Tuesday, January 27, 2009

Stochastic vs. Limited Senses

While reading through the book today, I came up with a question. Where's the line between a lack of good senses and a stochastic environment? The examples we've had in class of what makes an environment stochastic (e.g. car trouble with the taxi) could be monitored with an appropriately advanced sensor array. An omniscient agent (or omniscient objective observer) would consider every environment fully deterministic.
So is there a clear line between the two? I would think that something that is beyond practical (such as monitoring the surfaces of a taxi's tires to know when it will weaken enough to burst from the pressure) would be in the stochastic column, but what about not knowing that a tire is going flat, because the taxi lacks a tire pressure monitoring system (which is practical)?


  1. This is a good question. When we do not have complete models of a world, then what is inherently a "deterministic world" may well look like a non-deterministic/stochastic one to the agent.

    About the only "natural" world that can be said to be inherently stochastic is again the quantum world. In every other case, you can--if you prefer--think that the underlying world is deterministic and we just didn't model it adequately. [Even in the quantum case, many scientists--Einstein in particular--fought tooth and nail to convince the scientific community that the uncertainty is *not* inherent and that we get it only because we are not modeling the system completely. See the celebrated EPR paradox--and how it was eventually shown that the "paradox" is really not a paradox and quantum uncertainty is very much inherent: http://en.wikipedia.org/wiki/EPR_paradox ]

    Notice that the "completeness" we are talking about doesn't have to involve as high a granularity as "modeling the imperfections on the coin surface and the eddies in the room air to predict the coin toss outcome".

    Remember that our ancestors, not too long ago, assumed that many phenomena that we now know as deterministic--such as eclipses-- are actually non-deterministic (and thus would associate with them superstitions like "the eclipse shows the gods being angry with the ruler" etc).


    ps: Of course, we humans are also equally adept at introducing determinism where there is none (e.g. my favorite god created this whole darned entire universe and all its life forms over a weekend some 6000 years ago....

    Check out http://www.tv.com/the-simpsons/lisa-the-skeptic/episode/1471/summary.html

    where Lisa laments that the expected answer to every question on her science test was "God made it" ;-)

  2. I think a good way to separate Stochastic and Deterministic is to look at the states and see if you could determine all the possible states. For example the Taxi driver, I could map all the possible states that I know of, but I am sure it could encounter something I haven't thought of. It seems almost an infinite amount of states could occur. This goes back to the amount of knowledge that we have. On the other hand If I created a game where if a 1 was picked I win if a 2 was picked I lose. Here I can easily map every state in the game.

    My question is if there was a problem that was programmed to be Stochastic, but with more knowledge, sensors, actuators available could it be made into a deterministic problem?

    Also just to clarify, should we consider a problem stochastic if we can't create an agent that is deterministic because lack of knowledge, sensors, actuators. Or should we consider it deterministic but the agent is stochastic?

  3. Firstly I think that the book stresses that the stochastism must be viewed from the point of view of the agent.
    True that there is a strong tendency to take Inaccesssable environments as stochastic.
    But if we continue to expand the openended side of the environment and expect the sensors to play catch we will be in a pickle.
    I think after a reasonable delibration and selection over the choice of sensors and backing the data with world knowledge we should ask our selves "With the information from the sensors and the world knowledge is the environment accessible?"
    If it is then we can say that our actions are deterministic, if not then I think it is stochastic and the degree of non-determinism will be proportional to what is deemed as ungatherable percepts affecting the task environment.
    What do you think?

  4. What about if an agent had poor parts, given everything else was the same. Could that have any affect on whether the agent's environment was described as deterministic or stochastic. If we look at the vacuum agent again what would happened if the agent detected dirt, went to suck it but because of a poor design of the hardware could not pick up all the dirt ever time. Then the action could not be deterministic since there is only a probability that the action would lead to having a clean room. If we were to combine this fault with removing the sensing ability of the agent, I believe the agent could never reach the goal of having both rooms clean.


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