decent_bench.centralized_algorithms#

decent_bench.centralized_algorithms.gradient_descent(cost_function: CostFunction, x0: ndarray[tuple[Any, ...], dtype[float64]] | None, *, step_size: float, max_iter: int, stop_tol: float | None, max_tol: float | None) → ndarray[tuple[Any, ...], dtype[float64]][source]#

Find the x that minimizes the cost function using gradient descent.

Parameters:

  • cost_function – cost function to minimize

  • x0 – initial guess, defaults to np.zeros() if None is provided

  • step_size – scaling factor for each update

  • max_iter – maximum number of iterations to run

  • stop_tol – early stopping criteria - stop if norm(x_new - x) <= stop_tol

  • max_tol – maximum tolerated norm(x_new - x) at the end

Raises:

RuntimeError – if norm(x_new - x) > max_tol at the end

Returns:

x that minimizes the cost function.

decent_bench.centralized_algorithms.accelerated_gradient_descent(cost_function: CostFunction, x0: ndarray[tuple[Any, ...], dtype[float64]] | None, *, max_iter: int, stop_tol: float | None, max_tol: float | None) → ndarray[tuple[Any, ...], dtype[float64]][source]#

Find the x that minimizes the cost function using accelerated gradient descent.

Parameters:

  • cost_function – cost function to minimize

  • x0 – initial guess, defaults to np.zeros() if None is provided

  • max_iter – maximum number of iterations to run

  • stop_tol – early stopping criteria - stop if norm(x_new - x) <= stop_tol

  • max_tol – maximum tolerated norm(x_new - x) at the end

Raises:

  • RuntimeError – if norm(x_new - x) > max_tol at the end

  • ValueError – if cost_function.m_smooth < 0, cost_function.m_cvx < 0, or cost function is affine

Returns:

x that minimizes the cost function.

decent_bench.centralized_algorithms.proximal_solver(cost_function: CostFunction, y: ndarray[tuple[Any, ...], dtype[float64]], rho: float) → ndarray[tuple[Any, ...], dtype[float64]][source]#

Find the proximal at y using accelerated gradient descent.

This is the solution to the proximal operator defined as:

\[\operatorname{prox}_{\rho f}(\mathbf{y}) = \arg\min_{\mathbf{x}} \left\{ f(\mathbf{x}) + \frac{1}{2\rho} \| \mathbf{x} - \mathbf{y} \|^2 \right\}\]

where \(\rho > 0\) is the penalty and \(f\) the cost function.

Raises:

ValueError – if cost_function’s domain and y don’t have the same shape, or if rho is not greater than 0