double strategytdexp4::getOutputBackgammonWinValue( const vector<double>& middles, const board& brd ) const
{
// special case - if the other player has taken any pieces in, the gammon win prob is zero
if( brd.bornIn1Raw() > 0 ) return 0;
// also if there are no other player pieces in the player's box, the backgammon win prob is zero
vector<int> checks( brd.checkers1Raw() );
bool foundOne = brd.hit1Raw() > 0;
if( !foundOne )
for( int i=0; i<6; i++ )
if( checks.at(i) > 0 )
{
foundOne = true;
break;
}
if( !foundOne ) return 0;
// otherwise calculate the network value
double val=0;
for( int i=0; i<nMiddle; i++ )
val += outputBackgammonWinWeights.at(i) * middles.at(i);
val += outputBackgammonWinWeights.at(nMiddle); // bias node
return 1. / ( 1 + exp( -val ) );
}
vector<double> strategytdexp4::getInputValues( const board& brd, int turn ) const
{
vector<double> inputs;
inputs.resize(198,0);
vector<int> checks = brd.checkers0Raw();
vector<int> otherChecks = brd.checkers1Raw();
int hit = brd.hit0Raw();
int otherHit = brd.hit1Raw();
int borneIn = brd.bornIn0Raw();
int otherBorneIn = brd.bornIn1Raw();
int i, j;
// we put values for the first player in the first half of the inputs and for the second player
// in the second half.
for( i=0; i<24; i++ )
{
// each spot gets four units. The first is 1 if there is at least one checker on the point,
// else 0; the 2nd is 1 if there are at least two checkers; the 3rd if there are at least
// three; and the fourth = max(0,(n-3)/2), where n=# of checkers. That's done for both players.
for( j=0; j<3; j++ )
{
if( checks.at(i) > j ) inputs.at(4*i+j) = 1;
if( otherChecks.at(i) > j ) inputs.at(4*i+j+99) = 1;
}
if( checks.at(i) > 3 ) inputs.at(4*i+3) = ( checks[i]-3 ) / 2.;
if( otherChecks.at(i) > 3 ) inputs.at(4*i+3+99) = ( otherChecks[i]-3 ) / 2.;
}
// one spot for each player records the number on the bar
inputs.at(96) = hit / 2.;
inputs.at(195) = otherHit / 2.;
// one spot for each player records the number born in
inputs.at(97) = borneIn / 15.;
inputs.at(196) = otherBorneIn / 15.;
// one spot for each player notes whose turn it is
inputs.at(98) = turn == 0 ? 1 : 0;
inputs.at(197) = turn == 0 ? 0 : 1;
return inputs;
}
void strategytdexp4::update( const board& oldBoard, const board& newBoard )
{
// get the values from the old board
vector<double> oldInputs = getInputValues( oldBoard, oldBoard.perspective() );
vector<double> oldMiddles = getMiddleValues( oldInputs );
double oldProbOutput = getOutputProbValue( oldMiddles );
double oldGammonWinOutput = getOutputGammonWinValue( oldMiddles, oldBoard );
double oldGammonLossOutput = getOutputGammonLossValue( oldMiddles, oldBoard );
double oldBgWinOutput = getOutputBackgammonWinValue( oldMiddles, oldBoard );
double oldBgLossOutput = getOutputBackgammonLossValue( oldMiddles, oldBoard );
// calculate all the partial derivatives we'll need (of output node values
// to the various weights)
int i, j;
// then do derivs of the prob nodes to each of the middle->input weights (that's a 2d array), and the derivs of each of
// the middle nodes to its weights->inputs.
double mid, input, v1, v2, v3, v4, v5;
for( i=0; i<nMiddle; i++ )
{
mid = oldMiddles.at(i);
v1 = outputProbWeights.at(i);
v2 = outputGammonWinWeights.at(i);
v3 = outputGammonLossWeights.at(i);
v4 = outputBackgammonWinWeights.at(i);
v5 = outputBackgammonLossWeights.at(i);
probDerivs.at(i) = mid * oldProbOutput * ( 1 - oldProbOutput );
gamWinDerivs.at(i) = mid * oldGammonWinOutput * ( 1 - oldGammonWinOutput );
gamLossDerivs.at(i) = mid * oldGammonLossOutput * ( 1 - oldGammonLossOutput );
bgWinDerivs.at(i) = mid * oldBgWinOutput * ( 1 - oldBgWinOutput );
bgLossDerivs.at(i) = mid * oldBgLossOutput * ( 1 - oldBgLossOutput );
for( j=0; j<198; j++ )
{
input = oldInputs.at(j);
probInputDerivs.at(i).at(j) = v1 * input * oldProbOutput * ( 1 - oldProbOutput ) * mid * ( 1 - mid );
gamWinInputDerivs.at(i).at(j) = v2 * input * oldGammonWinOutput * ( 1 - oldGammonWinOutput ) * mid * ( 1 - mid );
gamLossInputDerivs.at(i).at(j) = v3 * input * oldGammonLossOutput * ( 1 - oldGammonLossOutput ) * mid * ( 1 - mid );
bgWinInputDerivs.at(i).at(j) = v4 * input * oldBgWinOutput * ( 1 - oldBgWinOutput ) * mid * ( 1 - mid );
bgLossInputDerivs.at(i).at(j) = v5 * input * oldBgLossOutput * ( 1 - oldBgLossOutput ) * mid * ( 1 - mid );
}
probInputDerivs.at(i).at(198) = v1 * oldProbOutput * ( 1 - oldProbOutput ) * mid * ( 1 - mid );
gamWinInputDerivs.at(i).at(198) = v2 * oldGammonWinOutput * ( 1 - oldGammonWinOutput ) * mid * ( 1 - mid );
gamLossInputDerivs.at(i).at(198) = v3 * oldGammonLossOutput * ( 1 - oldGammonLossOutput ) * mid * ( 1 - mid );
bgWinInputDerivs.at(i).at(198) = v4 * oldBgWinOutput * ( 1 - oldBgWinOutput ) * mid * ( 1 - mid );
bgLossInputDerivs.at(i).at(198) = v5 * oldBgLossOutput * ( 1 - oldBgLossOutput ) * mid * ( 1 - mid );
}
probDerivs.at(nMiddle) = oldProbOutput * ( 1 - oldProbOutput );
gamWinDerivs.at(nMiddle) = oldGammonWinOutput * ( 1 - oldGammonWinOutput );
gamLossDerivs.at(nMiddle) = oldGammonLossOutput * ( 1 - oldGammonLossOutput );
bgWinDerivs.at(nMiddle) = oldBgWinOutput * ( 1 - oldBgWinOutput );
bgLossDerivs.at(nMiddle) = oldBgLossOutput * ( 1 - oldBgLossOutput );
// now calculate the next estimate of the outputs. That's known if the game is over; otherwise we use the network's
// estimate on the new board as a proxy. Note that the update fn is only ever called by the game when the player wins, not when
// the player loses, just because the winner is the last one to play. But we need to train on prob of losing a gammon too,
// so we flip board perspective and train again based on that.
bool trainGammonLoss = true;
bool trainGammonWin = true;
bool trainBgLoss = true;
bool trainBgWin = true;
double newProbOutput, newGammonWinOutput, newGammonLossOutput, newBgWinOutput, newBgLossOutput;
if( newBoard.bornIn0Raw() == 15 )
{
trainGammonLoss = false; // can't train the conditional prob of a gammon loss if there isn't a loss
trainBgLoss = false; // ditto for backgammon loss
newProbOutput = 1.;
if( newBoard.bornIn1Raw() == 0 ) // gammon or backgammon
{
newGammonWinOutput = 1.;
vector<int> checks( newBoard.checkers1Raw() );
bool foundOne = newBoard.hit1Raw() > 0;
if( !foundOne )
{
for( int i=0; i<6; i++ )
if( checks.at(i) > 0 )
{
foundOne = true;
break;
}
}
newBgWinOutput = foundOne ? 1 : 0;
}
else
{
newGammonWinOutput = 0.;
trainBgWin = false; // no gammon win so can't train conditional bg win prob
}
}
else if( newBoard.bornIn1Raw() == 15 )
{
trainGammonWin = false;
trainBgWin = false;
newProbOutput = 0.;
if( newBoard.bornIn0Raw() == 0 ) // gammon loss or backgammon loss
{
newGammonLossOutput = 1;
vector<int> checks( newBoard.checkers0Raw() );
bool foundOne = newBoard.hit0Raw() > 0;
if( !foundOne )
{
for( int i=18; i<24; i++ )
if( checks.at(i) > 0 )
{
foundOne = true;
break;
}
}
newBgLossOutput = foundOne ? 1 : 0;
}
else
{
newGammonLossOutput = 0;
trainBgLoss = false;
}
}
else
{
// estimate from the new board's outputs, remembering that after the move is done,
// the other player gets the dice.
vector<double> midVals( getMiddleValues( getInputValues( newBoard, !newBoard.perspective() ) ) );
newProbOutput = getOutputProbValue( midVals );
newGammonWinOutput = getOutputGammonWinValue( midVals, newBoard );
newGammonLossOutput = getOutputGammonLossValue( midVals, newBoard );
newBgWinOutput = getOutputBackgammonWinValue( midVals, newBoard );
newBgLossOutput = getOutputBackgammonLossValue( midVals, newBoard );
}
// train the nodes as appropriate
for( i=0; i<nMiddle; i++ )
{
outputProbWeights.at(i) += alpha * ( newProbOutput - oldProbOutput ) * probDerivs.at(i);
if( trainGammonWin )
outputGammonWinWeights.at(i) += alpha * ( newGammonWinOutput - oldGammonWinOutput ) * gamWinDerivs.at(i);
if( trainGammonLoss )
outputGammonLossWeights.at(i) += alpha * ( newGammonLossOutput - oldGammonLossOutput ) * gamLossDerivs.at(i);
if( trainBgWin )
outputBackgammonWinWeights.at(i) += alpha * ( newBgWinOutput - oldBgWinOutput ) * bgWinDerivs.at(i);
if( trainBgLoss )
outputBackgammonLossWeights.at(i) += alpha * ( newBgLossOutput - oldBgLossOutput ) * bgLossDerivs.at(i);
for( j=0; j<199; j++ )
{
middleWeights.at(i).at(j) += beta * ( newProbOutput - oldProbOutput ) * probInputDerivs.at(i).at(j);
if( trainGammonWin )
middleWeights.at(i).at(j) += beta * ( newGammonWinOutput - oldGammonWinOutput ) * gamWinInputDerivs.at(i).at(j);
if( trainGammonLoss )
middleWeights.at(i).at(j) += beta * ( newGammonLossOutput - oldGammonLossOutput ) * gamLossInputDerivs.at(i).at(j);
if( trainBgWin )
middleWeights.at(i).at(j) += beta * ( newBgWinOutput - oldBgWinOutput ) * bgWinInputDerivs.at(i).at(j);
if( trainBgLoss )
middleWeights.at(i).at(j) += beta * ( newBgLossOutput - oldBgLossOutput ) * bgLossInputDerivs.at(i).at(j);
}
}
outputProbWeights.at(nMiddle) += alpha * ( newProbOutput - oldProbOutput ) * probDerivs.at(nMiddle);
if( trainGammonWin )
outputGammonWinWeights.at(nMiddle) += alpha * ( newGammonWinOutput - oldGammonWinOutput ) * gamWinDerivs.at(nMiddle);
if( trainGammonLoss )
outputGammonLossWeights.at(nMiddle) += alpha * ( newGammonLossOutput - oldGammonLossOutput ) * gamLossDerivs.at(nMiddle);
if( trainBgWin )
outputBackgammonWinWeights.at(nMiddle) += alpha * ( newBgWinOutput - oldBgWinOutput ) * bgWinDerivs.at(nMiddle);
if( trainBgLoss )
outputBackgammonLossWeights.at(nMiddle) += alpha * ( newBgLossOutput - oldBgLossOutput ) * bgLossDerivs.at(nMiddle);
}