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My research over Bayesian Optimization and Gaussian Processes Eduardo C. GarridoMerch an PhD student. Teacher Assistant. Universidad Aut onoma de Madrid 1/13 Index Introduction: Bayesian Optimization and Gaussian Processes. 2/13

  1. My research over Bayesian Optimization and Gaussian Processes Eduardo C. Garrido–Merch´ an PhD student. Teacher Assistant. Universidad Aut´ onoma de Madrid 1/13

  2. Index ◮ Introduction: Bayesian Optimization and Gaussian Processes. 2/13

  3. Index ◮ Introduction: Bayesian Optimization and Gaussian Processes. ◮ Predictive Entropy Search for Constrained Multiobjective Scenarios. 2/13

  4. Index ◮ Introduction: Bayesian Optimization and Gaussian Processes. ◮ Predictive Entropy Search for Constrained Multiobjective Scenarios. ◮ Dealing with Integer and Categorical Valued Variables in GP-BO. 2/13

  5. Index ◮ Introduction: Bayesian Optimization and Gaussian Processes. ◮ Predictive Entropy Search for Constrained Multiobjective Scenarios. ◮ Dealing with Integer and Categorical Valued Variables in GP-BO. ◮ Parallel PESMOC. 2/13

  6. Index ◮ Introduction: Bayesian Optimization and Gaussian Processes. ◮ Predictive Entropy Search for Constrained Multiobjective Scenarios. ◮ Dealing with Integer and Categorical Valued Variables in GP-BO. ◮ Parallel PESMOC. ◮ Applications over Bayesian Networks, Wave Energy and Cooking. 2/13

  7. Index ◮ Introduction: Bayesian Optimization and Gaussian Processes. ◮ Predictive Entropy Search for Constrained Multiobjective Scenarios. ◮ Dealing with Integer and Categorical Valued Variables in GP-BO. ◮ Parallel PESMOC. ◮ Applications over Bayesian Networks, Wave Energy and Cooking. ◮ Ideas for DarkMachines unsupervised learning project. 2/13

  8. Challenges in Engineering Design The society demands new products of better quality, functionality, usability, etc.! 3/13

  9. Challenges in Engineering Design The society demands new products of better quality, functionality, usability, etc.! 3/13

  10. Challenges in Engineering Design The society demands new products of better quality, functionality, usability, etc.! ◮ Many choices at each step. 3/13

  11. Challenges in Engineering Design The society demands new products of better quality, functionality, usability, etc.! ◮ Many choices at each step. ◮ Complicated and high dimensional. 3/13

  12. Challenges in Engineering Design The society demands new products of better quality, functionality, usability, etc.! ◮ Many choices at each step. ◮ Complicated and high dimensional. ◮ Difficult for individuals to reason about. 3/13

  13. Challenges in Engineering Design The society demands new products of better quality, functionality, usability, etc.! ◮ Many choices at each step. ◮ Complicated and high dimensional. ◮ Difficult for individuals to reason about. ◮ Prone to human bias. 3/13

  14. Challenges in Engineering Design The society demands new products of better quality, functionality, usability, etc.! ◮ Many choices at each step. ◮ Complicated and high dimensional. ◮ Difficult for individuals to reason about. ◮ Prone to human bias. Optimization is a challenging task in new products design! 3/13

  15. Example: Deep Neural Network for object recognition. 4/13

  16. Example: Deep Neural Network for object recognition. Parameters to tune : Number of neurons ( Integer-Valued ), number of layers ( Integer-Valued ), learning-rate, activation function ( Categorical-Valued ), etc. 4/13

  17. Optimization Problems: Common Features ◮ Very expensive evaluations. 5/13

  18. Optimization Problems: Common Features ◮ Very expensive evaluations. ◮ The objective is a black-box. 5/13

  19. Optimization Problems: Common Features ◮ Very expensive evaluations. ◮ The objective is a black-box. 1 0 ◮ The evaluation can be −1 noisy. 0 1 5/13

  20. Optimization Problems: Common Features ◮ Very expensive evaluations. ◮ The objective is a black-box. 1 0 ◮ The evaluation can be −1 noisy. 0 1 Bayesian optimization methods can be used to solve these problems! 5/13

  21. Bayesian Optimization in Practice objective 1. Get initial sample. 6/13

  22. Bayesian Optimization in Practice objective 1. Get initial sample. objective 6/13

  23. Bayesian Optimization in Practice objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 6/13

  24. Bayesian Optimization in Practice objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 6/13

  25. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 6/13

  26. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 4. Optimize acquisition function α ( x ). Acquisition Function α ( x ) 6/13

  27. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 4. Optimize acquisition function α ( x ). Acquisition Function α ( x ) 5. Collect data and update model. 6/13

  28. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 4. Optimize acquisition function α ( x ). Acquisition Function α ( x ) 5. Collect data and update model. 6. Repeat! 6/13

  29. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 4. Optimize acquisition function α ( x ). Acquisition Function α ( x ) 5. Collect data and update model. 6. Repeat! 6/13

  30. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 4. Optimize acquisition function α ( x ). Acquisition Function α ( x ) 5. Collect data and update model. 6. Repeat! 6/13

  31. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 4. Optimize acquisition function α ( x ). Acquisition Function α ( x ) 5. Collect data and update model. 6. Repeat! 6/13

  32. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 4. Optimize acquisition function α ( x ). Acquisition Function α ( x ) 5. Collect data and update model. 6. Repeat! 6/13

  33. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 4. Optimize acquisition function α ( x ). Acquisition Function α ( x ) 5. Collect data and update model. 6. Repeat! 6/13

  34. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 4. Optimize acquisition function α ( x ). Acquisition Function α ( x ) 5. Collect data and update model. 6. Repeat! 6/13

  35. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 4. Optimize acquisition function α ( x ). Acquisition Function α ( x ) 5. Collect data and update model. 6. Repeat! 6/13

  36. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 4. Optimize acquisition function α ( x ). Acquisition Function α ( x ) 5. Collect data and update model. 6. Repeat! 6/13

  37. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 4. Optimize acquisition function α ( x ). Acquisition Function α ( x ) 5. Collect data and update model. 6. Repeat! 6/13

  38. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 4. Optimize acquisition function α ( x ). Acquisition Function α ( x ) 5. Collect data and update model. 6. Repeat! 6/13

  39. Bayesian Optimization in Practice Objective 1. Get initial sample. 2. Fit a model to the data: p ( y | x , D n ) . 3. Select data collection strategy: α ( x ) = E p ( y | x , D n ) [ U ( y | x , D n )] . 4. Optimize acquisition function α ( x ). Acquisition Function α ( x ) 5. Collect data and update model. 6. Repeat! 6/13

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