Intelligent Agent Foundations Forumsign up / log in
by Alex Appel 151 days ago | Vadim Kosoy likes this | link | parent

A summary that might be informative to other people: Where does the \(\omega(\frac{2}{3})\) requirement on the growth rate of the “rationality parameter” \(\beta\) come from?

Well, the expected loss of the agent comes from two sources. Making a suboptimal choice on its own, and incurring a loss from consulting a not-fully-rational advisor. The policy of the agent is basically “defer to the advisor when the expected loss over all time of acting (relative to the optimal move by an agent who knew the true environment) is too high”. Too high, in this case, cashes out as “higher than \(\beta(t)^{-1}t^{-1/x}\)”, where t is the time discount parameter and \(\beta\) is the level-of-rationality parameter. Note that as the operator gets more rational, the agent gets less reluctant about deferring. Also note that t is reversed from what you might think, high values of t mean that the agent has a very distant planning horizon, low values mean the agent is more present-oriented.

On most rounds, the agent acts on its own, so the expected all-time loss on a single round from taking suboptimal choices is on the order of \(\beta(t)^{-1}t^{-1/x}\), and also we’re summing up over about t rounds (technically exponential discount, but they’re similar enough). So the loss from acting on its own ends up being about \(\beta(t)^{-1}t^{(x-1)/x}\).

On the other hand, delegation will happen on at most ~\(t^{2/x}\) rounds, with a loss of \(\beta(t)^{-1}\) value, so the loss from delegation ends up being around \(\beta(t)^{-1}t^{2/x}\).

Setting these two losses equal to each other/minimizing the exponent on the t when they are smooshed together gets you x=3. And then \(\beta(t)\) must grow asymptotically faster than \(t^{2/3}\) to have the loss shrink to 0. So that’s basically where the 2/3 comes from, it comes from setting the delegation threshold to equalize long-term losses from the AI acting on its own, and the human picking bad choices, as the time horizon t goes to infinity.





Note: I currently think that
by Jessica Taylor on Predicting HCH using expert advice | 0 likes

Counterfactual mugging
by Jessica Taylor on Doubts about Updatelessness | 0 likes

What do you mean by "in full
by David Krueger on Doubts about Updatelessness | 0 likes

It seems relatively plausible
by Paul Christiano on Maximally efficient agents will probably have an a... | 1 like

I think that in that case,
by Alex Appel on Smoking Lesion Steelman | 1 like

Two minor comments. First,
by Sam Eisenstat on No Constant Distribution Can be a Logical Inductor | 1 like

A: While that is a really
by Alex Appel on Musings on Exploration | 0 likes

> The true reason to do
by Jessica Taylor on Musings on Exploration | 0 likes

A few comments. Traps are
by Vadim Kosoy on Musings on Exploration | 1 like

I'm not convinced exploration
by Abram Demski on Musings on Exploration | 0 likes

Update: This isn't really an
by Alex Appel on A Difficulty With Density-Zero Exploration | 0 likes

If you drop the
by Alex Appel on Distributed Cooperation | 1 like

Cool! I'm happy to see this
by Abram Demski on Distributed Cooperation | 0 likes

Caveat: The version of EDT
by 258 on In memoryless Cartesian environments, every UDT po... | 2 likes

[Delegative Reinforcement
by Vadim Kosoy on Stable Pointers to Value II: Environmental Goals | 1 like


Privacy & Terms