Lecture 17

• Lecture 17
  • video
  • Convex Curve
  • Hill-Climbing algo (steepest-ascent/descent)
  • Random Restart Hill-Climbing algo
  • Simulated Annealing

video

link

Convex Curve

• take any 2 points within region under curve, join them by straight line, if that remains within region, function is convex

• are good bcz have single max/minima

Hill-Climbing algo (steepest-ascent/descent)

• steepest-ascent version
• is is simply a loop that continually moves in dirn of increasing value that is uphill
• terminates when it reaches a peak where no neighbor has higher value
• algo does not match a search tree so that data structure fort current node need only record state and value of objective fn
• hill climbing does not look ahead beyond immediate neighbors of current state

• gets stuck at local max/min (saddle point)

Random Restart Hill-Climbing algo

• once I get stack (idk local pe ho ya global pe)
  • choose another random value
  • after some number of tries, I might reach global max
  • tho tab bhi i will not know ki I have reached or not global max/min
• for a convex curve, always we will reach same global maximum

• prob ki initialization left wale region me aaye = 5/100, so .95 prob ki I get stuckj with local max

Simulated Annealing

• ball hai slope hai
• shake the table, taki ball bounces on some side
• depending upon temp, some barriers I can cross, some I cannot
• depends upon ball me kitni energy hai
• t->0 is hill finding
• T->infinity = random walk