ϑi)SSKJr SSKJrJr SSKrSSKrSSKJ r SSK J r J r J r \(a SSKJr SSKJr S S S jjrg) ) annotations) TYPE_CHECKINGLiteralN) strong_wolfe)_value_and_gradient&check_initial_inverse_hessian_estimatecheck_input_type)Callable)Tensorc ^^^^^^^^ ^T S;a[ST S35eSn [USU 5 [R"URST S9mUcTnO[USU 5 [ U5 [R "U5n [R "UR55n [TU 5up[R"S /S S S 9n[R"S /SS S 9n[R"S /S S S 9n[R"S /S S S 9nU4SjnUU UUUUUU4Sjn[RRRUUUUUUXX/S9 UUXX4$)ao Minimizes a differentiable function `func` using the BFGS method. The BFGS is a quasi-Newton method for solving an unconstrained optimization problem over a differentiable function. Closely related is the Newton method for minimization. Consider the iterate update formula: .. math:: x_{k+1} = x_{k} + H_k \nabla{f_k} If :math:`H_k` is the inverse Hessian of :math:`f` at :math:`x_k`, then it's the Newton method. If :math:`H_k` is symmetric and positive definite, used as an approximation of the inverse Hessian, then it's a quasi-Newton. In practice, the approximated Hessians are obtained by only using the gradients, over either whole or part of the search history, the former is BFGS, the latter is L-BFGS. Reference: Jorge Nocedal, Stephen J. Wright, Numerical Optimization, Second Edition, 2006. pp140: Algorithm 6.1 (BFGS Method). Args: objective_func: the objective function to minimize. ``objective_func`` accepts a 1D Tensor and returns a scalar. initial_position (Tensor): the starting point of the iterates, has the same shape with the input of ``objective_func`` . max_iters (int, optional): the maximum number of minimization iterations. Default value: 50. tolerance_grad (float, optional): terminates if the gradient norm is smaller than this. Currently gradient norm uses inf norm. Default value: 1e-7. tolerance_change (float, optional): terminates if the change of function value/position/parameter between two iterations is smaller than this value. Default value: 1e-9. initial_inverse_hessian_estimate (Tensor, optional): the initial inverse hessian approximation at initial_position. It must be symmetric and positive definite. If not given, will use an identity matrix of order N, which is size of ``initial_position`` . Default value: None. line_search_fn (str, optional): indicate which line search method to use, only support 'strong wolfe' right now. May support 'Hager Zhang' in the future. Default value: 'strong wolfe'. max_line_search_iters (int, optional): the maximum number of line search iterations. Default value: 50. initial_step_length (float, optional): step length used in first iteration of line search. different initial_step_length may cause different optimal result. For methods like Newton and quasi-Newton the initial trial step length should always be 1.0. Default value: 1.0. dtype ('float32' | 'float64', optional): data type used in the algorithm, the data type of the input parameter must be consistent with the dtype. Default value: 'float32'. name (str, optional): Name for the operation. For more information, please refer to :ref:`api_guide_Name`. Default value: None. Returns: output(tuple): - is_converge (bool): 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 regarding to the initial position. - objective_value (Tensor): objective function value at the `position`. - objective_gradient (Tensor): objective function gradient at the `position`. - inverse_hessian_estimate (Tensor): the estimate of inverse hessian at the `position`. Examples: .. code-block:: python :name: code-example1 >>> # Example1: 1D Grid Parameters >>> import paddle >>> # Randomly simulate a batch of input data >>> inputs = paddle. normal(shape=(100, 1)) >>> labels = inputs * 2.0 >>> # define the loss function >>> def loss(w): ... y = w * inputs ... return paddle.nn.functional.square_error_cost(y, labels).mean() >>> # Initialize weight parameters >>> w = paddle.normal(shape=(1,)) >>> # Call the bfgs method to solve the weight that makes the loss the smallest, and update the parameters >>> for epoch in range(0, 10): ... # Call the bfgs method to optimize the loss, note that the third parameter returned represents the weight ... w_update = paddle.incubate.optimizer.functional.minimize_bfgs(loss, w)[2] ... # Use paddle.assign to update parameters in place ... paddle. assign(w_update, w) .. code-block:: python :name: code-example2 >>> # Example2: Multidimensional Grid Parameters >>> import paddle >>> def flatten(x): ... return x. flatten() >>> def unflatten(x): ... return x.reshape((2,2)) >>> # Assume the network parameters are more than one dimension >>> def net(x): ... assert len(x.shape) > 1 ... return x.square().mean() >>> # function to be optimized >>> def bfgs_f(flatten_x): ... return net(unflatten(flatten_x)) >>> x = paddle.rand([2,2]) >>> for i in range(0, 10): ... # Flatten x before using minimize_bfgs ... x_update = paddle.incubate.optimizer.functional.minimize_bfgs(bfgs_f, flatten(x))[2] ... # unflatten x_update, then update parameters ... paddle.assign(unflatten(x_update), x) )float32float64z?The dtype must be 'float32' or 'float64', but the specified is . minimize_bfgsinitial_positionrdtype initial_inverse_hessian_estimaterint64shape fill_valuerFboolc>UT:U)-$)N) kdone is_convergenum_func_callsxkvalueg1Hk max_iterss i/var/www/html/banglarbhumi/venv/lib/python3.13/site-packages/paddle/incubate/optimizer/functional/bfgs.pycondminimize_bfgs..condsI $&&c >^[R"Xv5*nTS:Xa[TUUTTTS9uppO[STS35eX;- nX-n X- n XL-nU n[R"U S5n [R"U S5n [R "X5m[R RRTS:HU4SjU4Sj5nTX-U R5-- nTX-U R5-- n[R"[R"X5U5X-U R5--nUS - n[RRU[RS 9n[RRU[RS 9n[R"UUT:-UT:-U5 [R"X5 [R"XS:H-U5 XX#XEXg/$) Nr)fr!pkr%initial_step_lengthrzNCurrently only support line_search_fn = 'strong_wolfe', but the specified is ''rgc2>[R"S/STS9$)Nrg@@r)paddlefullrsr&-minimize_bfgs..body..sFKKqcfEJr)c>ST- $)N?r)rhok_invsr&r2r3s C(Nr)r)p)r0matmulrNotImplementedError unsqueezedotstaticnnr'tlinalgnormnpinfassign)rrrr r!r"r#r$r,alphag2 ls_func_callsskykrhok Vk_transposeVkgnormpk_normr6Irr-line_search_fnmax_line_search_itersobjective_functolerance_changetolerance_grads @r&bodyminimize_bfgs..bodysmmB# # ^ +.: /$7 / +E"m&`ao`ppqr  'Z W W    b! $   b! $::b%}}$$ O J "  49rttv-- RTTV# # MM&-- 92 >i"$$&  ! Q ""2"0--$$R266$2 EN* +w9I/I JD   d( dsl+T2bHHr))r'rT loop_vars) ValueErrorr r0eyerr rCdetachrr1r<r= while_loop)rQrr%rSrRrrOrPr-rnameop_namer$r!r"r#r rrrr'rTrNs` ``` ```` @r&rr$sbF **MeWTU V  G%'97C #))!,E:A'/+,( , .  //OP 7 8B '..0 1B#NB7IE[[sqHN  1#!7;A ;;aSU& AD++QCEHK'7I7Ir MM  dKBK  2 99r)) 2gHz>g& .>Nrr]r5rN)rQzCallable[[Tensor], Tensor]rr r%intrSfloatrRr_rz Tensor | NonerOzLiteral['strong_wolfe']rPr^r-r_rzLiteral['float32', 'float64']r[z str | Nonereturnz0tuple[bool, int, Tensor, Tensor, Tensor, Tensor]) __future__rtypingrrnumpyrAr0 line_searchrutilsrr r collections.abcr r rrr)r&rgs#) % (  "6:.