from ..tdagent import TDAgent
import numpy as np
from cvxopt import solvers, matrix
solvers.options['show_progress'] = False
class ONS(TDAgent):
"""
Online newton step algorithm.
Reference:
A.Agarwal, E.Hazan, S.Kale, R.E.Schapire.
Algorithms for Portfolio Management based on the Newton Method, 2006.
http://machinelearning.wustl.edu/mlpapers/paper_files/icml2006_AgarwalHKS06.pdf
"""
def __init__(self, delta=0.125, beta=1., eta=0., A = None):
"""
:param delta, beta, eta: Model parameters. See paper.
"""
super(ONS, self).__init__()
self.delta = delta
self.beta = beta
self.eta = eta
self.A = A
def init_portfolio(self, X):
m = X.size
self.A = np.mat(np.eye(m))
self.b = np.mat(np.zeros(m)).T
def decide_by_history(self, x, last_b):
'''
:param x: input matrix
:param last_b: last portfolio
'''
x = self.get_last_rpv(x)
if self.A is None:
self.init_portfolio(x)
# calculate gradient
grad = np.mat(x / np.dot(last_b, x)).T
# update A
self.A += grad * grad.T
# update b
self.b += (1 + 1./self.beta) * grad
# projection of p induced by norm A
pp = self.projection_in_norm(self.delta * self.A.I * self.b, self.A)
return pp * (1 - self.eta) + np.ones(len(x)) / float(len(x)) * self.eta
def projection_in_norm(self, x, M):
""" Projection of x to simplex indiced by matrix M. Uses quadratic programming.
"""
m = M.shape[0]
P = matrix(2*M)
q = matrix(-2 * M * x)
G = matrix(-np.eye(m))
h = matrix(np.zeros((m,1)))
A = matrix(np.ones((1,m)))
b = matrix(1.)
sol = solvers.qp(P, q, G, h, A, b)
return np.squeeze(sol['x'])
