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| package bellman;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Random;
import Jama.*;
public class GridWorld_sql {
private boolean[][] grid;
private double[][] reward;
private int size_x;
private int size_y;
private int nbStates;
private double gamma = 0.5;
private Random rdmnum;
private long seed = 124;
private int MAX_REWARD = 20;
private HashMap<Integer,HashMap<String,Double>> action;
private HashMap<Integer, Integer> Rappel;
private HashMap<Integer, Integer> Rappel2;
private HashMap<String,HashMap<Integer,ArrayList<double[]>>> pi;
private ArrayList<String> dir;
GridWorld_sql(int size_x, int size_y, int n_rew) {
this.rdmnum = new Random(this.seed);
this.grid = new boolean[size_x][size_y];
this.reward = new double[size_x][size_y];
this.size_x = size_x;
this.size_y = size_y;
this.nbStates = size_x*size_y;
// list of actions
this.dir = new ArrayList<String>();
this.dir.add("left");
this.dir.add("up");
this.dir.add("right");
this.dir.add("down");
this.dir.add("stay");
for(int i=0; i<size_x; i++) {
for(int j=0; j<size_y; j++)
grid[i][j] = false;
}
//this.ChooseRdmState();
// put n_rew reward randomly
this.PutRdmReward(n_rew);
// initialize the random policy
this.InitRdmPol();
// initialize the transition matrices
this.InitTransitionMat();
}
// choose a random coordinate in the grid
private void ChooseRdmState() {
int i = rdmnum.nextInt(size_x);
int j = rdmnum.nextInt(size_y);
grid[i][j] = true;
}
// add a reward randomly on the grid
private void PutRdmReward(int n_rew) {
int n = 0;
while(n<n_rew) {
int i = rdmnum.nextInt(size_x);
int j = rdmnum.nextInt(size_y);
if(reward[i][j] == 0) {
reward[i][j] = rdmnum.nextInt(MAX_REWARD);
n++;
}
}
}
// return a state given a coordinate on the grid
private int GridToState(int i, int j) {
return (i+1)+size_x*(j+1);
}
// return the coordinate on the grid given the state
private int[] StateToGrid(int s) {
int[] index = new int[2];
index[1] = (int) s/size_x;
index[0] = s-index[1]*size_x;
return index;
}
// add the possible actions for all states
private void InitRdmPol() {
action = new HashMap<Integer,HashMap<String,Double>>();
HashMap<String,Double> mapinter = new HashMap<String,Double>();
HashMap<String,Integer> casesPossibles = new HashMap<String, Integer>();
double Prob = 0;
int count = 0;
this.Rappel = new HashMap<Integer, Integer>();
this.Rappel2 = new HashMap<Integer, Integer>();
for(int i=0; i<size_x; i++) {
for(int j=0; j<size_y; j++) {
count++;
int a = 0;
if(i-1 < 0) {
casesPossibles.put(dir.get(0),1);
} else {
casesPossibles.put(dir.get(0),0);
}
if(i+1 >= size_x) {
casesPossibles.put(dir.get(2),1);
} else {
casesPossibles.put(dir.get(2),0);
}
if(j-1 < 0) {
casesPossibles.put(dir.get(3),1);
} else {
casesPossibles.put(dir.get(3),0);
}
if(j+1 >= size_y) {
casesPossibles.put(dir.get(1),1);
} else {
casesPossibles.put(dir.get(1),0);
}
casesPossibles.put(dir.get(4),1);
for(String m : casesPossibles.keySet()) {
if(casesPossibles.get(m) == 1) {
a++;
}
}
Prob = 1/a;
for(int k=0; k<dir.size(); k++) {
mapinter.put(dir.get(k), Prob);
}
this.action.put(count, mapinter);
this.Rappel.put(count, GridToState(i,j));
this.Rappel2.put(GridToState(i,j),count);
mapinter.clear();
casesPossibles.clear();
}
}
}
// return the direction (on the grid) for a given action
private int[] getDirNeighbor(String act) {
int[] d = new int[2];
if(act.equals("left")) d[0]=-1;
if(act.equals("right")) d[0]=1;
if(act.equals("up")) d[1]=1;
if(act.equals("down")) d[1]=-1;
return d;
}
// To each state, give the reachable states given an action
private HashMap<Integer,ArrayList<double[]>> computeTrans(String act) {
HashMap<Integer,ArrayList<double[]>> trans = new HashMap<Integer,ArrayList<double[]>>();
int[] d = getDirNeighbor(act);
for(int i=0; i<size_x; i++) {
for(int j=0; j<size_y; j++) {
ArrayList<double[]> p = new ArrayList<double[]>();
double[] q = new double[2];
if(i+d[0] < 0 || i+d[0] >= size_x || j+d[1] < 0 || j+d[1] >= size_y) {
q[0] = GridToState(i+d[0], j+d[1]);
q[1] = 0;
p.add(q);
} else {
q[0] = GridToState(i+d[0], j+d[1]);
q[1] = 1.0;
p.add(q);
}
trans.put(GridToState(i,j), p);
}
}
return trans;
}
// initiate values of P
private void InitTransitionMat() {
pi = new HashMap<String,HashMap<Integer,ArrayList<double[]>>>();
for(String act : this.dir) {
pi.put(act,computeTrans(act));
}
}
// compute the vector r
private double[] computeVecR() {
double[] R = new double[nbStates];
for(int s=0; s<nbStates; s++) {
double sum = 0;
HashMap<String,Double> a = action.get(s);
int c= Rappel.get(s);
int[] coord = StateToGrid(c);
// compute the reward obtained from state s, by doing all potential action a
for(String act : this.dir) {
ArrayList<double[]> d = pi.get(act).get(c);
double[] doub = d.get(0);
double e = doub[1];
sum += a.get(act) * e * reward[coord[0]][coord[1]];
}
R[s] = sum;
}
return R;
}
private double[][] computeMatP() {
double[][] P = new double[nbStates][nbStates];
for(int s=0; s<nbStates; s++) {
int state = Rappel.get(s);
// from state s, compute P^{\pi}(s,s')
for(String act : this.dir) {
int[] coord = StateToGrid(state);
int[] d = getDirNeighbor(act);
coord[0] = coord[0]+ d[0];
coord[1] = coord[1]+ d[1];
int newstate = GridToState(coord[0], coord[1]);
int s2 = Rappel2.get(newstate);
P[s][s2] = action.get(s).get(act) * pi.get(act).get(state).get(0)[1];
}
}
return P;
}
// converting to matrix for the inverse
private Matrix BuildMatA() {
double[][] f_A = new double[nbStates][nbStates];
double[][] P = computeMatP();
for(int s=0; s<nbStates; s++) {
f_A[s][s] = 1;
for(int sp=0; sp<nbStates; sp++) {
f_A[s][sp] -= this.gamma*P[s][sp];
}
}
Matrix matP = new Matrix(f_A);
return new Matrix(f_A);
}
// converting to matrix for the inverse
private Matrix BuildMatb() {
double[] vec_b = computeVecR();
double[][] b = new double[vec_b.length][1];
for(int i=0; i<vec_b.length; i++) {
b[i][0] = vec_b[i];
}
return new Matrix(b);
}
// solving the linear system
private double[][] SolvingP() {
Matrix x = BuildMatA().solve(BuildMatb());
return x.getArray();
}
private void showGrid() {
for(int i=0; i<size_x; i++) {
for(int j=0; j<size_y; j++)
System.out.print((this.grid[i][j]?1:0));
System.out.println();
}
}
private void showRewGrid() {
for(int i=0; i<size_x; i++) {
for(int j=0; j<size_y; j++)
System.out.print(this.reward[i][j]+" ");
System.out.println();
}
}
// improve the policy by looking at the best_a Q(s,a)
private void ImprovePolicy(double[][] V) {
action = new HashMap<Integer,HashMap<String,Double>>();
for(int i=0; i<size_x; i++) {
for(int j=0; j<size_y; j++) {
// TODO
}
}
}
public static void main(String[] args) {
GridWorld_sql gd = new GridWorld_sql(5,5,2);
gd.showRewGrid();
double[][] V = gd.SolvingP();
// show V
for(int i=0; i<gd.nbStates; i++) {
if(i%5==0) System.out.println();
System.out.print(V[i][0]+" ");
}
System.out.println("\n");
// Improve the policy !
gd.ImprovePolicy(V);
}
} |
