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Markov, find a selection strategy which maximizes probability

  1. Mar 12, 2012 #1
    1. The problem statement, all variables and given/known data
    There are three patchs in which an animal can forage.
    Patch 1: Risk of predation is 0. Probability of finding food is 0. Energy value is 0.
    Patch 2: Risk of predation is 0.004. Probability of finding food is 0.4 and energy gain is 3.
    patch 3: risk of predation is 0.02. Probability of finding food is 0.6 and energy gain is 5.

    Foraging in any patch uses one unit of energy reserves. Energy reserves below 4 indicate death. maximum energy capacity for animal is ten units.

    Solve this problem for 20 foraging periods to find a patch selection strategy which maximizes the animals probability of survival over this period.

    2. Relevant equations

    ?

    3. The attempt at a solution

    Three patchs; N=3
    States: risk, food findings and energy gain.
    action: Choosing patchs 1, 2 or 3.

    How do I solve this problem?
     
    Last edited: Mar 12, 2012
  2. jcsd
  3. Mar 12, 2012 #2

    Ray Vickson

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    You could try to set it up as a standard Markov Decision Problem, where you want to maximize the expected value of a reward function. In this case, the reward is r = 1 if energy at t = 20 is >= 5 and is 0 otherwise. You need to identify states, decisions and decision-dependent transition probabilities.

    RGV
     
  4. Mar 12, 2012 #3
    Why is the reward r=1 if energy is >= 5 (not 4?) and why 0 otherwice?
     
  5. Mar 12, 2012 #4
    Do you have any sample problems to show me?
     
  6. Mar 12, 2012 #5

    Ray Vickson

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    OK, it should be r = 1 if energy >= 4 and 0 otherwise.

    RGV
     
  7. Mar 12, 2012 #6

    Ray Vickson

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    Do you not have a textbook? Are there no lecture notes? Anyway, Google is your friend: try "Markov decision problem".

    RGV
     
  8. Mar 12, 2012 #7
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