optiviz 1.0.0

Educational tool for visualising PyTorch-compatible optimisers on any differentiable 1D or 2D function.

OptiViz

Walk along loss landscapes and ride along as your favourite optimisers battle it out for the global minimum with OptiViz 1.0, the latest update to OptiViz.

Optiviz is a python package that enables effortless visualisation of any PyTorch optimiser on any differentiable function in one or two variables. OptiViz might find educational use in an introductory nonlinear optimisation or deep learning class.

Installation

To install OptiViz, please use:

pip install optiviz

Usage

All functionality of OptiViz is exposed through the optiviz.optimise and optiviz.optimise_interactive functions.

import torch
from optiviz import optimise, optimise_interactive

Any optimisation problem has an objective function. OptiViz works with differentiable, real-valued objective functions in one or two variables.

f : \mathbb{R} \rightarrow \mathbb{R}

g : \mathbb{R}^2 \rightarrow \mathbb{R}

In code, every input and output to the objective function must be a torch.Tensor of shape (1,)

def f(x: torch.Tensor) -> torch.Tensor:
    """
    Example of an objective function in one variable.
    """
    return x ** 2
def g(x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
    """
    Example of an objective function in two variables.
    """
    return x ** 2 + y ** 2 + x.sin() * y.sin()

The optiviz.optimise function (please see docstring for complete usage) is used to visualise the optimisation sequence of a 1D or 2D objective function using a PyTorch optimiser.

arg_g_min = optimise(
        g, # objective function
        (12.5, 12.5), # initial values of the parameters being adjusted
        plot_centre=(0, 0), # plot options
        plot_boundary=25,
        iters=100,
        optimiser=torch.optim.Adam, # PyTorch-compatible optimiser
        lr=5e-1 # any keyword arguments for the optimiser
    )

[NEW] The optiviz.optimise_interactive function (please see docstring for complete usage) provides interactive visualisation of 2D objective functions with multiple optimisers, navigation along the landscape, optimiser tracking, music and more.

optimise_interactive(
        g, # objective function
        (12.5, 12.5), # initial values of the parameters being adjusted
        plot_centre=(0, 0), # plot options
        plot_boundary=25,
        iters=100,
        optimisers = [("Vanilla GD", lambda params: torch.optim.SGD(params, lr=0.1))], # PyTorch-compatible optimisers
        iter_delay: int = 100,
        gimbal_radius: float = 4.0, # advanced visualisation options
        gimbal_hover: float = 8.0,
    )

Example programs

OptiViz 0.x/1.x:

import torch
from optiviz import optimise

f = lambda x,y: ×**2+y**2

optimise(f, init_vector=(12.5, 12.5), optimiser=torch.optim.SGD, lr=le-2)

Optiviz 1.x:

import torch
from optiviz import optimise_interactive

def egg_carton(x, y):
    return 0.05*(x**2+y**2)+2.5*(torch.sin(0.5*x)**2+torch.sin(0.5*y)**2)

optimise_interactive(fn=egg_carton, optimisers=[("SGD with momentum", lambda params: torch.optim.SGD(params, lr=0.1, momentum=0.99)), ("Adam", lambda params: torch.optim.Adam(params, lr=0.5))])