Variational inequalities under different noise profiles

This the code for Sifting through the noise: Universal first-order methods for stochastic variational inequalities at NeurIPS 2021.

Setup

python setup.py develop

File structure

Experiments (they support vscode's matlab like block execution):

├── experiments
│   ├── kelly_auction2d.py
│   ├── kelly_auction.py
│   ├── kelly_auction_highdim.py
│   ├── learning_covariance.py
│   └── least_squares.py

Code base:

├── virn
│   ├── logging.py
│   ├── methods.py
│   ├── plot.py
│   └── problems.py

Optimal solution for the Kelly auction is computed with the Mathematica script found in Kelly.nb.

Usage

See experiments/ to recreate existing experiments. They can be run interactively in e.g. with vscodes block execution or directly from the terminal:

cd experiments
python kelly_action.py
python kelly_action_highdim.py
python kelly_action_covariance.py

To try a different configuration see the example script below:

from cycler import cycler
import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np
from argparse import Namespace

from virn.logging import Metrics
from virn.methods import OG, DualAvg, DualX, DualOpt
from virn.problems import KellyAuction, KellyAuction2D, KellyAuction4D, NoiseProfile
from virn.plot import plot_kelly, savefigs


# Use Namespace instead of a dict for easy dot notation access (e.g. config.name)
metrics_dict = {}
configs = [
    Namespace(name="DualX non-adaptive", method=DualX(lr=1.0, adaptive=False)),
    Namespace(name="DualX", method=DualX(lr=200.0)),
]

for config in configs:
    kelly = KellyAuction4D()
    noise_profile = NoiseProfile(sigma_abs=0.0, sigma_rel=0.1)
    
    T = 10000
    N  = 10
    X = np.zeros((N, kelly.dim()))
    metrics = Metrics(T)

    for t in range(T):
        grad = kelly.grad(X)
        stoc_grad = noise_profile.add_noise(grad)
        X = config.method.step(X, stoc_grad)
        metrics.add('trajectory', X, t)
        metrics.add('grads', grad, t)
        metrics.add('stoc_grads', stoc_grad, t)

    metrics_dict[config.name] = metrics

# Generate and save the plots
figs, axes = plot_kelly(kelly, metrics_dict, T, num_points=1000)
savefigs("example", figs)