Contextual Bayesian Optimization of Heating Curves

Buildings in Switzerland contribute significantly to energy consumption, accounting for 42% of total energy use and 26% of CO2 emissions, with heating representing 68% of this energy. Addressing the challenge of reduc-ing heating energy consumption is critical, though it must be done while maintaining tenant comfort. One approach to this is the implementation of an adaptive system. Our adaptive system is based on optimiz-ing heating curves using Contextual Bayesian Optimization. Heating curves are general function that describes the relationship between ambient temperatures and supplied heating power to secure a pleasant environment for the tenants. The simplest heating curves are 2 point linear heating curves described by two parameters. The optimization process involves adjusting the underlying heating parameters, we call the process of finding new parameters short action, through simulation, measuring energy and comfort costs to minimize energy use while ensuring comfort and update the heating curve with the additional information, before starting the next iteration. In our current setting we optimize a 2 point linear heating curve limit to 1 action and 1 contextual information. A key advantage of our approach is its simplicity, that makes it easy to set-up and choose parameters for and representing the benefits in a way that is understandable for the target audience (see additional information attached). However, while adaptive systems offer substantial improvements over static models, their complexi-ty and black-box nature can pose challenges in understanding, which may hinder broader adoption. Ensuring the model's transparency and usability is essential for its success. For more details see the attachment AHA: Contextual Bayesian Optimization of Heating Curves. This semester thesis will build on the existing system and take a closer look at the following research ques-tions: Heating Curve Parameterization We want to answer is which parametrization of the heating curve could be most beneficial. Some simple ex-amples of curves that could be used are: linear curve, segmented linear curve, quadratic interpolation and clipped quadratic interpolation. A more complex curve (for example one with multiple inflection points) could also be considered. Interpretability and Interactivity To maximize the model's benefits, it must not only achieve the stated objective of reducing cost while maintaining comfort, but also surpass the difficult hurdle of representing the benefits in a way that is understandable for the target audience. The plan is to create a simple interface showing the acquired data-points, along with what the model estimates is: - the "safe" region of the parameter space based on constraints imposed by the maximum tolerated dis-comfort and physical limitations; - the mean of the cost function, showing the quantity explained by the comfort level and the one explained by the energy cost; - confidence bound of the cost function. The breakdown of the cost function is the most significant part in this interface, as it could show a trade-off between the achieved comfort levels and the energy cost. The safe region is also an essential element as it displays the trade-off between exploration and exploitation in the model: a narrow safety region may suggest that the model is being too conservative, leading to subop-timal results. To get a clearer idea of the model behavior, the interface will include an interactive feature, allowing users to drag the various points of the heating curve. New values for safety regions and cost functions will then be computed based on the updated interpolated curve. The interface will offer two kinds of visualizations of the heating curve: one displaying the cost function esti-mates for every point, and another that focuses on one of the two boundary points. The second visualization will show the two-dimensional cost function level sets and allows dragging the endpoints in any direction, which might be too unintuitive for the first visualization. Choice of Algorithm The final research question revolves around choosing the algorithm, particularly focusing on two aspects: in-corporation of context and safety considerations. 1. Regarding incorporation of context, following the suggestions in [1], we aim to understand how integrating contextual information influences the model. In particular we consider the following alternatives: - Ignore the context; - Divide the data into buckets of equal width; - Use a composite kernel to combine context and parameters. 2. Regarding Safety considerations in the acquisition function, different algorithms offer varying guarantees in how they approach safety while trading-off exploration and exploitation. Exploring multiple approaches could lead to an algorithm that optimizes effectively while ensuring safety. The main options under consideration in-clude: - SafeOPT [2], an approach that ensures that every sampled point is safe with high probability. At each iteration, it selects a point that could expand the safe set (expander) or one that could improve the upper confidence bound (maximizer); - Safe GP-LCB as proposed in [3], this approach extends the GP Lower Confidence Bound by including a safe region, this could lead to faster convergence; - Including a large penalty for points which are likely to be unsafe. The algorithms will be compared on several criteria: - convergence speed; - optimality; - cumulative violations regret; - cumulative cost regret. Understanding the effects of various forms of non-linearities on the mentioned criteria is also crucial - [1] Krause, Andreas and Ong, Cheng Soon (2011). Contextual Gaussian process bandit optimization, https://dl.acm.org/doi/10.5555/2986459.2986732. - [2] Sui, Yanan and Gotovos, Alkis and Burdick, Joel and Krause, Andreas (2015). Safe Exploration for Optimiza-tion with Gaussian Processes, https://proceedings.mlr.press/v37/sui15.html. - [3] Marcello, Fiducioso and Sebastian, Curi and Benedikt, Schumacher and Markus, Gwerder and Andreas, Krause (2019). Safe Contextual Bayesian Optimization for Sustainable Room Temperature PID Control Tuning, https://arxiv.org/abs/1906.12086.

Buildings in Switzerland contribute significantly to energy consumption, accounting for 42% of total energy use and 26% of CO2 emissions, with heating representing 68% of this energy. Addressing the challenge of reduc-ing heating energy consumption is critical, though it must be done while maintaining tenant comfort.
One approach to this is the implementation of an adaptive system. Our adaptive system is based on optimiz-ing heating curves using Contextual Bayesian Optimization. Heating curves are general function that describes the relationship between ambient temperatures and supplied heating power to secure a pleasant environment for the tenants. The simplest heating curves are 2 point linear heating curves described by two parameters. The optimization process involves adjusting the underlying heating parameters, we call the process of finding new parameters short action, through simulation, measuring energy and comfort costs to minimize energy use while ensuring comfort and update the heating curve with the additional information, before starting the next iteration.
In our current setting we optimize a 2 point linear heating curve limit to 1 action and 1 contextual information. A key advantage of our approach is its simplicity, that makes it easy to set-up and choose parameters for and representing the benefits in a way that is understandable for the target audience (see additional information attached). However, while adaptive systems offer substantial improvements over static models, their complexi-ty and black-box nature can pose challenges in understanding, which may hinder broader adoption. Ensuring the model's transparency and usability is essential for its success. For more details see the attachment AHA: Contextual Bayesian Optimization of Heating Curves.
This semester thesis will build on the existing system and take a closer look at the following research ques-tions:
Heating Curve Parameterization
We want to answer is which parametrization of the heating curve could be most beneficial. Some simple ex-amples of curves that could be used are: linear curve, segmented linear curve, quadratic interpolation and clipped quadratic interpolation. A more complex curve (for example one with multiple inflection points) could also be considered.
Interpretability and Interactivity
To maximize the model's benefits, it must not only achieve the stated objective of reducing cost while
maintaining comfort, but also surpass the difficult hurdle of representing the benefits in a way that is
understandable for the target audience. The plan is to create a simple interface showing the acquired data-points, along with what the model estimates is:
- the "safe" region of the parameter space based on constraints imposed by the maximum tolerated dis-comfort and physical limitations;
- the mean of the cost function, showing the quantity explained by the comfort level and the one explained by the energy cost;
- confidence bound of the cost function.
The breakdown of the cost function is the most significant part in this interface, as it could show a trade-off between the achieved comfort levels and the energy cost.
The safe region is also an essential element as it displays the trade-off between exploration and exploitation in the model: a narrow safety region may suggest that the model is being too conservative, leading to subop-timal results.
To get a clearer idea of the model behavior, the interface will include an interactive feature, allowing users to drag the various points of the heating curve. New values for safety regions and cost functions will then be computed based on the updated interpolated curve.
The interface will offer two kinds of visualizations of the heating curve: one displaying the cost function esti-mates for every point, and another that focuses on one of the two boundary points. The second visualization will show the two-dimensional cost function level sets and allows dragging the endpoints in any direction, which might be too unintuitive for the first visualization.
Choice of Algorithm
The final research question revolves around choosing the algorithm, particularly focusing on two aspects: in-corporation of context and safety considerations.
1. Regarding incorporation of context, following the suggestions in [1], we aim to understand how integrating contextual information influences the model. In particular we consider the following alternatives:
- Ignore the context;
- Divide the data into buckets of equal width;
- Use a composite kernel to combine context and parameters.
2. Regarding Safety considerations in the acquisition function, different algorithms offer varying guarantees in how they approach safety while trading-off exploration and exploitation. Exploring multiple approaches could lead to an algorithm that optimizes effectively while ensuring safety. The main options under consideration in-clude:
- SafeOPT [2], an approach that ensures that every sampled point is safe with high probability. At each iteration, it selects a point that could expand the safe set (expander) or one that could improve the upper confidence bound (maximizer);
- Safe GP-LCB as proposed in [3], this approach extends the GP Lower Confidence Bound by including a safe region, this could lead to faster convergence;
- Including a large penalty for points which are likely to be unsafe.
The algorithms will be compared on several criteria:
- convergence speed;
- optimality;
- cumulative violations regret;
- cumulative cost regret.
Understanding the effects of various forms of non-linearities on the mentioned criteria is also crucial

- [1] Krause, Andreas and Ong, Cheng Soon (2011). Contextual Gaussian process bandit optimization, https://dl.acm.org/doi/10.5555/2986459.2986732.
- [2] Sui, Yanan and Gotovos, Alkis and Burdick, Joel and Krause, Andreas (2015). Safe Exploration for Optimiza-tion with Gaussian Processes, https://proceedings.mlr.press/v37/sui15.html.
- [3] Marcello, Fiducioso and Sebastian, Curi and Benedikt, Schumacher and Markus, Gwerder and Andreas, Krause (2019). Safe Contextual Bayesian Optimization for Sustainable Room Temperature PID Control Tuning, https://arxiv.org/abs/1906.12086.

**Deliverables:** - Literature Review und study of software tools - Parametrization of Heating Curves: Implementations of various heating curve models (linear, quadratic, etc.), Documentation comparing the performance of these models under different conditions, Analysis of the pros and cons of complex vs. simple heating curve - Development of a prototype of a UI that visualizes: Safe regions of the parameter space. Cost function components (comfort level vs. energy cost). Confidence bounds of the cost function. Interactive feature allowing users to modify the heating curve and observe changes in the safety region and cost function. - Algorithm Selection and Implementation: Implementation of various algorithms (SafeOPT, Safe GP-LCB, etc.) to ensure safe and efficient ex-ploration of the parameter space. - Comparison of algorithms based on: Convergence speed, optimality, cumulative violation and cost regret. - Evaluation of Context Incorporation: Simulation on integrating contextual information into the model. Comparison of methods (ignoring context, dividing data into buckets, composite kernel). Documentation of the impact of contextual information on performance. - Discussion and Conclusion: Insights on the most effective heating curve parametrization for different scenarios. Recommendations on the best algorithms for balancing safety and optimality. Future work directions for extending the model or improving user interactivity. **Requirement:** - We are seeking a student with experience in machine learning or optimization, who is enthusiastic about contributing to a project with practical applicability. - Prior knowledge in Gaussian Process (GP) and Bayesian Optimization (BO) is not expected but will be part of your literature studies. - Basic knowledge in python is mandatory and nice to have are conceptual ideas of digital twin and building energy simulation programs e.g. EnergyPlus. - Students need to find a supervisor at their home university.

**Deliverables:**

- Literature Review und study of software tools

- Parametrization of Heating Curves: Implementations of various heating curve models (linear, quadratic, etc.), Documentation comparing the performance of these models under different conditions, Analysis of the pros and cons of complex vs. simple heating curve

- Development of a prototype of a UI that visualizes: Safe regions of the parameter space. Cost function components (comfort level vs. energy cost). Confidence bounds of the cost function. Interactive feature allowing users to modify the heating curve and observe changes in the safety region and cost function.

- Algorithm Selection and Implementation: Implementation of various algorithms (SafeOPT, Safe GP-LCB, etc.) to ensure safe and efficient ex-ploration of the parameter space.

- Comparison of algorithms based on: Convergence speed, optimality, cumulative violation and cost regret.

- Evaluation of Context Incorporation: Simulation on integrating contextual information into the model. Comparison of methods (ignoring context, dividing data into buckets, composite kernel). Documentation of the impact of contextual information on performance.

- Discussion and Conclusion: Insights on the most effective heating curve parametrization for different scenarios. Recommendations on the best algorithms for balancing safety and optimality. Future work directions for extending the model or improving user interactivity.

**Requirement:**

- We are seeking a student with experience in machine learning or optimization, who is enthusiastic about contributing to a project with practical applicability.

- Prior knowledge in Gaussian Process (GP) and Bayesian Optimization (BO) is not expected but will be part of your literature studies.

- Basic knowledge in python is mandatory and nice to have are conceptual ideas of digital twin and building energy simulation programs e.g. EnergyPlus.

- Students need to find a supervisor at their home university.

Contact Details If this thesis looks interesting reach out to us and let’s chat about your background and explore how your skills align with our project: michael.locher@empa.ch

Contact Details
If this thesis looks interesting reach out to us and let’s chat about your background and explore how your skills align with our project: michael.locher@empa.ch