Control device and method for selecting evaluation points for Bayesian optimization method

Abstract

Control apparatus and method for selecting evaluation points for Bayesian optimization. A method for selecting evaluation points for Bayesian optimization of a physical or chemical process modeled by a statistical model is described, the method comprising: determining a posterior model of the statistical model based on the results of one or more evaluations at previous evaluation points; and selecting the next evaluation point by optimizing a collection function with respect to a search space, the next evaluation point being given by a pre-given limit of the predicted variance of points in the search space given by the posterior model.

Description

Technical Field

[0001] Different embodiments generally relate to control devices and methods for selecting evaluation points for Bayesian optimization. Background Technology

[0002] In control processes, such as controlling facilities used to produce products, process workpieces, or move robots, the relationship between the values ​​of control parameters and the results—that is, the observable output parameter values—can be very complex. Furthermore, such evaluation of control parameter values ​​can be costly and error-prone. In such cases, Bayesian optimization (BO) is suitable for determining control parameter values ​​because it allows for the optimization of an unknown black-box function when only noisy evaluations are available. The efficiency of Bayesian optimization depends heavily on how the evaluation points are chosen. Correspondingly, it is desirable to have methods for selecting evaluation points for Bayesian optimization that enable efficient control of, for example, robots. Summary of the Invention

[0003] According to different implementations, a method is provided for selecting evaluation points for Bayesian optimization used to optimize a physical or chemical process modeled by a statistical model, the method comprising: determining a posterior model of the statistical model based on the results of one or more evaluations at previous evaluation points; and selecting a next evaluation point by optimizing a collection function with respect to a search space, the next evaluation point being given by a pre-given limit of the predicted variance of points in the search space given by the posterior model.

[0004] Bayesian optimization is a very general method for optimizing functions. Its advantages include: high efficiency due to the small number of function evaluations required to find the optimal value; the ability to handle noisy function evaluations; and the lack of gradient information. Therefore, it is suitable for numerous applications where experimental parameters must be optimized to maximize certain parameters.

[0005] The method described above for selecting evaluation points for Bayesian optimization fully utilizes prior knowledge about good control parameter values ​​and carefully explores the control parameter space. This local approach (rather than a global approach) allows Bayesian optimization to be applied to control parameter spaces with relatively high dimensions (e.g., dimensions 10 to 100). Examples of applications include the design of control devices, the optimization of process parameters in manufacturing technologies, or the optimization of components with a large number of control parameters.

[0006] The above approach enables efficient optimization in terms of the number of required functional assessments (low so-called "Simple Regret") and careful investigation of the control parameter space, so that damage (e.g., in controlled devices like robots) is avoided (low so-called "Cumulative Regret").

[0007] Different embodiments are described below.

[0008] Example 1 is a method for selecting evaluation points for Bayesian optimization as described above.

[0009] Example 2 follows the method of Example 1, wherein the static model is a Gaussian process and the predetermined limit is a predetermined fraction of the signal variance of the kernel of the Gaussian process.

[0010] Efficient Bayesian optimization can be achieved by modeling the process using Gaussian processes. A pre-defined limit is determined based on the signal variance of the Gaussian process kernel, thus fitting the search space to the kernel of the Gaussian process.

[0011] Example 3 follows the method of Example 1 or 2, wherein a set of alternative schemes for the next evaluation point is determined by sampling from the evaluation point range, and one of these alternative schemes is selected as the next evaluation point for which the acquisition function takes the optimal value in the set of alternative schemes.

[0012] This enables efficient optimization of the search space.

[0013] Example 4 follows the method of Example 3, wherein the evaluation range is a subset of the parameter range and the set of alternatives is determined by sampling using a rejection method from the parameter range, wherein samples not in the search space are discarded.

[0014] As described above, the search space is typically discontinuous. The approach described in claim 4 still allows for efficient sampling (i.e., selecting samples from the search space) in this case.

[0015] Example 5 follows the method of Example 4, wherein sampling within the parameter range involves sampling in subspaces of the parameter range, each subspace containing one or more of the previously evaluated points.

[0016] In this way, it can be guaranteed that all related components of the search space are detected during sampling. Sampling can also be performed at low cost by choosing a simple subspace (especially a low-dimensional subspace, such as a one-dimensional subspace).

[0017] Example 6 is a control device configured to implement the method according to any one of Examples 1 to 5.

[0018] Example 7 is a production system comprising: a control device according to Example 6; production equipment configured to manufacture a product by means of a physical or chemical process; and at least one sensor configured to provide the control device with output parameter values ​​of the physical or chemical process assigned to control parameter values; wherein the control device is configured to determine one or more optimal control parameter values ​​of the physical or chemical process by means of Bayesian optimization, wherein the control device evaluates the control parameter values ​​using the output parameter values, and controls the production equipment according to the determined one or more control parameter values.

[0019] Example 8 is a processing system comprising: a control device according to Example 6; a processing apparatus configured to process a workpiece by means of a physical or chemical process; at least one sensor configured to provide the control device with an output parameter value of the physical or chemical process assigned to control parameter values; wherein the control device is configured to: determine one or more optimal control parameter values ​​of the physical or chemical process by means of Bayesian optimization, wherein the control device evaluates the control parameter values ​​using the output parameter values; and control the processing apparatus according to the determined one or more control parameter values.

[0020] Example 9 is a robot system comprising: a control device according to Example 6; a robot element configured to perform movement by means of a physical or chemical process; at least one sensor configured to provide the control device with output parameter values ​​of the physical or chemical process assigned to control parameter values; wherein the control device is configured to determine one or more optimal control parameter values ​​of the physical or chemical process by means of a Bayesian optimization method, wherein the control device evaluates the control parameter values ​​using the output parameter values, and controls the robot element according to the determined one or more control parameter values.

[0021] Example 10 is a computer program having program instructions that, when implemented by one or more processors, cause the one or more processors to perform the method according to any one of Examples 1 to 5.

[0022] Example 11 is a computer-readable storage medium having stored thereon program instructions that, when implemented by one or more processors, cause the one or more processors to perform the method according to any one of Examples 1 to 5. Attached Figure Description

[0023] Embodiments of the invention are shown in the accompanying drawings and described in detail below. In the drawings, the same reference numerals generally refer to the same parts in various views. These drawings are not necessarily to scale, but their emphasis is generally on illustrating the principles of the invention.

[0024] Figure 1 A robot according to an embodiment is shown.

[0025] Figure 2 A flowchart illustrating a method for determining control parameters by means of Bayesian optimization according to an embodiment is shown.

[0026] Figure 3 A flowchart illustrating a method for selecting evaluation points for Bayesian optimization according to an embodiment is shown. Detailed Implementation

[0027] Different implementations, particularly the embodiments described below, can be implemented using one or more circuits. In one implementation, "circuit" can be understood as any type of logical implementation entity, which can be hardware, software, firmware, or a combination thereof. Thus, in one implementation, "circuit" can be hardwired logic circuitry or programmable logic circuitry, such as a programmable processor, for example, a microprocessor. "Circuit" can also be software implemented or carried out by a processor, such as any type of computer program. According to an alternative implementation, any other type of implementation of the corresponding functionality can be understood as "circuit," which is described in more detail below.

[0028] Figure 1 Robot 100 is shown.

[0029] Robot 100 includes a robot arm 101 (typically a robotic element), such as an industrial robot arm for moving, mounting, or processing workpieces. Robot arm 101 has robot links 102, 103, and 104 and a base (or typically a support) 105, through which these robot links 102, 103, and 104 are supported. The term "robot link" refers to the movable portion of robot arm 101, the manipulation of which enables physical interaction with the surrounding environment, for example, to perform a task. For control purposes, robot 100 includes a control device 106 configured to interact with the surrounding environment according to a control program. The last element 104 of robot links 102, 103, and 104 (viewed from the base 105) is also called an end effector 104 and may contain one or more tools, such as a welding torch, a gripping tool, a painting device, etc.

[0030] Other robot links 102, 103 (closer to the base 105) can form a positioning device such that a robot arm (or articulated arm) with an end effector 104 at its end is positioned together with the end effector 104. The robot arm 101 is a robotic arm that can perform activities similar to those of a human arm (possibly using tools at its end).

[0031] The robotic arm 101 may include connecting elements 107, 108, and 109 that connect robotic links 102, 103, and 104 to each other and to a base 105. Connecting elements 107, 108, and 109 may have one or more joints, each of which can provide rotational and / or translational (i.e., displacement) motion of its associated robotic link relative to each other. The movement of robotic links 102, 103, and 104 can be guided by means of an adjusting element controlled by a control device 106.

[0032] The term "regulatory element" can be understood as a component adapted to influence a mechanism in response to its actuation. The regulator can convert a command (so-called activation) output by the control device 106 into mechanical motion. The regulator, for example, an electromechanical converter, can be configured to convert electrical energy into mechanical energy in response to its manipulation.

[0033] The term "control device" (also known as "Controller") can be understood as any type of logical implementation unit, which may include, for example, circuitry and / or a processor capable of implementing software, firmware, or a combination thereof stored in a storage medium and issuing commands to, for example, the regulating element in the current example. The control device can be configured, for example, as a control system, or in the current example, the operation of a robot, through program code (e.g., software).

[0034] In the current example, the control device 106 includes a memory 111 and one or more processors 110. The memory stores code and data, and the processors 110 control the robot arm 101 based on this code and data. In different implementations, the control device 106 controls the robot arm 101 based on control rules (also known as "policies") 112 stored in the memory 111.

[0035] It should be noted that the design of the robot 100 with a robotic arm is merely an example, and the robot can be designed in the form of any machine in which mechanical components (including valves or other movable parts) can be controlled.

[0036] Examples of robots include manufacturing machines that are improved with the help of artificial intelligence, such as milling machines, lathes, and deep hole drills, where the control device 106 adjusts, for example, the feed rate of the deep hole drill, the rotational speed of the milling head, etc., as a function of the machine's current state (and / or time).

[0037] Here, control rule 112 has, for example, control parameters that affect control behavior in order to, for example, balance production speed and wear and tear between machines.

[0038] These parameters can be adjusted by an expert with years of expertise (and then left unchanged). However, even for an expert, it is difficult to adjust a control device with more than about 10 parameters (this number may, of course, vary from machine to machine).

[0039] One possible application of the implementation described below is to adjust these control parameters based on initial expert adjustments to optimize a quality standard, such as production speed. Other applications could include control devices in vehicles used for ESP (Electronic Stability Program) or ABS (Anti-lock Braking System).

[0040] In cases of complex robots (such as robots with a large number of degrees of freedom, like a robotic arm 101), it is very rare for experts to tune the control parameters, as the number of parameters often exceeds 20 to 50. Therefore, simulation is typically used to tune these parameters. However, simulations often do not precisely match reality, and the parameters optimized in simulation do not meet the quality standards of the real system (i.e., the real robot in its real environment). Nevertheless, the parameter values ​​obtained through simulation can serve as a good starting point for fine-tuning the real system, similar to what experts did in the aforementioned example with simpler machines. In this case, how the control criteria are parameterized is not important. A very specific application here is, for example, the field of manipulator robots used for automated installation or disassembly of components.

[0041] The control device 106 can not only drive the actuator to adjust its position in the space of the component (such as the end effector 104), but can also generally control it to adjust process parameters in the production or processing process, such as process temperature, process time, vacuum or gas atmosphere, etc., so as to obtain the desired properties of the workpiece, such as hardness, strength, thermal conductivity, electrical conductivity, etc., by adjusting controlled components such as valves or power supplies.

[0042] In control scenarios involving robots, machines, production, or processing facilities, output parameters are often noisy. This means that, although the position of the manipulated object or the characteristics achieved by the workpiece depends on the input parameter values ​​(i.e., the control parameters, which in turn cause specific process parameters), these output parameter values ​​can vary even if the control parameter values ​​are the same.

[0043] To obtain the desired output parameter values, the control parameters should be determined such that the objective function, which depends on the output parameters, is optimized. For example, the object to be moved should be moved as close to its destination as possible, a specific temperature should be adjusted as precisely as possible, or the product's hardness should be as close as possible to the target value.

[0044] Because the output parameter values ​​are noisy and the objective function depends on these output parameter values, the objective function is also noisy. Furthermore, the objective function is often unknown because it represents a complex relationship between the input parameter values ​​and the output parameters (the value of which depends on the objective function).

[0045] The control device 106 can acquire sensor data from one or more sensors 113 (e.g., cameras in the robot example, and temperature sensors, current sensors, etc. in other applications) to obtain information about the output parameter values ​​for a specific input parameter value (i.e., the control parameter value), that is, to evaluate the objective function. The sensor 113 may also be, for example, part of the robot arm 101.

[0046] Depending on the implementation method, control parameters are determined for optimizing physical or chemical processes (i.e., the objective function given above) using Bayesian optimization.

[0047] If an unknown function f (a so-called "black-box" function, such as the objective function in the example above) should be optimized (minimized or maximized), then Bayesian optimization can be applied. This unknown function f is one that can be evaluated or measured only for the value x and observed (possibly due to noise). The observed value y is then y = f(x) + e, where e represents the noise component. It is also assumed that each evaluation (measurement) of the unknown function f is expensive, meaning it incurs costs, as is the case when conducting experiments on a lab bench. Since evaluating the unknown function is expensive, it is desirable to perform only a small number of evaluations during optimization. Under certain preconditions, such as the continuity of the unknown function, a statistical model can be used to approximate the unknown function. Gaussian processes (also known as Gausscher Prozess) are typically used as statistical models, which means performing Gaussian process regression on evaluation points (x1, ..., xn) and the evaluations at these evaluation points, that is, on the observations of the corresponding function values ​​(y1, ..., yn) at these evaluation points.

[0048] The characteristic of a Gaussian process is that, within the range of the evaluation point, the model predictions are very good and the unknown function is well approximated. This is reflected in the low uncertainty of the model predictions. As one moves away from previous evaluation points, the model predictions for the unknown function worsen, and the uncertainty increases with distance from these evaluation points. One possible strategy for optimizing the function f is to evaluate the unknown function at multiple different locations (e.g., on a regular grid) and adopt the lowest observed function value as the optimization result. However, this approach is inefficient and requires a correspondingly high number of evaluations to find the optimum.

[0049] Alternatively, the Gaussian process itself can be used to select new evaluation points. For this purpose, new evaluation points are chosen such that, on the one hand, the persuasiveness of the model is improved, for example, the uncertainty of the estimated expected value of the unknown function is reduced. For this purpose, evaluation points are typically selected within a range where the unknown function has not yet been evaluated (exploration). On the other hand, new evaluation points for evaluating the unknown function are chosen such that the goal of finding the optimal value is achieved as quickly as possible or with a small number of measurements at these evaluation points. For this purpose, evaluation points (according to the Gaussian process) are preferably selected that predict low function values ​​(in the case of minimization) or high function values ​​(in the case of maximization) (exploration). These two conflicting criteria are balanced by selecting evaluation points using a pre-given acquisition function. The acquisition function uses a Gaussian process, i.e., the expected value μ(x) and the standard deviation σ(x) assigned to that expected value.

[0050] The example is the so-called LCB (Lower Confidence Bound) acquisition function, which is given below:

[0051] LCB(x) = μ(x) - kσ(x).

[0052] The factor k is, for example, constantly specified to a specific value, such as k = 2. This criterion can be efficiently minimized using common gradient-based methods, and the location of the minimum of LCB(x) then forms a new evaluation point for the unknown function f.

[0053] In this case, it is important to note that the acquisition function should be optimized for a specific range, that is, the range within which the next evaluation point is searched.

[0054] After evaluating the function f at the selected next evaluation point, the Gaussian process is updated using the new data, and the next evaluation point is selected according to the method described above. Typically, the selection of the evaluation point, the evaluation at the selected evaluation point, and the update of the Gaussian process based on the evaluation are iteratively repeated until the interruption criterion is met, i.e., until the time required to optimize the unknown function f is reached.

[0055] In the case of minimizing the function, the point that minimizes the expected value of the Gaussian process (i.e., the input parameter value vector or control parameter value vector) is then output as the location of the minimum value of the function. Similarly, in the case of maximizing, the point that maximizes the expected value of the Gaussian process is output. This point then represents the control parameter value vector by which the robot, machine, or facility is controlled.

[0056] In addition to the LCB acquisition function, other acquisition functions can be used, which are based on other acquisition criteria, such as EI (Expected Improvement), UCB (Upper Confidence Bound), PI (Probability of Improvement), or the so-called entropy-search method, which is based on information theory considerations.

[0057] As mentioned above, the acquisition function is optimized over a specific range of control parameter values ​​and combinations thereof (i.e., the control parameter vector, hereinafter referred to as the control parameter space or points in the search space). For this purpose, the user can define an optimization range (i.e., the search space) from which the user assumes the global optimum of the function to be optimized lies. It should be noted here that:

[0058] 1) The choice of the optimization domain has a great influence on convergence to the optimal value, and it should not be chosen too large (too long a convergence time) nor too small (may lack good parameter values).

[0059] 2) In the case of hardware applications, there may be control parameter adjustments that could damage or impair the system, making these areas unsuitable for study.

[0060] 3) If the optimization process starts with a good initial estimate based on expert knowledge, the optimization is not global, but more likely local.

[0061] In different implementations, these three facts are taken into account by evaluating near the already evaluated point during optimization. Therefore, this eliminates the need for the user to specify the optimization range, carefully study the control parameter space, and remain near the initial estimate.

[0062] According to different implementation methods, the search space varies depending on the evaluation: it is defined based on the prediction variance given by the current posterior Gaussian process (i.e., the updated Gaussian process using the previous evaluation). For example, the next evaluation point is selected as follows:

[0063]

[0064] in

[0065]

[0066] It is a confidence range that includes all points where the predicted posterior variance (that is, the variance of the posterior model, such as the posterior Gaussian model) is less than a pre-given limit.

[0067] In this example, the pre-given limit is the signal variance through the kernel of the Gaussian process. A small portion given in advance To give. The kernel of a Gaussian process, for example, is through...

[0068]

[0069] To give, among which It is the distance between two input parameter vectors (that is, possible evaluation points), and It is the kernel length scaling (Längenskalierung).

[0070] It should be noted that if a new evaluation point has been selected, evaluated, and the Gaussian process has been updated (i.e., the posterior Gaussian process additionally considers the new evaluation at the new evaluation point), the confidence range expands. The relative size of the search space can be reconciled by adjusting the confidence parameter γ, which determines the degree of "caution" in the optimized exploration behavior. The confidence parameter γ can also be set to a fixed value, such as less than 1, like 0.1 or 0.5, or it can be adapted based on this value during iterations (e.g., reduced).

[0071] It should be noted that choosing the limit according to the variance of the kernel signal of the Gaussian process is merely an example. Other statistical models that make confidence conclusions (i.e., conclusions about the variance of the points) can also be used, such as Bayesian neural networks, and the limit can be given in advance accordingly (e.g., absolutely or according to the (hyper)parameters of the statistical model as in the example above).

[0072] Figure 2 A flowchart illustrating the method for determining control parameters using Bayesian optimization is shown.

[0073] In 201, an initial evaluation point x0 is given (e.g., the first estimate based on expert knowledge) and the function f to be optimized is evaluated at that evaluation point to obtain (“the 0th”) observation y0 = f(x0) + e0.

[0074] In 202, the While loop continues as long as the stopping criteria are not met (e.g., the maximum number of iterations has not been reached).

[0075] In each iteration:

[0076] • In section 203, determine the confidence range. (For example, in the case of using the prediction variance as described in the current Gaussian process (that is, a posterior Gaussian process in which all evaluations up to this point are incorporated).

[0077] • In 204, the acquisition function (e.g., LCB) is optimized with respect to this confidence range in order to obtain a new (i.e., the next) evaluation point xi;

[0078] • In 205, the function f is evaluated at position xi to obtain the new (i-th) observation yi = f(xi) + ei;

[0079] • In 206, the Gaussian process is updated using the i-th evaluation.

[0080] After the While loop ends, output the estimate of the optimal value (e.g., the control parameter vector of the Gaussian process with the maximum or minimum expected value) in 207.

[0081] Optimization of the acquisition function can be achieved through a two-step process:

[0082] 1) Sample from the optimized range (i.e., the confidence range), for example, uniformly distributed, or according to the Sobol sequence, or when using Latin Hypercube sampling (i.e., extract sampling).

[0083] 2) For example, when using Sequential Quadratic Programming (SQP) or the so-called TrustRegion Interior Point Technique, local optimization is performed around the sampling points where the acquisition function is the largest.

[0084] Since confidence ranges are typically discontinuous and non-convex, one implementation uses rejection sampling to sample points within the confidence range, for example, in the case of sequentially selected one-dimensional subspaces. Algorithm 1 (in pseudocode form) is an example of this approach.

[0085]

[0086] Sampling according to the proposed distribution is another possibility for optimizing the acquisition function, which is updated in the direction of the desired range of control parameters during each evaluation (acquisition function). When using confidence ranges, the step size between updates can be implicitly reduced.

[0087] In summary, according to different implementation methods, it provides... Figure 3 The method shown in the figure.

[0088] Figure 3 A flowchart 300 is shown illustrating a method for selecting evaluation points for Bayesian optimization, which is used to optimize physical or chemical processes modeled by statistical models.

[0089] In 301, the posterior model of the statistical model (e.g., the posterior Gaussian process for a Gaussian process) is determined based on one or more evaluations at previous evaluation points.

[0090] In 302, the next evaluation point is selected by optimizing the acquisition function with respect to the search space, which is given by a pre-given limit of the prediction variance of the points in the search space given by the posterior model.

[0091] In other words, according to different implementations, the acquisition function used in Bayesian optimization is optimized for determining the next evaluation point within a range of points, which includes points for which the prediction variance of the posterior model is less than a pre-given limit. In other words, the search range for the next evaluation point is limited to a range of points containing points for which the prediction variance of the posterior model is less than a pre-given limit.

[0092] Bayesian optimization can be used, for example, to determine control parameters for a robot. Each evaluation point corresponds, for example, to a vector of control parameters with multiple (e.g., 10 to 20) components, where each component describes the value of a control parameter (e.g., temperature, speed, voltage, etc.) for the physical or chemical process.

[0093] "Robot" can be understood as any physical system (with mechanical parts whose movements are controlled), such as computer-controlled machines, vehicles, household appliances, power tools, manufacturing machines, personal assistants, or access control systems.

[0094] Although the invention has been shown and described primarily with reference to specific embodiments, those skilled in the art will understand that numerous changes in design and detail can be made without departing from the spirit and scope of the invention as defined by the following claims. Therefore, the scope of the invention is determined by the appended claims and is intended to cover all changes falling within the literal meaning or equivalent scope of the claims.

Claims

1. A method for a control device to select optimal control parameter values ​​using a Bayesian optimization method for optimizing a physical or chemical process, the physical or chemical process being modeled by a statistical model and executed by a production device, processing device, or robot, wherein the statistical model is a Gaussian process, the method comprising: The output parameter values ​​of the physical or chemical process, assigned to control parameter values, are provided by at least one sensor as evaluation results for previous evaluation points; The posterior Gaussian process model is determined based on the results of one or more evaluations at previous evaluation points, where the previous evaluation points are control parameter values; and The next evaluation point is selected by optimizing the acquisition function with respect to the search space, the next evaluation point being given by a pre-given limit of the prediction variance of the point in the search space, as given by the posterior Gaussian process model; and The next evaluation point is used as the optimal control parameter value, and the production equipment, processing equipment, or robot is controlled according to the optimal control parameter value.

2. The method of claim 1, wherein the predetermined limit is a predetermined fraction of the signal variance of the kernel of the Gaussian process.

3. The method according to claim 1 or 2, wherein a set of alternatives for the next evaluation point is determined by sampling from the range of evaluation points, and an alternative among the alternatives for which the acquisition function takes the optimal value in the set of alternatives is selected as the next evaluation point.

4. The method of claim 3, wherein the evaluation range is a subset of the parameter range and the set of alternatives is determined by sampling using a rejection method from the parameter range, wherein samples not in the search space are discarded.

5. The method of claim 4, wherein sampling within the parameter range includes sampling within subspaces of the parameter range, each subspace containing one or more of the previously evaluated points.

6. A control device configured to implement the method according to any one of claims 1 to 5.

7. A production system, which has: The control device according to claim 6; Production equipment, which is configured to manufacture products by means of physical or chemical processes; and At least one sensor is configured to provide the control device with an output parameter value of the physical or chemical process that is assigned to a control parameter value. The control device is configured as follows: One or more optimal control parameter values ​​for the physical or chemical process are determined using Bayesian optimization by evaluating the control parameter values ​​using the output parameter values; and The production equipment is controlled according to one or more determined control parameter values.

8. A processing system, which has: The control device according to claim 6; Processing equipment, said processing equipment being configured to process workpieces by means of physical or chemical processes; and At least one sensor is configured to provide the control device with an output parameter value that corresponds to a control parameter value for a physical or chemical process. The control device is configured as follows: One or more optimal control parameter values ​​for the physical or chemical process are determined using Bayesian optimization by evaluating the control parameter values ​​using the output parameter values; and The processing equipment is controlled according to one or more determined control parameter values.

9. A robot system, which has: The control device according to claim 6; Robotic elements, said robotic elements being configured to perform movement by means of physical or chemical processes; and At least one sensor is configured to provide the control device with an output parameter value that corresponds to a control parameter value for a physical or chemical process. The control device is configured as follows: One or more optimal control parameter values ​​for the physical or chemical process are determined using Bayesian optimization by evaluating the control parameter values ​​using the output parameter values; and The robot components are controlled according to one or more determined control parameter values.

10. A computer program product having a computer program, said computer program having program instructions that, when implemented by one or more processors, cause said one or more processors to perform the method according to any one of claims 1 to 5.

11. A computer-readable storage medium having stored thereon program instructions that, when executed by one or more processors, cause the one or more processors to perform the method according to any one of claims 1 to 5.

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