Distributed Dual Subgradient

Warning

This example is currently under development

This is an example on how to use the DualSubgradientMethod class. See also the reference [FaMa17].

examples/setups/distributed_dual_subgradient/launcher.py

# WARNING: this file is currently under development

import dill as pickle
import numpy as np
from mpi4py import MPI
from disropt.agents import Agent
from disropt.algorithms.dual_subgradient import DualSubgradientMethod
from disropt.functions import QuadraticForm, Variable, AffineForm
from disropt.utils.utilities import is_pos_def
from disropt.constraints.projection_sets import Box
from disropt.utils.graph_constructor import binomial_random_graph, metropolis_hastings
from disropt.problems.constraint_coupled_problem import ConstraintCoupledProblem

# get MPI info
comm = MPI.COMM_WORLD
nproc = comm.Get_size()
local_rank = comm.Get_rank()

# Generate a common graph (everyone use the same seed)
Adj = binomial_random_graph(nproc, p=0.3, seed=1)
W = metropolis_hastings(Adj)

# reset local seed
np.random.seed()

agent = Agent(
    in_neighbors=np.nonzero(Adj[local_rank, :])[0].tolist(),
    out_neighbors=np.nonzero(Adj[:, local_rank])[0].tolist(),
    in_weights=W[local_rank, :].tolist())

# local variable dimension - random in [2,5]
n_i = np.random.randint(2, 6)

# number of coupling constraints
S = 3

# generate a positive definite matrix
P = np.random.randn(n_i, n_i)
while not is_pos_def(P):
    P = np.random.randn(n_i, n_i)
bias = np.random.randn(n_i, 1)

# declare a variable
x = Variable(n_i)

# define the local objective function
fn = QuadraticForm(x - bias, P)

# define the local constraint set
constr = [x>=-2, x<=2]

# define the local contribution to the coupling constraints
A = np.random.randn(S, n_i)
coupling_fn = A.transpose() @ x

# create local problem and assign to agent
pb = ConstraintCoupledProblem(objective_function=fn,
                              constraints=constr,
                              coupling_function=coupling_fn)
agent.set_problem(pb)

# initialize the dual variable
lambda0 = np.random.rand(S, 1)
xhat0   = np.zeros((n_i, 1))

algorithm = DualSubgradientMethod(agent=agent,
                                  initial_condition=lambda0,
                                  initial_runavg=xhat0,
                                  enable_log=True)


def step_gen(k): # define a stepsize generator
    return 0.1/np.sqrt(k+1)

# run the algorithm
lambda_sequence, xhat_sequence = algorithm.run(iterations=1000, stepsize=step_gen)
lambda_t, xhat_t = algorithm.get_result()
print("Agent {}: dual {} primal {}".format(agent.id, lambda_t.flatten(), xhat_t.flatten()))

np.save("agents.npy", nproc)

# save agent and sequence
with open('agent_{}_obj_function.pkl'.format(agent.id), 'wb') as output:
    pickle.dump(agent.problem.objective_function, output, pickle.HIGHEST_PROTOCOL)
with open('agent_{}_coup_function.pkl'.format(agent.id), 'wb') as output:
    pickle.dump(agent.problem.coupling_function, output, pickle.HIGHEST_PROTOCOL)
np.save("agent_{}_dual_sequence.npy".format(agent.id), lambda_sequence)
np.save("agent_{}_runavg_sequence.npy".format(agent.id), xhat_sequence)

examples/setups/distributed_dual_subgradient/results.py

import numpy as np
import matplotlib.pyplot as plt
import pickle

N = np.load("agents.npy")
S = 3

lambda_sequence = {}
xhat_sequence = {}
local_obj_function = {}
local_coup_function = {}
for i in range(N):
    lambda_sequence[i] = np.load("agent_{}_dual_sequence.npy".format(i))
    xhat_sequence[i] = np.load("agent_{}_runavg_sequence.npy".format(i))
    with open('agent_{}_obj_function.pkl'.format(i), 'rb') as input:
        local_obj_function[i] = pickle.load(input)
    with open('agent_{}_coup_function.pkl'.format(i), 'rb') as input:
        local_coup_function[i] = pickle.load(input)

# plot dual solutions
plt.figure()
plt.title("Dual solutions")
colors = {}
for i in range(N):
    colors[i] = np.random.rand(3, 1).flatten()
    dims = lambda_sequence[i].shape
    iterations = dims[0]
    for j in range(dims[1]):
        plt.plot(np.arange(iterations), lambda_sequence[i][:, j, 0], color=colors[i])

# plot cost of running average
plt.figure()
plt.title("Primal cost (running average)")

obj_function = np.zeros([iterations, 1])
for k in range(iterations):
    for i in range(N):
        obj_function[k] += local_obj_function[i].eval(xhat_sequence[i][k, :, 0].reshape(-1,1)).flatten()

plt.plot(obj_function)

# plot coupling constraint utilization
plt.figure()
plt.title("Coupling constraint utilization (running average)")

coup_function = np.zeros([iterations, S])
for k in range(iterations):
    for i in range(N):
        coup_function[k] += local_coup_function[i].eval(xhat_sequence[i][k, :, 0].reshape(-1,1)).flatten()

plt.plot(coup_function)

plt.show()

The two files can be executed by issuing the following commands in the example folder:

> mpirun -np 30 --oversubscribe python launcher.py
> python results.py