pyotc.otc_backend.policy_iteration package

Subpackages

• pyotc.otc_backend.policy_iteration.dense package
  • Submodules
  • pyotc.otc_backend.policy_iteration.dense.approx_tce module
    • approx_tce()
  • pyotc.otc_backend.policy_iteration.dense.entropic module
    • entropic_otc()
  • pyotc.otc_backend.policy_iteration.dense.entropic_tci module
    • entropic_tci()
  • pyotc.otc_backend.policy_iteration.dense.exact module
    • exact_otc()
    • exact_otc_lp()
  • pyotc.otc_backend.policy_iteration.dense.exact_tce module
    • exact_tce()
  • pyotc.otc_backend.policy_iteration.dense.exact_tci_lp module
    • check_constant()
    • exact_tci()
    • setup_ot()
  • pyotc.otc_backend.policy_iteration.dense.exact_tci_pot module
    • exact_tci()
    • setup_ot()
  • Module contents
• pyotc.otc_backend.policy_iteration.sparse package
  • Submodules
  • pyotc.otc_backend.policy_iteration.sparse.exact module
    • exact_otc()
  • pyotc.otc_backend.policy_iteration.sparse.exact_tce module
    • exact_tce()
  • pyotc.otc_backend.policy_iteration.sparse.exact_tci module
    • exact_tci()
    • setup_ot()
  • Module contents

Submodules

pyotc.otc_backend.policy_iteration.utils module

pyotc.otc_backend.policy_iteration.utils.get_best_stat_dist(P, c)

Given a transition matrix P and a cost vector c, this function computes the stationary distribution that minimizes the expected cost via linear programming.

Parameters:

• P (np.ndarray) – Transition matrix.

• c (np.ndarray) – Cost vector.

Returns:

Best stationary distribution. exp_cost (float): Corresponding expected cost.

Return type:

stat_dist (np.ndarray)

pyotc.otc_backend.policy_iteration.utils.get_stat_dist(P, method='best', c=None)

Computes the stationary distribution of a Markov chain given its transition matrix P.

Supports multiple methods:

• ‘best’: Solves a linear program that minimizes cost under stationarity constraints.

• ‘eigen’: Solves for the stationary distribution using the eigenvalue method.

• ‘iterative’: Uses power iteration for large or sparse matrices.

Parameters:

• P (np.ndarray) – Transition matrix of the Markov chain, shape (n, n).

• method (str) – Method used to compute the stationary distribution. One of ‘eigen’, ‘iterative’, or ‘best’. Defaults to ‘best’.

• c (np.ndarray, optional) – Cost vector of shape (n,) used only when method=’best’.

Returns:

Stationary distribution vector of shape (n,), summing to 1.

Return type:

pi (np.ndarray)

Raises:

ValueError – If method is ‘best’ but cost vector c is not provided, or if an invalid method name is given.

Module contents