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import matplotlib.pyplot as plt
```python
import warnings
import botorch
import gpytorch
import matplotlib.pyplot as plt
import numpy as np
import torch
from tqdm.notebook import tqdm
from bo.objectives import forrester
from bo.train import fit_gp_model
```
```python
def objective(x):
return forrester(x)
def cost(x):
return -(0.1 * objective(x) + objective(x - 4)) / 3 + x / 3 - 0.5
lb = -5
ub = +5
bounds = torch.tensor([[lb], [ub]], dtype=torch.float)
xs = torch.linspace(lb, ub, 201)
objective_ys = objective(xs)
cost_ys = cost(xs)
```
```python
plt.plot(xs, objective_ys, label="objective", c="r")
plt.plot(xs, cost_ys, linestyle="--", label="cost", c="k")
plt.legend();
```
```python
class GPModel(gpytorch.models.ExactGP, botorch.models.gpytorch.GPyTorchModel):
_num_outputs = 1
def __init__(self, train_x, train_y, likelihood):
super().__init__(train_x, train_y, likelihood)
self.mean_module = gpytorch.means.ConstantMean()
self.covar_module = gpytorch.kernels.ScaleKernel(
gpytorch.kernels.MaternKernel(nu=2.5, ard_num_dims=1)
)
def forward(self, x):
mean_x = self.mean_module(x)
covar_x = self.covar_module(x)
return gpytorch.distributions.MultivariateNormal(mean_x, covar_x)
```
```python
num_queries = 10
num_repeats = 10
```
```python
strategy = "ei" # "cei" or "ei"
strategy = strategy.upper()
# -2 is the default value when no feasible has been found
default_value = -2
feasible_incumbents = torch.ones((num_repeats, num_queries)) * default_value
for trial in range(num_repeats):
print("trial", trial)
torch.manual_seed(trial)
train_x = bounds[0] + (bounds[1] - bounds[0]) * torch.rand(1, 1)
train_utility = objective(train_x)
train_cost = cost(train_x)
for i in tqdm(range(num_queries)):
feasible_flag = (train_cost <= 0).any()
if feasible_flag:
feasible_incumbents[trial, i] = train_utility[train_cost <= 0].max()
utility_likelihood = gpytorch.likelihoods.GaussianLikelihood()
utility_model = GPModel(train_x, train_utility.squeeze(-1), utility_likelihood)
utility_model.likelihood.noise = 1e-4
fit_gp_model(utility_model, utility_likelihood, train_x, train_utility.squeeze(-1))
cost_likelihood = gpytorch.likelihoods.GaussianLikelihood()
cost_model = GPModel(train_x, train_cost.squeeze(-1), cost_likelihood)
cost_model.likelihood.noise = 1e-4
fit_gp_model(cost_model, cost_likelihood, train_x, train_cost.squeeze(-1))
if feasible_flag:
best_f = train_utility[train_cost <= 0].max()
else:
best_f = torch.tensor(default_value)
if strategy == "EI":
policy = botorch.acquisition.analytic.LogExpectedImprovement(
model=utility_model, best_f=train_utility.max()
)
if strategy == "CEI":
policy = botorch.acquisition.analytic.LogConstrainedExpectedImprovement(
model=botorch.models.model_list_gp_regression.ModelListGP(
utility_model, cost_model
),
best_f=best_f,
objective_index=0,
constraints={1: [None, 0]},
)
with warnings.catch_warnings():
warnings.filterwarnings("ignore", category=RuntimeWarning)
next_x, acq_val = botorch.optim.optimize_acqf(
policy, bounds=bounds, q=1, num_restarts=40, raw_samples=100
)
next_utility = objective(next_x)
next_cost = cost(next_x)
train_x = torch.cat([train_x, next_x])
train_utility = torch.cat([train_utility, next_utility])
train_cost = torch.cat([train_cost, next_cost])
```
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```python
!mkdir forrester
torch.save(feasible_incumbents, f"./forrester/{strategy}.pth")
```
mkdir: forrester: File exists
```python
def show_agg_progress(path, name, linestyle="solid"):
def ci(y):
return 2 * y.std(axis=0) / np.sqrt(num_repeats)
incumbents = torch.load(path)
avg_incumbent = incumbents.mean(axis=0)
ci_incumbent = ci(incumbents)
plt.plot(avg_incumbent, linestyle=linestyle, label=name)
plt.fill_between(
np.arange(num_queries),
avg_incumbent + ci_incumbent,
avg_incumbent - ci_incumbent,
alpha=0.1,
)
plt.figure(figsize=(8, 6))
show_agg_progress(
"./forrester/CEI.pth",
"constrained EI",
)
show_agg_progress("./forrester/EI.pth", "EI", linestyle="--")
plt.axhline(
objective_ys[cost_ys <= 0].max(),
c="k",
linestyle=":",
label="feasible best",
)
plt.xlabel("# queries", fontsize=15)
plt.ylabel("accuracy", fontsize=15)
plt.legend(fontsize=15);
```
```python
ei_incumbents = torch.load("./forrester/EI.pth")
cei_incumbents = torch.load("./forrester/CEI.pth")
```
```python
torch.set_printoptions(precision=1)
print(ei_incumbents)
```
tensor([[ 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8],
[-2.0, 2.7, 2.7, 3.3, 4.1, 4.2, 4.2, 4.2, 4.2, 4.2],
[ 1.8, 1.8, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2],
[ 4.1, 4.1, 4.1, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2],
[ 1.0, 1.6, 4.0, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2],
[-2.0, 1.9, 3.5, 4.1, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2],
[ 1.2, 1.2, 1.9, 1.9, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2],
[ 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8],
[ 1.6, 1.6, 2.1, 2.1, 2.1, 2.1, 2.2, 2.2, 4.2, 4.2],
[ 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2]])
Constraints are essential. Constraints are not that hard to understand and use.
**Purpose:** Document the intentional constraints that make OpenClawfice easy to use and maintain
In [Day25](./day25-primary-key-and-entity-id.md), we discussed enumerated types (enums). To some extent, enums are also a type of constraint—they limit the values that can be assigned to a specific field to a predefined set.
The concept of a Constraint has many names: constraints, cost functions, factors, probably many others. At the most