Anja

• AnjaNov 19, 2012, 4:44 AM

  5 points

  in reply to: timtyler’s comment on: Univer­sal agents and util­ity functions

  There is also a more detailed paper by Lattimore and Hutter (2011) on discounting and time consistency that is interesting in that context.

• AnjaNov 19, 2012, 4:26 AM

  4 points

  in reply to: AlexMennen’s comment on: Univer­sal agents and util­ity functions

  I am starting to see what you mean. Let’s stick with utility functions over histories of length m_k (whole sequences) like you proposed and denote them with a capital U to distinguish them from the prefix utilities. I think your Agent 4 runs into the following problem: modeled_action(n,m) actually depends on the actions and observations yx_{k:m-1} and needs to be calculated for each combination, so y_m is actually

  

  )

  which clutters up the notation so much that I don’t want to write it down anymore.

  We also get into trouble with taking the expectation, the observations x_{k+1:n} are only considered in modeling the actions of the future agents, but not now. What is M(yx_<k,yx_k:n) even supposed to mean, where do the x’s come from?

  So let’s torture some indices:

  

  =\textrm{arg}\max_{y_n}\sum_{x_{n:m_k}}U_n(yx_{1:n}\hat{y}_{n+1,k}(yx_{1:n})x_{n+1}\dots)

  

  x_{m_k})M(\.{y}\.{x}_{%3Ck}yx_{k:n-1}\hat{y}\underline{x}_{n:m_k}))

  where n>=k and

  

  This is not really AIXI anymore and I am not sure what to do with it, but I like it.

• AnjaNov 18, 2012, 3:06 AM

  0 points

  in reply to: AlexMennen’s comment on: Univer­sal agents and util­ity functions

  I second the general sentiment that it would be good for an agent to have these traits, but if I follow your equations I end up with Agent 2.

• AnjaNov 17, 2012, 10:03 PM

  0 points

  in reply to: AlexMennen’s comment on: Univer­sal agents and util­ity functions

  First, replace the action-perception sequence with an action-perception-utility sequence u1,y1,x1,u2,y2,x2,etc.

  This seems unnecessary. The information u_i is already contained in x_i.

  modeled_action(n, k) = argmax(y_k) uk(yx\<k, yx_k:n)*M(uyx_<k, uyx_k:n)

  This completely breaks the expectimax principle. I assume you actually mean something like

  

  =\textrm{arg}\max_{y_k}\sum_{x_k}u_k(\.{y}\.{x}_{%3Ck}y\underline{x}_{k:n})M(\.{y}\.{x}_{%3Ck}y\underline{x}_{k:n}))

  which is just Agent 2 in disguise.

• AnjaNov 17, 2012, 9:49 PM

  0 points

  in reply to: AlexMennen’s comment on: Univer­sal agents and util­ity functions

  This generalizes to the horizon problem: If at time k you only look ahead to time step m_k but have unlimited life span you will make infinitely large mistakes.

• AnjaNov 16, 2012, 8:46 AM

  0 points

  in reply to: Manfred’s comment on: Univer­sal agents and util­ity functions

  I would assume that it is not smart enough to forsee its own future actions and therefore dynamically inconsistent. The original AIXI does not allow for the agent to be part of the environment. If we tried to relax the dualism then your question depends strongly on the approximation to AIXI we would use to make it computable. If this approximation can be scaled down in a way such that it is still a good estimator for the agent’s future actions, then maybe an environment containing a scaled down, more abstract AIXI model will, after a lot of observations, become one of the consistent programs with lowest complexity. Maybe. That is about the only way I can imagine right now that we would not run into this problem.

• AnjaNov 15, 2012, 1:30 AM

  0 points

  in reply to: Manfred’s comment on: Univer­sal agents and util­ity functions

  I am pretty sure that Agent 2 will wirehead on the Simpleton Gambit, depending heavily on the number of time cycles to follow, the comparative advantage that can be gained from wireheading and the negative utility the current utility function assigns to the change.

  Agent 1 will have trouble modeling how its decision to change its utility function now will influence its own decisions later, as described in AIXI and existential despair. So basically the two futures look very similar to the agent except that for the part where the screen says something different and then it all comes down to whether the utility function has preferences over that particular fact.

• AnjaNov 15, 2012, 1:12 AM

  4 points

  in reply to: Kawoomba’s comment on: Univer­sal agents and util­ity functions

  I am quite sure that pareto optimality is untouched by the proposed changes, but I haven’t written down a proof yet.

Univer­sal agents and util­ity functions

• AnjaNov 3, 2012, 11:45 PM

  50 points

  on: 2012 Less Wrong Cen­sus/​Survey

  Took the survey. Does the god question include simulators? I answered under the assumption that it did not.