Multi-objective Optimization with Optuna

This tutorial showcases Optuna’s multi-objective optimization feature by optimizing the validation accuracy of Fashion MNIST dataset and the FLOPS of the model implemented in PyTorch.

We use fvcore to measure FLOPS.

Note that when optimizing many objectives, a large fraction of trials may become non-dominated due to the curse of dimensionality in the objective space. If possible, consider modeling some objectives as constraints. Constraints can be passed via the constraints_func argument at the sampler initialization. Currently, NSGAIISampler, NSGAIIISampler, TPESampler, and GPSampler support constrained multi-objective optimization. Since Bayesian optimization is often sample efficient, use TPESampler, or GPSampler for n_trials < 1000.

import torch
import torch.nn as nn
import torch.nn.functional as F
import torchvision
from fvcore.nn import FlopCountAnalysis

import optuna


DEVICE = torch.device("cuda") if torch.cuda.is_available() else torch.device("cpu")
DIR = ".."
BATCHSIZE = 128
N_TRAIN_EXAMPLES = BATCHSIZE * 30
N_VALID_EXAMPLES = BATCHSIZE * 10


def define_model(trial):
    n_layers = trial.suggest_int("n_layers", 1, 3)
    layers = []

    in_features = 28 * 28
    for i in range(n_layers):
        out_features = trial.suggest_int(f"n_units_l{i}", 4, 128)
        layers.append(nn.Linear(in_features, out_features))
        layers.append(nn.ReLU())
        p = trial.suggest_float(f"dropout_{i}", 0.2, 0.5)
        layers.append(nn.Dropout(p))

        in_features = out_features

    layers.append(nn.Linear(in_features, 10))
    layers.append(nn.LogSoftmax(dim=1))

    return nn.Sequential(*layers)


# Defines training and evaluation.
def train_model(model, optimizer, train_loader):
    model.train()
    for batch_idx, (data, target) in enumerate(train_loader):
        data, target = data.view(-1, 28 * 28).to(DEVICE), target.to(DEVICE)
        optimizer.zero_grad()
        F.nll_loss(model(data), target).backward()
        optimizer.step()


def eval_model(model, valid_loader):
    model.eval()
    correct = 0
    with torch.no_grad():
        for batch_idx, (data, target) in enumerate(valid_loader):
            data, target = data.view(-1, 28 * 28).to(DEVICE), target.to(DEVICE)
            pred = model(data).argmax(dim=1, keepdim=True)
            correct += pred.eq(target.view_as(pred)).sum().item()

    accuracy = correct / N_VALID_EXAMPLES

    flops = FlopCountAnalysis(model, inputs=(torch.randn(1, 28 * 28).to(DEVICE),)).total()
    return flops, accuracy

Define multi-objective objective function. Objectives are FLOPS and accuracy.

def objective(trial):
    train_dataset = torchvision.datasets.FashionMNIST(
        DIR, train=True, download=True, transform=torchvision.transforms.ToTensor()
    )
    train_loader = torch.utils.data.DataLoader(
        torch.utils.data.Subset(train_dataset, list(range(N_TRAIN_EXAMPLES))),
        batch_size=BATCHSIZE,
        shuffle=True,
    )

    val_dataset = torchvision.datasets.FashionMNIST(
        DIR, train=False, transform=torchvision.transforms.ToTensor()
    )
    val_loader = torch.utils.data.DataLoader(
        torch.utils.data.Subset(val_dataset, list(range(N_VALID_EXAMPLES))),
        batch_size=BATCHSIZE,
        shuffle=True,
    )
    model = define_model(trial).to(DEVICE)

    optimizer = torch.optim.Adam(
        model.parameters(), trial.suggest_float("lr", 1e-5, 1e-1, log=True)
    )

    for epoch in range(10):
        train_model(model, optimizer, train_loader)
    flops, accuracy = eval_model(model, val_loader)
    return flops, accuracy

Run multi-objective optimization

If your optimization problem is multi-objective, Optuna assumes that you will specify the optimization direction for each objective. Specifically, in this example, we want to minimize the FLOPS (we want a faster model) and maximize the accuracy. So we set directions to ["minimize", "maximize"].

study = optuna.create_study(directions=["minimize", "maximize"])
study.optimize(objective, n_trials=30, timeout=300)

print("Number of finished trials: ", len(study.trials))

Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Unsupported operator aten::log_softmax encountered 1 time(s)
Number of finished trials:  30

Note that the following sections requires the installation of Plotly for visualization and scikit-learn for hyperparameter importance calculation:

$ pip install plotly
$ pip install scikit-learn
$ pip install nbformat  # Required if you are running this tutorial in Jupyter Notebook.

Check trials on Pareto front visually.

optuna.visualization.plot_pareto_front(study, target_names=["FLOPS", "accuracy"])

Fetch the list of trials on the Pareto front with best_trials.

For example, the following code shows the number of trials on the Pareto front and picks the trial with the highest accuracy.

print(f"Number of trials on the Pareto front: {len(study.best_trials)}")

trial_with_highest_accuracy = max(study.best_trials, key=lambda t: t.values[1])
print("Trial with highest accuracy: ")
print(f"\tnumber: {trial_with_highest_accuracy.number}")
print(f"\tparams: {trial_with_highest_accuracy.params}")
print(f"\tvalues: {trial_with_highest_accuracy.values}")

Number of trials on the Pareto front: 9
Trial with highest accuracy:
        number: 23
        params: {'n_layers': 1, 'n_units_l0': 127, 'dropout_0': 0.3851532529389119, 'lr': 0.005254345176677965}
        values: [100838.0, 0.8359375]

Learn which hyperparameters are affecting the flops most with hyperparameter importance.

optuna.visualization.plot_param_importances(
    study, target=lambda t: t.values[0], target_name="flops"
)