Source code for picos.constraints.con_kldiv

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# Copyright (C) 2018-2019 Maximilian Stahlberg
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"""Implementation of :class:`KullbackLeiblerConstraint`."""

from collections import namedtuple

from .. import glyphs
from ..apidoc import api_end, api_start
from ..caching import cached_property
from .constraint import Constraint, ConstraintConversion

_API_START = api_start(globals())
# -------------------------------

[docs]class KullbackLeiblerConstraint(Constraint): """Upper bound on a Kullback-Leibler divergence. This is the upper bound on a negative or relative entropy, both represented by :class:`~picos.expressions.NegativeEntropy`. """
[docs] class ExpConeConversion(ConstraintConversion): """Kullback-Leibler to exponential cone constraint conversion."""
[docs] @classmethod def predict(cls, subtype, options): """Implement :meth:`~.constraint.ConstraintConversion.predict`.""" from ..expressions import RealVariable from . import AffineConstraint, ExpConeConstraint n = subtype.argdim yield ("var", RealVariable.make_var_type(dim=n, bnd=0), 1) yield ("con", AffineConstraint.make_type(dim=1, eq=False), 1) yield ("con", ExpConeConstraint.make_type(), n)
[docs] @classmethod def convert(cls, con, options): """Implement :meth:`~.constraint.ConstraintConversion.convert`.""" from ..expressions import ExponentialCone from ..modeling import Problem x = con.numerator y = con.denominator n = con.divergence.n b = con.upperBound P = Problem() u = P.add_variable("__u", n) P.add_constraint((u | 1) >= -b) for i in range(n): P.add_constraint((y[i] // x[i] // u[i]) << ExponentialCone()) return P
[docs] def __init__(self, divergence, upperBound): """Construct a :class:`KullbackLeiblerConstraint`. :param ~picos.expressions.NegativeEntropy divergence: Constrained expression. :param ~picos.expressions.AffineExpression upperBound: Upper bound on the expression. """ from ..expressions import AffineExpression, NegativeEntropy assert isinstance(divergence, NegativeEntropy) assert isinstance(upperBound, AffineExpression) assert len(upperBound) == 1 self.divergence = divergence self.upperBound = upperBound super(KullbackLeiblerConstraint, self).__init__(divergence._typeStr)
@property def numerator(self): """The :math:`x` of the divergence.""" return self.divergence.x
[docs] @cached_property def denominator(self): """The :math:`y` of the divergence, or :math:`1`.""" from ..expressions import AffineExpression if self.divergence.y is None: return AffineExpression.from_constant(1, self.divergence.x.shape) else: return self.divergence.y
Subtype = namedtuple("Subtype", ("argdim",)) def _subtype(self): return self.Subtype(len(self.numerator)) @classmethod def _cost(cls, subtype): # NOTE: Twice the argument dimension due to the denominator. return 2*subtype.argdim + 1 def _expression_names(self): yield "divergence" yield "upperBound" def _str(self): return glyphs.le(self.divergence.string, self.upperBound.string) def _get_slack(self): return self.upperBound.safe_value - self.divergence.safe_value
# -------------------------------------- __all__ = api_end(_API_START, globals())