minimize_lbfgs

paddle.incubate.optimizer.functional. minimize_lbfgs ( objective_func, initial_position, history_size=100, max_iters=50, tolerance_grad=1e-08, tolerance_change=1e-08, initial_inverse_hessian_estimate=None, line_search_fn='strong_wolfe', max_line_search_iters=50, initial_step_length=1.0, dtype='float32', name=None ) [source]

Minimizes a differentiable function func using the L-BFGS method. The L-BFGS is simalar as BFGS, the only difference is that L-BFGS use historical sk, yk, rhok rather than H_k-1 to compute Hk. Reference:

System Message: ERROR/3 (/usr/local/lib/python3.8/site-packages/paddle/incubate/optimizer/functional/lbfgs.py:docstring of paddle.incubate.optimizer.functional.lbfgs.minimize_lbfgs, line 5)

Unexpected indentation.

Jorge Nocedal, Stephen J. Wright, Numerical Optimization, Second Edition, 2006. pp179: Algorithm 7.5 (L-BFGS).

Following summarizes the the main logic of the program based on L-BFGS.Note: _k represents value of k_th iteration, ^T represents the transposition of a vector or matrix. repeat

System Message: ERROR/3 (/usr/local/lib/python3.8/site-packages/paddle/incubate/optimizer/functional/lbfgs.py:docstring of paddle.incubate.optimizer.functional.lbfgs.minimize_lbfgs, line 11)

Unexpected indentation.

compute p_k by two-loop recursion alpha = strong_wolfe(f, x_k, p_k) x_k+1 = x_k + alpha * p_k s_k = x_k+1 - x_k y_k = g_k+1 - g_k rho_k = 1 / (s_k^T * y_k) update sk_vec, yk_vec, rhok_vec check_converge

System Message: WARNING/2 (/usr/local/lib/python3.8/site-packages/paddle/incubate/optimizer/functional/lbfgs.py:docstring of paddle.incubate.optimizer.functional.lbfgs.minimize_lbfgs, line 19)

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end

Parameters

  • objective_func – the objective function to minimize. func accepts a multivariate input and returns a scalar.

  • initial_position (Tensor) – the starting point of the iterates. For methods like Newton and quasi-Newton

  • (the initial trial step length should always be 1.0) –

  • history_size (Scalar) – the number of stored vector pairs {si,yi}.

  • max_iters (Scalar) – the maximum number of minimization iterations.

  • tolerance_grad (Scalar) – terminates if the gradient norm is smaller than this. Currently gradient norm uses inf norm.

  • tolerance_change (Scalar) – terminates if the change of function value/position/parameter between two iterations is smaller than this value.

  • initial_inverse_hessian_estimate (Tensor) – the initial inverse hessian approximation.

  • line_search_fn (str) – indicate which line search method to use, only support ‘strong wolfe’ right now. May support ‘Hager Zhang’ in the futrue.

  • max_line_search_iters (Scalar) – the maximum number of line search iterations.

  • initial_step_length – step length used in first iteration of line search. different initial_step_length

  • result. (may cause different optimal) –

  • dtype ('float' | 'float32' | 'float64' | 'double') – the data type to be used.

Returns

Indicates whether found the minimum within tolerance. num_func_calls (int): number of objective function called. position (Tensor): the position of the last iteration. If the search converged, this value is the argmin of the objective function regrading to the initial position. objective_value (Tensor): objective function value at the position. objective_gradient (Tensor): objective function gradient at the position.

Return type

is_converge (bool)

Examples

import paddle

def func(x):
    return paddle.dot(x, x)

x0 = paddle.to_tensor([1.3, 2.7])
results = paddle.incubate.optimizer.functional.minimize_lbfgs(func, x0)
print("is_converge: ", results[0])
print("the minimum of func is: ", results[2])
# is_converge:  is_converge:  Tensor(shape=[1], dtype=bool, place=Place(gpu:0), stop_gradient=True,
#        [True])
# the minimum of func is:  Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        [0., 0.])