def log_sum_exp(objectives, weights, gamma):
"""Combines objectives as log_sum_exp of weighted terms.
Args:
objectives: A list of Minimize/Maximize objectives.
weights: A vector of weights.
gamma: Parameter interpolating between sum and max.
Returns:
A Minimize objective.
"""
num_objs = len(objectives)
terms = [(objectives[i]*weights[i]).args[0] for i in range(num_objs)]
expr = atoms.log_sum_exp(atoms.vstack(terms))
return Minimize(expr)
def log_sum_exp(objectives, weights, gamma=1):
"""Combines objectives as log_sum_exp of weighted terms.
The objective takes the form
log(sum_{i=1}^n exp(gamma*weights[i]*objectives[i]))/gamma
As gamma goes to 0, log_sum_exp approaches weighted_sum. As gamma goes to infinity,
log_sum_exp approaches max.
Args:
objectives: A list of Minimize/Maximize objectives.
weights: A vector of weights.
gamma: Parameter interpolating between weighted_sum and max.
Returns:
A Minimize objective.
"""
num_objs = len(objectives)
terms = [(objectives[i] * weights[i]).args[0] for i in range(num_objs)]
expr = atoms.log_sum_exp(gamma * atoms.vstack(terms)) / gamma
return Minimize(expr)