Pei, many thanks for your comments. Good input on rationality and AIXI.
Kind regards, Stefan On Nov 14, 2007 10:13 PM, Pei Wang <[EMAIL PROTECTED]> wrote: > Stefan, > > Though I agree with most of your analysis on inter-agent relationship, > I don't share your conception of rationality. > > To me, "rationality" itself is relativistic, that is, what > behavior/action is rational is always judged according to the > assumptions and postulations on a system's goal, knowledge, resources, > etc. There is no single "rationality" that can be used in all > situations. > > Similar ideas have been argued by I.J. Good, H.A. Simon, and some others. > > In the context of AGI, AIXI is an important model of rationality, but > not the only one. At least there are NARS and OSCAR, which are based > on different assumptions about the system and its environment. Being > impractical is not the only problem of AIXI. As soon as one of its > assumptions (infinite resources is only one of them) is dropped, its > conclusions become inapplicable. > > Some people think "in theory" we should accept unrealistic > assumptions, like infinite resources, since they lead to rigorous > models; then, in implementation, the realistic restrictions (on > resources etc.) can be introduced, which lead to approximations of the > idealized model. What they fail to see is that when a new restriction > is added, it may change the problem to the extent that the "ideal > theory" becomes mostly irrelevant. To me, it is much better to start > with more realistic assumptions in the first place, even though it > will make the problem harder to solve. > > Pei > > On Nov 13, 2007 10:40 PM, Stefan Pernar <[EMAIL PROTECTED]> wrote: > > Would be great if people could poke the following with their > metaphorical > > sticks: > > > > > > Imagine two agents A(i) each one with a utility function F(i), > capability > > level C(i) and no knowledge as to the other agents F and C values. Both > > agents are given equal resources and are tasked with devising the most > > efficient and effective way to maximize their respective utility with > said > > resources. > > > > Scenario 1: Both agents have fairly similar utility functions F(1) = > F(2), > > level of knowledge, cognitive complexity, experience - in short > capability > > C(1) = C(2) - and a high level of mutual trust T(1->2) = T(2->1) = 1. > They > > will quickly agree on the way forward, pool their resources and execute > > their joint plan. Rather boring. > > > > Scenario 2: Again we assume F(1) = F(2), however C(1) > C(2) - again > T(1->2) > > = T(2->1) = 1. The more capable agent will devise a plan, the less > capable > > agent will provide its resources and execute the plan trusted by C(2). A > bit > > more interesting. > > > > Scenario 3: F(1) = F(2), C(1) > C(2) but this time T(1->2) = 1 and > T(2->1) = > > 0.5 meaning the less powerful agent assumes with a probability of 50% > that > > A(1) is in fact a self serving optimizer who's difference in plan will > turn > > out to be decremental to A(2) while A(1) is certain that this is all > just > > one big misunderstanding. The optimal plan devised under scenario 2 will > now > > face opposition by A(2) although it would be in A(2)'s best interest to > > actually support it with its resources to maximize (F2) while A(1) will > see > > A(2)'s objection as being detrimental to maximizing their shared utility > > function. Fairly interesting: based on lack of trust and differences in > > capability each agent perceives the other agent's plan as being > irrational > > from their respective points of view. > > > > Under scenario 3, both agents now have a variety of strategies at their > > disposal: > > deny pooling of part or all of ones resources = If we do not do it my > way > > you can do it alone. > > use resources to sabotage the other agent's plan = I must stop him with > > these crazy ideas! > > deceive the other agent in order to skew how the other agent is > deploying > > strategies 1 and 2 > > spend resources to explain the plan to the other agent = Ok - let's help > him > > see the light > > spend resources on self improvement to understand the other agent's plan > > better = Let's have a closer look, the plan might not be so bad after > all > > strike a compromise to ensure a higher level of pooled resources = If we > > don't compromise we both loose out > > > > Number 1 is a given under scenario 3. Number 2 is risky, particularly as > it > > would cause a further reduction in trust on both sides if this strategy > gets > > deployed assuming the other party would find out similarly with number > 3. > > Number 4 seems like the way to go but may not always work particularly > with > > large differences in C(i) among the agents. Number 5 is a likely > strategy > > with a fairly high level of trust. Most likely however is strategy 6. > > > > Striking a compromise is trust building in repeated encounters and thus > > promises less objection and thus higher total payoff the next times > around. > > > > Assuming the existence of an arguably optimal path leading to a > maximally > > possible satisfaction of a given utility function anything else would be > > irrational. Actually such a maximally intelligent algorithm exists in > the > > form of Hutter's universal algorithmic agent AIXI. The only problem > being > > however that the execution of said algorithm requires infinite resources > and > > is thus rather unpractical as every decision will always have to be made > > under resource constrains. > > > > Consequentially every decision will be irrational to that degree that it > > differs from the unknowable optimal path that AIXI would produce. Throw > in a > > lack of trust and varying levels of capability among the agents and all > > agents will always have to adopt their plans and strike a compromise > based > > on the other agent's relativistic irrationality independent of their > > capabilities in oder to minimize the other agents objection cost and > thus > > maximizing their respective utility function. -- > > Stefan Pernar > > 3-E-101 Silver Maple Garden > > #6 Cai Hong Road, Da Shan Zi > > Chao Yang District > > 100015 Beijing > > P.R. CHINA > > Mobil: +86 1391 009 1931 > > Skype: Stefan.Pernar ________________________________ > > This list is sponsored by AGIRI: http://www.agiri.org/email > > To unsubscribe or change your options, please go to: > > http://v2.listbox.com/member/?&; > > ----- > This list is sponsored by AGIRI: http://www.agiri.org/email > To unsubscribe or change your options, please go to: > http://v2.listbox.com/member/?&; > -- Stefan Pernar 3-E-101 Silver Maple Garden #6 Cai Hong Road, Da Shan Zi Chao Yang District 100015 Beijing P.R. CHINA Mobil: +86 1391 009 1931 Skype: Stefan.Pernar ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244&id_secret=64931915-a43013
