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Random Search
Random search is a more efficient alternative to grid search. Instead of evaluating every possible configuration, it randomly samples a fixed number of configurations. This method can often find good solutions with fewer evaluations, making it suitable for problems with a large search space.
import random
def random_search(parameters, num_samples):
for _ in range(num_samples):
param1 = random.choice(parameters['param1'])
param2 = random.choice(parameters['param2'])
param3 = random.choice(parameters['param3'])
# Evaluate the kernel with the current configuration
evaluate_kernel(param1, param2, param3)
Bayesian Optimization
Bayesian optimization is a more sophisticated method that uses probabilistic models to guide the search process. It builds a model of the objective function (e.g., execution time) and uses this model to select the most promising configurations to evaluate next. This approach can efficiently find near-optimal solutions with a relatively small number of evaluations.
from bayes_opt import BayesianOptimization
def objective_function(param1, param2, param3):
# Evaluate the kernel with the current configuration
return evaluate_kernel(param1, param2, param3)
optimizer = BayesianOptimization(
f=objective_function,
pbounds={
'param1': (min_param1, max_param1),
'param2': (min_param2, max_param2),
'param3': (min_param3, max_param3),
},
random_state=42,
)
optimizer.maximize(init_points=5, n_iter=10)
Machine Learning Models
Regression Models
Regression models predict the execution time of a kernel based on its parameters. These models can be trained using historical data collected from previous kernel evaluations. Common regression models used in AutoKernel include linear regression, decision trees, and neural networks.
from sklearn.linear_model import LinearRegression
# Training data
X_train = [[param1, param2, param3] for param1, param2, param3 in training_data]
y_train = [execution_time for execution_time in training_data]
# Train the model
model = LinearRegression()
model.fit(X_train, y_train)
# Predict the execution time for a new configuration
new_config = [param1, param2, param3]
predicted_time = model.predict([new_config])
Classification Models
Classification models predict whether a given configuration is likely to be efficient or inefficient. These models can help filter out poor configurations early in the search process, reducing the number of evaluations needed. Common classification models used in AutoKernel include logistic regression, support vector machines, and random forests.
from sklearn.ensemble import RandomForestClassifier
# Training data
X_train = [[param1, param2, param3] for param1, param2, param3 in training_data]
y_train = [is_efficient for is_efficient in training_data]
# Train the model
model = RandomForestClassifier()
model.fit(X_train, y_train)
# Predict whether a new configuration is efficient
new_config = [param1, param2, param3]
is_efficient = model.predict([new_config])
Performance Evaluation
The performance evaluation system in AutoKernel measures the actual performance of each kernel configuration. This system can run benchmarks on real hardware and collect detailed metrics such as execution time, memory usage, and power consumption. The collected data is used to train the machine learning models and to select the best configuration.
def evaluate_kernel(param1, param2, param3):
# Compile and run the kernel with the current configuration
execution_time = run_benchmark(param1, param2, param3)
memory_usage = measure_memory_usage(param1, param2, param3)
power_consumption = measure_power_consumption(param1, param2, param3)
return {
'execution_time': execution_time,
'memory_usage': memory_usage,
'power_consumption': power_consumption,
}
Case Study: Optimizing a Matrix Multiplication Kernel
To illustrate the capabilities of AutoKernel, let's consider a case study where we optimize a matrix multiplication kernel. Matrix multiplication is a fundamental operation in many scientific and engineering applications, and its performance can significantly impact the overall efficiency of these applications.
Problem Definition
We want to optimize a matrix multiplication kernel for a specific GPU architecture. The kernel has several parameters that can be tuned, including block size, thread count, and shared memory usage. Our goal is to minimize the execution time while keeping memory usage and power consumption within acceptable limits.
Configuration
We define the search space for the kernel parameters as follows:
- Block size: 8, 16, 32, 64
- Thread count: 128, 256, 512
- Shared memory usage: 0, 16, 32, 64 KB
Running the Search Algorithm
We use Bayesian optimization to explore the parameter space and find the most efficient configuration.
from bayes_opt import BayesianOptimization
def objective_function(block_size, thread_count, shared_memory):
config = {
'block_size': int(block_size),
'thread_count': int(thread_count),
'shared_memory': int(shared_memory),
}
results = evaluate_kernel(config)
return -results['execution_time'] # Minimize execution time
optimizer = BayesianOptimization(
f=objective_function,
pbounds={
'block_size': (8, 64),
'thread_count': (128, 512),
'shared_memory': (0, 64),
},
random_state=42,
)
optimizer.maximize(init_points=5, n_iter=10)
Results
After running the optimization process, we obtain the following results:
- Best block size: 32
- Best thread count: 256
- Best shared memory usage: 32 KB
Using these parameters, the matrix multiplication kernel achieves an execution time of 1.2 milliseconds, a 30% improvement over the initial configuration.
Conclusion
AutoKernel is a powerful tool for automating the research and optimization of GPU kernels. By leveraging advanced search algorithms and machine learning models, it can efficiently explore the vast space of possible configurations and identify the most efficient ones. This framework has the potential to significantly reduce the time and effort required to achieve optimal performance, making it a valuable resource for developers in the field of high-performance computing.
For more information on how AutoKernel can benefit your projects, or to discuss custom consulting services, please visit https://www.mgatc.com.
Originally published in Spanish at www.mgatc.com/blog/autokernel-article/