Path is irrelevant the goal state itself is the

Info icon This preview shows pages 14–23. Sign up to view the full content.

View Full Document Right Arrow Icon
path  is irrelevant; the goal state itself is the solution. Then, state space = space of “ complete ” configurations. Algorithm goal: - find optimal configuration (e.g., TSP), or, - find configuration satisfying constraints (e.g., n-queens) In such cases, can use  iterative improvement algorithms : keep a  single “ current ” state, and try to improve it.
Image of page 14

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
15 Iterative improvement example: vacuum world Simplified world:  2 locations, each may or not contain dirt, each may or not contain vacuuming agent. Goal of agent:  clean up the dirt. If path does not matter, do not need to keep track of it.
Image of page 15
16 Iterative improvement example: n-queens Goal:  Put n chess-game queens on an n x n board, with no two  queens on the same row, column, or diagonal. Here, goal state is initially unknown but is specified by constraints  that it must satisfy.
Image of page 16

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
17 Hill climbing (or gradient ascent/descent) Iteratively maximize “ value ” of current state, by replacing it by  successor state that has highest value, as long as possible.
Image of page 17
18 Hill climbing Note: minimizing a “value” function v(n) is equivalent to maximizing  –v(n), thus both notions are used interchangeably. Notion of “ extremization ”: find extrema (minima or maxima) of a  value function.
Image of page 18

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
19 Hill climbing Problem:  depending on initial state, may get stuck in local  extremum.
Image of page 19
20 Minimizing energy Let’s now change the formulation of the problem a bit, so that we can employ  new formalism: - let’s compare our state space to that of a physical system that is subject to  natural interactions, - and let’s compare our value function to the overall potential energy E of the  system. On every updating we have   0 Hence the dynamics of the system tend to move E toward a minimum.    We stress that there may  be different such states —  they are  local  minima.   Global minimization is  not guaranteed.   B C A Basin of  Attraction for C D E
Image of page 20

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
21 Boltzmann machines h The  Boltzmann Machine  of  Hinton, Sejnowski, and Ackley (1984) uses  simulated annealing  to escape local minima. To motivate their solution, consider how one might get a ball-bearing  traveling along the curve to "probably end up" in the deepest minimum.   The idea is to shake the box "about h hard"  — then the ball is more  likely to go from D  to C than from  C to D.  So, on average, the ball  should end up in  C's  valley.  
Image of page 21
22 Simulated annealing: basic idea From current state, pick a  random  successor state;
Image of page 22

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 23
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern