taco package

Subpackages

• taco.algorithms package
  • Submodules
  • taco.algorithms.bundle module
  • Module contents

Submodules

taco.chance_optimizer module

class taco.chance_optimizer.Optimizer(problem, p=0.01, starting_point=array([0.0, 0.0, 0.0]), pen1=None, pen2=None, factor_pen2=None, bund_mu_start=None, performance_warnings=False, numba=None, params=None)

Bases: object

Base class for optimization of chance constrained problems

For an problem instance providing a dataset and two first order oracles \(f\) and \(g\), this class is an interface for solving the minimization problem

Parameters

• problem – An instance of Problem

• p (np.float64) – Safety probability threshold for the problem

• starting_point (np.ndarray) – (optional) Starting point for the algorithm

• pen1 (np.float64) – (optional) First Penalization parameter

• pen2 (np.float64) – (optional) Second Penalization parameter

• factor_pen2 (np.float64) – (optional) Incremental factor for the second penalization parameter pen2

• bund_mu_start (np.float64) – Starting value for the proximal parameter \(\mu\) of the bundle method

• numba (bool) – If True, instantiate an Oracle with numba in no-python mode.

• performance_warning (bool) – If True, prints numba performance warnings.

• params (dict) – Dictionnary of parameters for the optimization process

run(verbose=False)

Runs the bundle method to solve the chance constrained problem.

Parameters

verbose (bool) – If true, prints advance of the process in the console

Returns

solution of the problem

taco.oracle module

class taco.oracle.Oracle(problem, p, pen1, pen2, rho)

Bases: object

Base class that instantiates a first-order oracle for the DC objective of the penalized chance constaint

For two input oracles \(f\) and \(g\) given through their function and gradients, and a sampled dataset from a random variable \(\xi\), this class is an interface to compute the value and the gradient of the function \(x, \eta \mapsto f(x) + \mu \max(\eta,0) + \lambda \left(G(x,\eta) - \text{CVaR}_p(g(x,\xi))\right)\) where \(G(x, \eta) = \eta + \frac{1}{1-p} \mathbb{E}[\max(g(x, \xi) - \eta]\)

Parameters

• problem – Instance of Problem

• p (np.float64) – Real number in [0,1]. Safety probability level

• pen1 (np.float64) – Penalization parameter, must be positive.

• pen2 (np.float64) – Penalization parameter, must be positive.

• rho (np.float64) – Smoothing parameter for the superquantile, must be positive.

constraint_func(x, z)

constraint_grad(x, z)

f(x)

Value of the DC objective

f1(x)

Value of the convex part of the DC objective \(x, \eta \mapsto f(x) + \mu \max(\eta,0) + \lambda G(x,\eta)\)

f1_cc_part(x)

f1_ncc_part(x)

f2(x)

Value of the concave part of the DC objective \(x, \eta \mapsto - {CVaR}_p(g(x,{\xi}))\)

first_order_oracle_f2(x)

g1(x)

Gradient of the convex part of the DC objective \(x, \eta \mapsto f(x) + \mu \max(\eta,0) + \lambda G(x,\eta)\)

g1_cc_part(x)

g1_ncc_part(x)

g2(x)

Gradient of the concave part of the DC objective \(x, \eta \mapsto - {CVaR}_p(g(x,{\xi}))\)

objective_func(x)

objective_grad(x)

right_eta(x)

Module contents

Core module .. moduleauthor:: Yassine LAGUEL

class taco.BundleAlgorithm(oracle, params)

Bases: object

Base class that combines the penalization procedure with a Bundle Method to solve the chance constraint problem. It is instantiated with a first-oder oracle for the DC objective and a dictionary of parameters. From time to time, the penalization parameters are increased to escape some critical point of the DC objective.

Parameters

• oracle – An oracle object.

• params (dict) – Python dictionary of parameters.

run(verbose=False)

Runs the optimization process :type verbose: bool :param verbose: If true, prints advance of the process in the console :return: solution of the problem

class taco.FastOracle(*args, **kwargs)

Bases: taco.oracle.FastOracle

Numba version of the class Oracle.

FastOracle works with numba in full no-python mode. It must take as an input an instance of problem that is a jitclass.

Parameters

• problem – Instance of Problem. Must be a numba jitclass.

• p (np.float64) – Real number in [0,1]. Safety probability level

• pen1 (np.float64) – Penalization parameter, must be positive.

• pen2 (np.float64) – Penalization parameter, must be positive.

• rho (np.float64) – Smoothing parameter for the superquantile, must be positive.

class_type = jitclass.FastOracle#113c93198<problem:instance.jitclass.ToyProblem#113c64748<a:array(float64, 1d, A),data:array(float64, 2d, A),geo_a:array(float64, 2d, A)>,sample_size:int32,p:float64,pen1:float64,pen2:float64,rho:float64>

class taco.Optimizer(problem, p=0.01, starting_point=array([0.0, 0.0, 0.0]), pen1=None, pen2=None, factor_pen2=None, bund_mu_start=None, performance_warnings=False, numba=None, params=None)

Bases: object

Base class for optimization of chance constrained problems

For an problem instance providing a dataset and two first order oracles \(f\) and \(g\), this class is an interface for solving the minimization problem

Parameters

• problem – An instance of Problem

• p (np.float64) – Safety probability threshold for the problem

• starting_point (np.ndarray) – (optional) Starting point for the algorithm

• pen1 (np.float64) – (optional) First Penalization parameter

• pen2 (np.float64) – (optional) Second Penalization parameter

• factor_pen2 (np.float64) – (optional) Incremental factor for the second penalization parameter pen2

• bund_mu_start (np.float64) – Starting value for the proximal parameter \(\mu\) of the bundle method

• numba (bool) – If True, instantiate an Oracle with numba in no-python mode.

• performance_warning (bool) – If True, prints numba performance warnings.

• params (dict) – Dictionnary of parameters for the optimization process

run(verbose=False)

Runs the bundle method to solve the chance constrained problem.

Parameters

verbose (bool) – If true, prints advance of the process in the console

Returns

solution of the problem

class taco.Oracle(problem, p, pen1, pen2, rho)

Bases: object

Base class that instantiates a first-order oracle for the DC objective of the penalized chance constaint

For two input oracles \(f\) and \(g\) given through their function and gradients, and a sampled dataset from a random variable \(\xi\), this class is an interface to compute the value and the gradient of the function \(x, \eta \mapsto f(x) + \mu \max(\eta,0) + \lambda \left(G(x,\eta) - \text{CVaR}_p(g(x,\xi))\right)\) where \(G(x, \eta) = \eta + \frac{1}{1-p} \mathbb{E}[\max(g(x, \xi) - \eta]\)

Parameters

• problem – Instance of Problem

• p (np.float64) – Real number in [0,1]. Safety probability level

• pen1 (np.float64) – Penalization parameter, must be positive.

• pen2 (np.float64) – Penalization parameter, must be positive.

• rho (np.float64) – Smoothing parameter for the superquantile, must be positive.

constraint_func(x, z)

constraint_grad(x, z)

f(x)

Value of the DC objective

f1(x)

Value of the convex part of the DC objective \(x, \eta \mapsto f(x) + \mu \max(\eta,0) + \lambda G(x,\eta)\)

f1_cc_part(x)

f1_ncc_part(x)

f2(x)

Value of the concave part of the DC objective \(x, \eta \mapsto - {CVaR}_p(g(x,{\xi}))\)

first_order_oracle_f2(x)

g1(x)

Gradient of the convex part of the DC objective \(x, \eta \mapsto f(x) + \mu \max(\eta,0) + \lambda G(x,\eta)\)

g1_cc_part(x)

g1_ncc_part(x)

g2(x)

Gradient of the concave part of the DC objective \(x, \eta \mapsto - {CVaR}_p(g(x,{\xi}))\)

objective_func(x)

objective_grad(x)

right_eta(x)

class taco.ToyProblem(*args, **kwargs)

Bases: taco.problems.toy_problem.ToyProblem

class_type = jitclass.ToyProblem#113c64748<a:array(float64, 1d, A),data:array(float64, 2d, A),geo_a:array(float64, 2d, A)>

constraint_grad(z)

mat_w()