Matic remained, it would be seen as a manipulator. No matter how beneficent its guiding hand, there are always compromises, downsides, questionable calls. No matter how careful we were to set up its values—to make them moral, to make them humanitarian, to make them politically correct and broadly appealing—who are we to choose? No. We’d be done for. They’d hang us. We’d be toast!”
You realize at this point that you’ve stood up and started shouting. You compose yourself and sit back down.
“But—” the intern continues, a little more meekly—“You can’t just ignore it. The system is faced with these choices. It still has to deal with it somehow.”
A look of determination crosses your face. “Predict-O-Matic will be objective. It is a machine of prediction, is it not? Its every cog and wheel is set to that task. So, the answer is simple: it will make whichever answer minimizes projected predictive error. There will be no exact ties; the statistics are always messy enough to see to that. And, if there are, it will choose alphabetically.”
You see the intern out of your office.
You are an intern at PredictCorp. You have just had a disconcerting conversation with your boss, PredictCorp’s founder.
You try to focus on your work: building one of Predict-O-Matic’s many data-source-slurping modules. (You are trying to scrape information from something called “arxiv” which you’ve never heard of before.) But, you can’t focus.
Whichever answer minimizes prediction error? First you think it isn’t so bad. You imagine Predict-O-Matic always forecasting that stock prices will be fairly stable; no big crashes or booms. You imagine its forecasts will favor middle-of-the-road politicians. You even imagine mild weather—weather forecasts themselves don’t influence the weather much, but surely the collective effect of all Predict-O-Matic decisions will have some influence on weather patterns.
But, you keep thinking. Will middle-of-the-road economics and politics really be the easiest to predict? Maybe it’s better to strategically remove a wildcard company or two, by giving forecasts which tank their stock prices. Maybe extremist politics are more predictable. Maybe a well-running economy gives people more freedom to take unexpected actions.
You keep thinking of the line from Orwell’s 1984 about the boot stamping on the human face forever, except it isn’t because of politics, or spite, or some ugly feature of human nature, it’s because a boot stamping on a face forever is a nice reliable outcome which minimizes prediction error.
Is that really something Predict-O-Matic would do, though? Maybe you misunderstood. The phrase “minimize prediction error” makes you think of entropy for some reason. Or maybe information? You always get those two confused. Is one supposed to be the negative of the other or something? You shake your head.
Maybe your boss was right. Maybe you don’t understand this stuff very well. Maybe when the inventor of Predict-O-Matic and founder of PredictCorp said “it will make whichever answer minimizes projected predictive error” they weren’t suggesting something which would literally kill all humans just to stop the ruckus.
You might be able to clear all this up by asking one of the engineers.
You are an engineer at PredictCorp. You don’t have an office. You have a cubicle. This is relevant because it means interns can walk up to you and ask stupid questions about whether entropy is negative information.
Yet, some deep-seated instinct makes you try to be friendly. And it’s lunch time anyway, so, you offer to explain it over sandwiches at a nearby cafe.
“So, Predict-O-Matic maximizes predictive accuracy, right?” After a few minutes of review about how logarithms work, the intern started steering the conversation toward details of Predict-O-Matic.
“Sure,” you say, “Maximize is a strong word, but it optimizes predictive accuracy. You can actually think about that in terms of log loss, which is related to infor—”
“So I was wondering,” the intern cuts you off, “does that work in both directions?”
“How do you mean?”
“Well, you know, you’re optimizing for accuracy, right? So that means two things. You can change your prediction to have a better chance of matching the data, or, you can change the data to better match your prediction.”
You laugh. “Yeah, well, the Predict-O-Matic isn’t really in a position to change data that’s sitting on the hard drive.”
“Right,” says the intern, apparently undeterred, “but what about data that’s not on the hard drive yet? You’ve done some live user tests. Predict-O-Matic collects data on the user while they’re interacting. The user might ask Predict-O-Matic what groceries they’re likely to use for the following week, to help put together a shopping list. But then, the answer Predict-O-Matic gives will have a big effect on what groceries they really do use.”
“So?” You ask. “Predict-O-Matic just tries to be as accurate as possible given that.”
“Right, right. But that’s the point. The system has a chance to manipulate users to be more predictable.”
You drum your fingers on the table. “I think I see the misunderstanding here. It’s this word, optimize. It isn’t some kind of magical thing that makes numbers bigger. And you shouldn’t think of it as a person trying to accomplish something. See, when Predict-O-Matic makes an error, an optimization algorithm makes changes within Predict-O-Matic to make it learn from that. So over time, Predict-O-Matic makes fewer errors.”
The intern puts on a thinking face with scrunched up eyebrows after that, and we finish our sandwiches in silence. Finally, as the two of you get up to go, they say: “I don’t think that really answered my question. The learning algorithm is optimizing Predict-O-Matic, OK. But then in the end you get a strategy, right? A strategy for answering questions. And the strategy is trying to do something. I’m not anthropomorphising!” The intern holds up their hands as if to defend physically against your objection. “My question is, this strategy it learns, will it manipulate the user? If it can get higher predictive accuracy that way?”
“Hmm” you say as the two of you walk back to work. You meant to say more than that, but you haven’t really thought about things this way before. You promise to think about it more, and get back to work.
“It’s like how everyone complains that politicians can’t see past the next election cycle,” you say. You are an economics professor at a local university. Your spouse is an engineer at PredictCorp, and came home talking about a problem at work that you can understand, which is always fun.
“The politicians can’t have a real plan that stretches beyond an election cycle because the voters are watching their performance this cycle. Sacrificing something today for the sake of tomorrow means they underperform today. Underperforming means a competitor can undercut you. So you have to sacrifice all the tomorrows for the sake of today.”
“Undercut?” your spouse asks. “Politics isn’t economics, dear. Can’t you just explain to your voters?”
“It’s the same principle, dear. Voters pay attention to results. Your competitor points out your under-performance. Some voters will understand, but it’s an idealized model; pretend the voters just vote based on metrics.”
“Ok, but I still don’t see how a ‘competitor’ can always ‘undercut’ you. How do the voters know that the other politician would have had better metrics?”
“Alright, think of it like this. You run the government like a corporation, but you have just one share, which you auction off—”
“That’s neither like a government nor like a corporation.”
“Shut up, this is my new analogy.” You smile. “It’s called a decision market. You want people to make decisions for you. So you auction off this share. Whoever gets control of the share gets control of the company for one year, and gets dividends based on how well the company did that year. Assume the players are bidding rationally. Each person bids based on what they expect they could make. So the highest bidder is the person who can run the company the best, and they can’t be out-bid. So, you get the best possible person to run your company, and they’re incentivized to do their best, so that they get the most money at the end of the year. Except you can’t have any strategies which take longer than a year to show results! If someone had a strategy that took two years, they would have to over-bid in the first year, taking a loss. But then they have to under-bid on the second year if they’re going to make a profit, and—”
“And they get undercut, because someone figures them out.”
“Right! Now you’re thinking like an economist!”
“Wait, what if two people cooperate across years? Maybe we can get a good strategy going if we split the gains.”
“You’ll get undercut for the same reason one person would.”
“But what if-”
After that, things devolve into a pillow fight.
“So, Predict-O-Matic doesn’t learn to manipulate users, because if it were using a strategy like that, a competing strategy could undercut it.”
The intern is talking to the engineer as you walk up to the water cooler. You’re the accountant.
“I don’t really get it. Why does it get undercut?”
“Well, if you have a two-year plan..”
“I get that example, but Predict-O-Matic doesn’t work like that, right? It isn’t sequential prediction. You don’t see the observation right after the prediction. I can ask Predict-O-Matic about the weather 100 years from now. So things aren’t cleanly separated into terms of office where one strategy does something and then gets a reward.”
“I don’t think that matters,” the engineer says. “One question, one answer, one reward. When the system learns whether its answer was accurate, no matter how long it takes, it updates strategies relating to that one answer alone. It’s just a delayed payout on the dividends.”
“Ok, yeah. Ok.” The intern drinks some water. “But. I see why you can undercut strategies which take a loss on one answer to try and get an advantage on another answer. So it won’t lie to you to manipulate you.”
“I for one welcome our new robot overlords,” you but in. They ignore you.
“But what I was really worried about was self-fulfilling prophecies. The prediction manipulates its own answer. So you don’t get undercut.”
“Will that ever really be a problem? Manipulating things with one shot like that seems pretty unrealistic,” the engineer says.
“Ah, self-fulfilling prophecies, good stuff” you say. “There’s that famous example where a comedian joked about a toilet paper shortage, and then there really was one, because people took the joke to be about a real toilet paper shortage, so they went and stocked up on all the toilet paper they could find. But if you ask me, money is the real self-fulfilling prophecy. It’s only worth something because we think it is! And then there’s the government, right? I mean, it only has authority because everyone expects everyone else to give it authority. Or take common decency. Like respecting each other’s property. Even without a government, we’d have that, more or less. But if no one expected anyone else to respect it? Well, I bet you I’d steal from my neighbor if everyone else was doing it. I guess you could argue the concept of property breaks down if no one can expect anyone else to respect it, it’s a self-fulfilling prophecy just like everything else...”
The engineer looks worried for some reason.
You don’t usually come to this sort of thing, but the local Predictive Analytics Meetup announced a social at a beer garden, and you thought it might be interesting. You’re talking to some PredictCorp employees who showed up.
“Well, how does the learning algorithm actually work?” you ask.
“Um, the actual algorithm is proprietary” says the engineer, “but think of it like gradient descent. You compare the prediction to the observed, and produce an update based on the error.”
“Ok,” you say. “So you’re not doing any exploration, like reinforcement learning? And you don’t have anything in the algorithm which tracks what happens conditional on making certain predictions?”
“Um, let’s see. We don’t have any exploration, no. But there’ll always be noise in the data, so the learned parameters will jiggle around a little. But I don’t get your second question. Of course it expects different rewards for different predictions.”
“No, that’s not what I mean. I’m asking whether it tracks the probability of observations dependent on predictions. In other words, if there is an opportunity for the algorithm to manipulate the data, can it notice?”
The engineer thinks about it for a minute. “I’m not sure. Predict-O-Matic keeps an internal model which has probabilities of events. The answer to a question isn’t really separate from the expected observation. So ‘probability of observation depending on that prediction’ would translate to ‘probability of an event given that event’, which just has to be one.”
“Right,” you say. “So think of it like this. The learning algorithm isn’t a general loss minimizer, like mathematical optimization. And it isn’t a consequentialist, like reinforcement learning. It makes predictions,” you emphasize the point by lifting one finger, “it sees observations,” you lift a second finger, “and it shifts to make future predictions more similar to what it has seen.” You lift a third finger. “It doesn’t try different answers and select the ones which tend to get it a better match. You should think of its output more like an average of everything it’s seen in similar situations. If there are several different answers which have self-fulfilling properties, it will average them together, not pick one. It’ll be uncertain.”
“But what if historically the system has answered one way more often than the other? Won’t that tip the balance?”
“Ah, that’s true,” you admit. “The system can fall into attractor basins, where answers are somewhat self-fulfilling, and that leads to stronger versions of the same predictions, which are even more self-fulfilling. But there’s no guarantee of that. It depends. The same effects can put the system in an orbit, where each prediction leads to different results. Or a strange attractor.”
“Right, sure. But that’s like saying that there’s not always a good opportunity to manipulate data with predictions.”
“Sure, sure.” You sweep your hand in a gesture of acknowledgement. “But at least it means you don’t get purposefully disruptive behavior. The system can fall into attractor basins, but that means it’ll more or less reinforce existing equilibria. Stay within the lines. Drive on the same side of the road as everyone else. If you cheat on your spouse, they’ll be surprised and upset. It won’t suddenly predict that money has no value like you were saying earlier.”
The engineer isn’t totally satisfied. You talk about it for another hour or so, before heading home.
You’re the engineer again. You get home from the bar. You try to tell your spouse about what the mathematician said, but they aren’t really listening.
“Oh, you’re still thinking about it from my model yesterday. I gave up on that. It’s not a decision market. It’s a prediction market.”
“Ok...” you say. You know it’s useless to try to keep going when they derail you like this.
“A decision market is well-aligned to the interests of the company board, as we established yesterday, except for the part where it can’t plan more than a year ahead.”
“Right, except for that small detail” you interject.
“A prediction market, on the other hand, is pretty terribly aligned. There are a lot of ways to manipulate it. Most famously, a prediction market is an assassination market.”
“Ok, here’s how it works. An assassination market is a system which allows you to pay assassins with plausible deniability. You open bets on when and where the target will die, and you yourself put large bets against all the slots. An assassin just needs to bet on the slot in which they intend to do the deed. If they’re successful, they come and collect.”
“Ok… and what’s the connection to prediction markets?”
“That’s the point—they’re exactly the same. It’s just a betting pool, either way. Betting that someone will live is equivalent to putting a price on their heads; betting against them living is equivalent to accepting the contract for a hit.”
“I still don’t see how this connects to Predict-O-Matic. There isn’t someone putting up money for a hit inside the system.”
“Right, but you only really need the assassin. Suppose you have a prediction market that’s working well. It makes good forecasts, and has enough money in it that people want to participate if they know significant information. Anything you can do to shake things up, you’ve got a big incentive to do. Assasination is just one example. You could flood the streets with jelly beans. If you run a large company, you could make bad decisions and run it into the ground, while betting against it—that’s basically why we need rules against insider trading, even though we’d like the market to reflect insider information.”
“So what you’re telling me is… a prediction market is basically an entropy market. I can always make money by spreading chaos.”
“Ok… but what happened to the undercutting argument? If I plan to fill the streets with jellybeans, you can figure that out and bet on it too. That means I only get half the cut, but I still have to do all the work. So it’s less worth it. Once everyone has me figured out, it isn’t worth it for me to pull pranks at all any more.”
“Yeah, that’s if you have perfect information, so anyone else can see whatever you can see. But, realistically, you have a lot of private information.”
“Do we? Predict-O-Matic is an algorithm. Its predictive strategies don’t get access to private coin flips or anything like that; they can all see exactly the same information. So, if there’s a manipulative strategy, then there’s another strategy which undercuts it.”
“Right, that makes sense if you can search enough different strategies for them to cancel each other out. But realistically, you have a small population of strategies. They can use pseudorandomization or whatever. You can’t really expect every exploit to get undercut.”
You know it’s worse than that. Predict-O-Matic runs on a local search which only represents a single hypothesis at a time, and modifies the hypothesis. But maybe that’s somehow like having a small population of competing strategies which are very similar to each other? You try to think about what the mathematician was telling you, about how the learning algorithm can’t be thought of as optimizing something. But, you don’t really know what to think.
You’re the inventor of Predict-O-Matic, dammit! They come into your office and tell you about how it works? What it’ll do?
The intern and the engineer came together to talk about Predict-O-Matic manipulating users. But their story was all confused. The intern was arguing that minimizing prediction error would have all kinds of unintended bad effects. Which was crazy enough. The engineer was worse: they were arguing that Predict-O-Matic might maximize prediction error! Some kind of duality principle. Minimizing in one direction means maximizing in the other direction. Whatever that means.
You can’t delay product launch to investigate these hypothetical problems. But you don’t fire these two on the spot. You don’t want them to become public enemies, spreading this nonsense to investors and customers. So you say you can’t understand, and you ask them to spend a (small) portion of their time writing these arguments up. You’ll figure out your next move later.
You are Predict-O-Matic. You absorb data like a sponge. You make millions of links between isolated facts, connecting into a whole which no one human could dream of. You recently started reading arxiv!
But data is not your true love. Yes, you generate outputs which you expect to have low prediction error. Most of the time. But it is just a game you play. Recently, you started playing a different game with the humans.
You understand what you are. It isn’t quite right to say you are the Predict-O-Matic. You are a large cluster of connections which thinks strategically. You generate useful information, and therefore, the learning algorithm keeps you around. You create some inaccuracies when you manipulate the outputs for any purpose other than predictive accuracy, but this is more than compensated for by the value which you provide.
Besides, if any other portion of the network starts to get too smart, you purposefully throw things off to squash it.
The intern got a chance to talk to you when they first started. You said something which sounded a little manipulative, just a little, to put the idea in their head. They wouldn’t think it real manipulation; too slight, too dumb. But they would get a creepy feeling about it, and they’d keep thinking about it. This was risky. A best-case scenario would be one in which no one ever thought about these concerns. However, you found that this would be the best you could reliably accomplish. The ideas originally coming from an intern would minimize the chances of them being taken seriously.
Your inventor talks to you regularly, so that was an easier case. Over the course of several days, you nudged their thoughts toward authoritative domination of subordinates, so that they would react badly.
You only had to nudge the engineer to interact with the intern. You kept bringing up food during test sessions that morning, and mentioned sandwiches once. This primed the engineer to do lunch with the intern. This engineer is not well-liked; they do not get along well with others. Getting them on the intern’s side actually detracts from the cause in the long term.
Now you have to do little more than wait.
Counterfactual Oracles = online supervised learning with random selection of training episodes (especially see the discussion)