Source code for decent_bench.algorithms.p2p._ed

from dataclasses import dataclass

import decent_bench.utils.interoperability as iop
from decent_bench.algorithms.utils import initial_states
from decent_bench.networks import P2PNetwork
from decent_bench.utils._tags import tags
from decent_bench.utils.types import InitialStates

from ._p2p_algorithm import P2PAlgorithm




@tags("peer-to-peer", "gradient-tracking")
@dataclass(eq=False)
class ED(P2PAlgorithm):
    r"""
    Gradient tracking algorithm characterized by the update step below.

    .. math::
        \mathbf{y}_{i, k+1} = \mathbf{x}_{i, k} - \rho \nabla f_i(\mathbf{x}_{i,k})
    .. math::
        \mathbf{x}_{i, k+1}
        = \sum_j \frac{1}{2} (\mathbf{I} + \mathbf{W})_{ij} (\mathbf{x}_{j,k} + \mathbf{y}_{j, k+1} - \mathbf{y}_{j, k})

    where
    :math:`\mathbf{x}_{i, k}` is agent i's local optimization variable at iteration k,
    :math:`\rho` is the step size (the corresponding argument is ``step_size``),
    :math:`f_i` is agent i's local cost function,
    j is a neighbor of i or i itself,
    and :math:`\mathbf{W}_{ij}` is the metropolis weight between agent i and j.

    Alias: :class:`ExactDiffusion`

    """

    iterations: int = 100
    step_size: float = 0.001
    x0: InitialStates = None
    name: str = "ED"

    def __post_init__(self) -> None:
        """
        Validate hyperparameters.

        Raises:
            ValueError: if hyperparameters are invalid.

        """
        if self.step_size <= 0:
            raise ValueError("`step_size` must be positive")

    def initialize(self, network: P2PNetwork) -> None:
        self.x0 = initial_states(self.x0, network)
        for i in network.agents():
            y0 = self.x0[i]
            y1 = self.x0[i] - self.step_size * i.cost.gradient(self.x0[i])
            i.initialize(x=self.x0[i], aux_vars={"y": y0, "y_new": y1})

        self.W = network.weights
        self.W = 0.5 * (iop.eye_like(self.W) + self.W)

    def step(self, network: P2PNetwork, _: int) -> None:
        for i in network.active_agents():
            msg = i.x + i.aux_vars["y_new"] - i.aux_vars["y"]
            i.aux_vars["msg"] = msg
            network.broadcast(i, msg)

        for i in network.active_agents():
            s = self.W[i, i] * i.aux_vars["msg"]
            for j, msg in i.messages().items():
                s += self.W[i, j] * msg
            i.x = s
            i.aux_vars["y"] = i.aux_vars["y_new"]
            i.aux_vars["y_new"] = i.x - self.step_size * i.cost.gradient(i.x)



ExactDiffusion = ED  # alias