Artificial Intelligence Lecture 6

Transcription

1 Artificial Intelligence Lecture 6

2 Lecture plan AI in general (ch. 1) Search based AI (ch. 4) search, games, planning, optimization (ch. 8) applied AI techniques in robots, software agents,... Knowledge representation (ch. 2) semantic networks, frames, logic, resolution Expert systems (ch. 3) forward/backward chaining, uncertainty, baysian networks Natural language processing (ch. 5) Machine learning (ch. 7) version spaces, decision trees, classification, neural networks 2

3 Optimization Problem Given a complex function F(x) with discrete arguments x, find x that gives the maximum (or minimum) value. Often F(x) is fairly easy to compute for individual values of X, but may have a complicated structure making it impossible to solve analytically Complete evaluation of F(x) for every x too expensive 3

4 Hill climbing Start with some initial guess for x, evalute F(x) Find all the neighbours N(x) of x Evalute F(x 2 ) for each neighbour x 2 Set x to be the x 2 that gives the highest value Repeat a fix amount of times or until no change 4

5 Example problem Traveling salesman problem Given a list of cities to visit, find an order to visit tham that minimizes the total length to travel Each city is given by a name, and distances to the other cities. 5

6 Traveling salesman cities = ["a", "b", "c", "d", "e", "f"] distance={} for i in cities: distance[i] = {} distance[i][i] = 0 def dist(a,b,cost): distance[a][b] = cost distance[b][a] = cost dist("a","b",3) ; dist("a","c",1) ; dist("a","d",3) ; dist("a","e",3);... dist("b","c", 3) ; dist("b","d", 1) ; dist("b","e", 2) ; dist("b","f", 2) dist("c","d", 3) ; dist("c","e", 1) ; dist("c","f", 1) dist("d","e", 4) ; dist("d","f", 2) dist("e","f", 5) # Takes an ordered of the cities and gives the total length def evaluate(l): cost = distance[l[0]][l[ 1]] for i in range(0,len(l) 1): cost = cost + distance[l[i]][l[i+1]] return cost 6

7 Evaluating the costs >>> print(cities,"costs",evaluate(cities) ) ['a', 'b', 'c', 'd', 'e'] costs 16 >>> L=["a", "c", "b", "e", "d"] >>> print( L, "costs", evaluate(l) ) ['a', 'c', 'b', 'e', 'd'] costs 13 7

8 Using Hill climbing to find a good path def HC(): L,e = cities, evaluate(cities) while True: bestl, beste = L, e print(l, "costs", e) for i in range(0,len(l) 1): for j in range(i,len(l)): L2 = list(l) L2[i], L2[j] = L2[j], L2[i] e2 = evaluate(l2) if e2 < beste: bestl, beste = L2, e2 if beste == e: return bestl, beste L,e=bestL, beste 8

9 Using Hill climbing to find a good path ['a', 'b', 'c', 'd', 'e', 'f'] costs 20 ['a', 'e', 'c', 'd', 'b', 'f'] costs 12 ['c', 'e', 'a', 'd', 'b', 'f'] costs 11 ['c', 'f', 'a', 'd', 'b', 'e'] costs 10 ['c', 'a', 'f', 'd', 'b', 'e'] costs 9 (['c', 'a', 'f', 'd', 'b', 'e'], 9) 9

10 Gradient search Hillclimbing but for continous variables Optimizing F(x) for continous x HC equivalent to: x = x + b * d/dx f(x) 10

11 Problem with Hill climbing / gradient search Algorithm can get stuck in local minim / maxima plateau's ridge 11

12 Simulated annealing Simulated annealing Inspired by the physical process of annealing Reduces the chance of getting stuck in local optima Algorithm Start at random state X and with a radius R Find a random neighbour X2 that is within radius D from X Evalute X2, if better than X then set X = X2 Iterate, with smaller and smaller value on R TSP example Random neighbour X2 is the result of doing R switches of cities (eg. 3, 4 switches at once). 12

13 Genetic algorithms Basic idea Genomes that represent solutions Evaluation of genomes performance The fittest individuals (best solutions) survive and create offspring (slightly different solutions) mutations and cross over in offspring Typical problems Optimization problems (TSP), circuit layout, electric design... Genetic programming (each genome is a functional program) 13

14 Genetic algorithms Algorithm: GeneticAlgorithm begin t = 0 P(t) = initial population evaluate P(t) while (not terminal condition): t = t+1 select and update P(t) from P(t 1) evaluate P(t) return best individual of P(t) end Initial population: Usually random solutions (individuals). Selection: Select the N fittest individuals from the whole population. Update: Create offspring by mutation and crossovers. Terminal condition: After X iterations, good enough solution, convergence speed, etc. 14

15 Coding in GA Assumption: a potential solution to the problem can be represented as a set of parameters. The parameters are joined together to form a string of values. Example: Maximize the function f(x,y,z). A solution is a triple with values for x, y and z. If we represent these values in binary notation with 16 digits we may get as a possible solution: x = y = z = Possible encoding:

16 Fitness function Fitness function: Return a numerical value for each individual representing it's utility. Example: Problem: Maximize the function f(x,y,z). fitness function = f The fitness function can measure a combination of things: Eg: Design of product. Fitness function is combination of size of product, functionality of product, construction cost, construction time, transportion cost etc. 16

17 Reproduction Selection: favouring good solutions. Crossover: for rapid exploration of the search space. Mutation: For randomness, no point has zero probability. 17

18 Example: Genetic Algorithm for TSP How can the genome code only valid solutions List of cities: risk visiting same city twice! Crossover Combining half of the list from each parent risk missing some cities in child solution! Mutation Changing permutation of list ok? 18

19 Example: choice of genome for TSP Let the genome be a list of priorities London 10, Paris 20, Örebro 5, Stockholm 8 means visit Paris London Stockholm > Örebro Paris Mutation Add/decrease priority of random city Crossover Take half the priorities from each parent Mix: [(L,10), (P, 20), (O, 5), (S, 8)] and [(L, 30), (P, 20), (O, 11), (S, 3)] using crossover point at index 2 gives: [(L, 10), (P, 20), (O, 11), (S, 3)] and [(L, 30), (P, 20), (O, 5), (S, 8) This guarantees that only valid solutions can be generated! 19

20 Example: initial population, breeding Let the genome be a list of priorities London 10, Paris 20, Örebro 5, Stockholm 8 means visit Paris London Stockholm > Örebro Paris Initial population: Random list of priorities Breeding a solution Population size, Mutation rate, Crossover selection scheme Stopping critera? Ex: 500 individuals, 10% mutation rate, keep 100 best individuals. 400 children with random parents from survivors. Run 50 generations. 20

21 Example: initial population, breeding def GA(): Individuals=[] for i in range(0,500): Individuals.append([randomGenome(),0]) for generation in range(0,50): # Evaluate all individuals for Ind in Individuals: Ind[1] = evaluate(genome2list(ind[0])) # Sort all individuals Individuals.sort(key=lambda g: g[1]) best=individuals[0][1] for i in range(100,len(individuals)): Individuals[i][0]=mixGenomes(Individuals[random.randrange(0,100)][0], Individuals[random.randrange(0,100)][0]) for i in range(0,len(individuals)): mutategenome(individuals[i][0]) return best 21

22 Characteristics of GA Blind search, non optimal solutions Use of codings, not decision variables Search from set of possible solutions, not from a point Use of randomized operators, non deterministic Good for hard problems / problems lacking specialized solutions Acceptably good solutions acceptably fast Genetic algorithms have no guarantee to work Depends on problem type, problem representation (genomes), implementation of mutations/crossover, population size etc. 22

23 Application of GA Numerical function optimisations Eg. sensor calibration, training of neural networks Image processing Eg. recognising persons, objects Combinatorial optimization task Eg. the traveling salesman problem, job scheduling, bin packing Design tasks Eg. graph layout, floor layout, circuit layouts Machine learning in control... 23

24 Lecture plan AI in general (ch. 1) Search based AI (ch. 4) search, games, planning, optimization (ch. 8) applied AI techniques in robots, software agents,... Knowledge representation (ch. 2) semantic networks, frames, logic, resolution Expert systems (ch. 3) forward/backward chaining, uncertainty, baysian networks Natural language processing (ch. 5) Machine learning (ch. 7) version spaces, decision trees, classification, neural networks 24

25 What is an agent? Russel and Norvig: An agent is anything that can be viewed as perceiving it's environment through sensors and acting upon that environment through effectors. Franklin's definition: An autonomous agent is a system situated within and as part of an environment that senses that environment and acts on it, over time, in pursuit of it's own agenda and so as to effect what it senses in the future. 25

26 What is an agent An agent interacts with its environments Perceive through sensors Human agent: eyes, ears, nose etc. Robotic agent: cameras, infrared range finder etc. Soft agent: receiving keystrokes, network packages etc. Act through actuators Human agent: hands, legs, mouse etc. Robotic agent: arms, wheels, motors etc. Soft agent: display, sending network packages etc. A rational agent is One that does the right thing Or one that acts so as to achieve best expected outcome 26

27 Example A simulated world Array of cells: dirty, clean, obstacle... Agent (vacuum cleaner) Percepts locations and cell contents here, e.g. [A, Dirty], [B, Clean] Actions: Right, Left, Suck, NoOp 27

28 A Vacuum cleaner agent Tabulation of agent functions A simple agent program 28

29 Rational agents Select action expected to maximize the performance measure given evidence provided by percept sequence to date and any prior knowledge. Performance measure defined the success criteria Percept sequence required to not just react to local percepts Prior knowledge of environment 29

30 Rational agents Select action expected to maximize the performance measure given evidence provided by percept sequence to date and any prior knowledge. Rational thinking may still fail due to lack of information Selecting the right performance measure and collecting information part of the problem Example: build a vacuum cleaning robot and give the criteria that all visible dirt should be gone when I get home Scenario 1: it doesn't see any dirt so it does nothing Scenario 2: it hides the dirt Success criteria: collect as much dirt as possible Scenario 3: It goes outdoors and vaccums up a big pile of dirt 30

31 Rational agents What is rational? The performance measure The percept sequence What an agent knows about the environment take all previous percepts into account. Model the environment The actions that the agent can perform consider also future effects of these actions. An ideal rational agent should do whatever action is expected to maximize it's performance measure, on the basis of the evidence provided by the percept sequence and whatever built in knowledge the agent has. Not forgetting to do actions in order to obtain useful information! 31

32 Agent can be described as a mapping from percept sequences to actions. Specifying which action to take for each possible percept sequence provides the ideal agent. cf. game playing, optimal strategies Table in memory mapping percept sequences to actions Size of table too large To difficult to build that table Lack of generality 32

33 Rationality versus perfection How and when should we evaluate the performance measure? Is it better to take an immediate action giving a small increase in performance, or a an action that will/might give a larger increase in performance later? Example: should I withdraw my money from the bank, or wait until next year when I have more interest? Or 100 years after that?... Amortized costs and utilities Autonomy The utility of getting a reward in the distant future is less (but not zero!) than compared to getting it right now. How much less? Rationality requires exploration, learning and autonomy 33