by Vadim Kosoy 181 days ago | link | parent Your confusion is because you are thinking about regret in an anytime setting. In an anytime setting, there is a fixed policy $$\pi$$, we measure the expected reward of $$\pi$$ over a time interval $$t$$ and compare it to the optimal expected reward over the same time interval. If $$\pi$$ has probability $$p > 0$$ to walk into a trap, regret has the linear lower bound $$\Omega(pt)$$. On other hand, I am talking about policies $$\pi_t$$ that explicitly depend on the parameter $$t$$ (I call this a “metapolicy”). Both the advisor and the agent policies are like that. As $$t$$ goes to $$\infty$$, the probability $$p(t)$$ to walk into a trap goes to $$0$$, so $$p(t)t$$ is a sublinear function. A second difference with the usual definition of regret is that I use an infinite sum of rewards with geometric time discount $$e^{-1/t}$$ instead of a step function time discount that cuts off at $$t$$. However, this second difference is entirely inessential, and all the theorems work about the same with step function time discount.

### NEW DISCUSSION POSTS

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

Intermediate update: The
 by Alex Appel on Further Progress on a Bayesian Version of Logical ... | 0 likes

Since Briggs [1] shows that
 by 258 on In memoryless Cartesian environments, every UDT po... | 2 likes

This doesn't quite work. The
 by Nisan Stiennon on Logical counterfactuals and differential privacy | 0 likes

I at first didn't understand
 by Sam Eisenstat on An Untrollable Mathematician | 1 like

This is somewhat related to
 by Vadim Kosoy on The set of Logical Inductors is not Convex | 0 likes

This uses logical inductors
 by Abram Demski on The set of Logical Inductors is not Convex | 0 likes

Nice writeup. Is one-boxing
 by Tom Everitt on Smoking Lesion Steelman II | 0 likes

Hi Alex! The definition of
 by Vadim Kosoy on Delegative Inverse Reinforcement Learning | 0 likes

A summary that might be
 by Alex Appel on Delegative Inverse Reinforcement Learning | 1 like

I don't believe that
 by Alex Appel on Delegative Inverse Reinforcement Learning | 0 likes

This is exactly the sort of
 by Stuart Armstrong on Being legible to other agents by committing to usi... | 0 likes

When considering an embedder
 by Jack Gallagher on Where does ADT Go Wrong? | 0 likes

The differences between this
 by Abram Demski on Policy Selection Solves Most Problems | 1 like

Looking "at the very
 by Abram Demski on Policy Selection Solves Most Problems | 0 likes