// Bellman recursion using row rearrangement
//[[Rcpp::export]]
Rcpp::List Bellman(const arma::mat& grid,
Rcpp::NumericVector reward_,
const arma::cube& scrap,
Rcpp::NumericVector control_,
const arma::cube& disturb,
const arma::vec& weight) {
// Passing R objects to C++
const std::size_t n_grid = grid.n_rows;
const std::size_t n_dim = grid.n_cols;
const arma::ivec r_dims = reward_.attr("dim");
const std::size_t n_pos = r_dims(3);
const std::size_t n_action = r_dims(2);
const std::size_t n_dec = r_dims(4) + 1;
const arma::cube
reward(reward_.begin(), n_grid, n_dim * n_action * n_pos, n_dec - 1, false);
const arma::ivec c_dims = control_.attr("dim");
arma::cube control2;
arma::imat control;
bool full_control;
if (c_dims.n_elem == 3) {
full_control = false;
arma::cube temp_control2(control_.begin(), n_pos, n_action, n_pos, false);
control2 = temp_control2;
} else {
full_control = true;
arma::mat temp_control(control_.begin(), n_pos, n_action, false);
control = arma::conv_to<arma::imat>::from(temp_control);
}
const std::size_t n_disturb = disturb.n_slices;
// Bellman recursion
arma::cube value(n_grid, n_dim * n_pos, n_dec);
arma::cube cont(n_grid, n_dim * n_pos, n_dec - 1, arma::fill::zeros);
arma::mat d_value(n_grid, n_dim);
Rcpp::Rcout << "At dec: " << n_dec - 1 << "...";
for (std::size_t pp = 0; pp < n_pos; pp++) {
value.slice(n_dec - 1).cols(n_dim * pp, n_dim * (pp + 1) - 1) =
scrap.slice(pp);
}
for (int tt = (n_dec - 2); tt >= 0; tt--) {
Rcpp::Rcout << tt;
// Approximating the continuation value
for (std::size_t pp = 0; pp < n_pos; pp++) {
cont.slice(tt).cols(n_dim * pp, n_dim * (pp + 1) - 1) =
Expected(grid,
value.slice(tt + 1).cols(pp * n_dim, n_dim * (pp + 1) - 1),
disturb, weight);
}
Rcpp::Rcout << "..";
// Optimise value function
if (full_control) {
BellmanOptimal(grid, control, value, reward, cont, tt);
} else {
BellmanOptimal2(grid, control2, value, reward, cont, tt);
}
Rcpp::Rcout << ".";
}
return Rcpp::List::create(Rcpp::Named("value") = value,
Rcpp::Named("expected") = cont);
}
//[[Rcpp::export]]
Rcpp::List AddDualBounds(const arma::cube& path,
Rcpp::NumericVector control_,
Rcpp::Function Reward_,
Rcpp::Function Scrap_,
const arma::cube& mart,
const arma::ucube& path_action) {
// Extract parameters
const std::size_t n_dec = path.n_slices;
const std::size_t n_path = path.n_rows;
const std::size_t n_dim = path.n_cols;
const arma::ivec c_dims = control_.attr("dim");
const std::size_t n_pos = c_dims(0);
const std::size_t n_action = c_dims(1);
arma::imat control; // full control
arma::cube control2; // partial control
bool full_control;
if (c_dims.n_elem == 3) {
full_control = false;
arma::cube temp_control2(control_.begin(), n_pos, n_action, n_pos, false);
control2 = temp_control2;
} else {
full_control = true;
arma::mat temp_control(control_.begin(), n_pos, n_action, false);
control = arma::conv_to<arma::imat>::from(temp_control);
}
// Initialise with scrap value
arma::cube primals(n_path, n_pos, n_dec);
primals.slice(n_dec - 1) = Rcpp::as<arma::mat>(
Scrap_(Rcpp::as<Rcpp::NumericMatrix>(Rcpp::wrap(path.slice(n_dec - 1)))));
arma::cube duals = primals;
// Perform the backward induction
arma::uword policy;
arma::cube reward(n_path, n_action, n_pos);
if (full_control) { // For the full control case
arma::uword next;
for (int tt = (n_dec - 2); tt >= 0; tt--) {
reward = Rcpp::as<arma::cube>(Reward_(
Rcpp::as<Rcpp::NumericMatrix>(Rcpp::wrap(path.slice(tt))), tt + 1));
#pragma omp parallel for private(policy, next)
for (std::size_t ii = 0; ii < n_path; ii++) {
for (std::size_t pp = 0; pp < n_pos; pp++) {
// Primal values
policy = path_action(ii, pp, tt) - 1; // R to C indexing
next = control(pp, policy) - 1;
primals(ii, pp, tt) = reward(ii, policy, pp) + mart(ii, next, tt)
+ primals(ii, next, tt + 1);
// Dual values
next = control(pp, 0) - 1;
duals(ii, pp, tt) = reward(ii, 0, pp) + mart(ii, next, tt)
+ duals(ii, next, tt + 1);
for (std::size_t aa = 1; aa < n_action; aa++) {
next = control(pp, aa) - 1;
duals(ii, pp, tt) = std::max(reward(ii, aa, pp) + mart(ii, next, tt)
+ duals(ii, next, tt + 1), duals(ii, pp, tt));
}
}
}
}
} else { // Positions evolve randomly
arma::rowvec mod(n_pos);
arma::rowvec prob_weight(n_pos);
for (int tt = (n_dec - 2); tt >= 0; tt--) {
reward = Rcpp::as<arma::cube>(Reward_(
Rcpp::as<Rcpp::NumericMatrix>(Rcpp::wrap(path.slice(tt))), tt + 1));
#pragma omp parallel for private(policy, prob_weight, mod)
for (std::size_t ii = 0; ii < n_path; ii++) {
for (std::size_t pp = 0; pp < n_pos; pp++) {
// Primal values
mod = primals.slice(tt + 1).row(ii) + mart.slice(tt).row(ii);
policy = path_action(ii, pp, tt) - 1;
prob_weight = control2.tube(pp, policy);
primals(ii, pp, tt) =
reward(ii, policy, pp) + arma::sum(prob_weight % mod);
// Dual values
mod = duals.slice(tt + 1).row(ii) + mart.slice(tt).row(ii);
prob_weight = control2.tube(pp, 0);
duals(ii, pp, tt) = reward(ii, 0, pp) + arma::sum(prob_weight % mod);
for (std::size_t aa = 1; aa < n_action; aa++) {
prob_weight = control2.tube(pp, aa);
duals(ii, pp, tt) =
std::max(reward(ii, aa, pp) + arma::sum(prob_weight % mod),
duals(ii, pp, tt));
}
}
}
}
}
return Rcpp::List::create(Rcpp::Named("primal") = primals,
Rcpp::Named("dual") = duals);
}