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We assume that, additionally to the training data from every user, local validation and test datasets are available. This assumption is only needed for the assessment purpose, in the normal operation of the MUSKETEER platform those datasets are not mandatory, and all of the algorithms are able to train a model without a validation set, although in some cases an improved convergence/speedup is obtained if such a validation dataset is provided. Anyhow, it is a common situation that the user in charge of aggregating the weights of a model has a test set, to evaluate the final performance achieved by the trained models.

Table 5 We assume that, additionally to the training data from every user, local validation and test datasets are available. This assumption is only needed for the assessment purpose, in the normal operation of the MUSKETEER platform those datasets are not mandatory, and all of the algorithms are able to train a model without a validation set, although in some cases an improved convergence/speedup is obtained if such a validation dataset is provided. Anyhow, it is a common situation that the user in charge of aggregating the weights of a model has a test set, to evaluate the final performance achieved by the trained models.

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This deliverable (D6.2 Scalability of machine learning algorithms over every POMs) is the result of task T6.2 (Assessing scalability and computational efficiency of federated privacy- preserving machine learning algorithms) and describes the results obtained after intensive tests carried out to analyse the main technical characteristics of every algorithm over every POM. We have followed the Goal Question Metric methodology described in D6.1, and the main goals are to assess the scalability, computational efficiency and performance of the proposed and implemented schemes in the MUSKETEER Machine Learning Library (MMLL). proposed and implemented schemes in the MUSKETEER Machine Learning Library (MMLL).
This deliverable (D6.2 Scalability of machine learning algorithms over every POMs) is the result of task T6.2 (Assessing scalability and computational efficiency of federated privacy- preserving machine learning algorithms) and describes the results obtained after intensive tests carried out to analyse the main technical characteristics of every algorithm over every POM. We have followed the Goal Question Metric methodology described in D6.1, and the main goals are to assess the scalability, computational efficiency and performance of the proposed and implemented schemes in the MUSKETEER Machine Learning Library (MMLL). proposed and implemented schemes in the MUSKETEER Machine Learning Library (MMLL).
List of Acronyms and Abbreviations
List of Acronyms and Abbreviations
As indicated in the PERT diagram below (Figure 1), the results from this deliverable wil provide input to WP7 (User Cases), such that they can better decide which POM/algorithms are the most adequate to solve a given task. Although not shown in that PERT diagram, the inputs are mainly defined by the project KPls and objectives that concern the performance of the implemented Machine Learning algorithms. Deliverables D4.5 and D4.7 describe in ful detail the implemented algorithms under the different Privacy Operation Modes, whict comprise the MUSKETEER Machine Learning Library (MMLL) [MMLL_2021]. This report focuses on the technical assessment of the developed ML library under the different POMs and this information will help in the selection of models while developing the use case: solutions in the context of WP7.
As indicated in the PERT diagram below (Figure 1), the results from this deliverable wil provide input to WP7 (User Cases), such that they can better decide which POM/algorithms are the most adequate to solve a given task. Although not shown in that PERT diagram, the inputs are mainly defined by the project KPls and objectives that concern the performance of the implemented Machine Learning algorithms. Deliverables D4.5 and D4.7 describe in ful detail the implemented algorithms under the different Privacy Operation Modes, whict comprise the MUSKETEER Machine Learning Library (MMLL) [MMLL_2021]. This report focuses on the technical assessment of the developed ML library under the different POMs and this information will help in the selection of models while developing the use case: solutions in the context of WP7.
report. The GQM approach is usually illustrated using the following Figure.
report. The GQM approach is usually illustrated using the following Figure.
D6.2 Scalability of machine learning algorithms over every POMs
D6.2 Scalability of machine learning algorithms over every POMs
D6.2 Scalability of machine learning algorithms over every POMs
D6.2 Scalability of machine learning algorithms over every POMs
Bytes received by the aggregator: D6.2 Scalability of machine learning algorithms over every POMs
Bytes received by the aggregator: D6.2 Scalability of machine learning algorithms over every POMs
RAM (MB) consumption by master and workers:
RAM (MB) consumption by master and workers:
The influence of number of workers and the POM cannot be observed.
The influence of number of workers and the POM cannot be observed.
Figure 4. Neural networks (binary)
Figure 4. Neural networks (binary)
Bytes received by the aggregator: D6.2 Scalability of machine learning algorithms over every POMs
Bytes received by the aggregator: D6.2 Scalability of machine learning algorithms over every POMs
RAM (MB) consumption by master and workers:
RAM (MB) consumption by master and workers:
D6.2 Scalability of machine learning algorithms over every POMs
D6.2 Scalability of machine learning algorithms over every POMs
Bytes received by the aggregator: D6.2 Scalability of machine learning algorithms over every POMs
Bytes received by the aggregator: D6.2 Scalability of machine learning algorithms over every POMs
RAM (MB) consumption by master and workers:
RAM (MB) consumption by master and workers:
D6.2 Scalability of machine learning algorithms over every POMs
D6.2 Scalability of machine learning algorithms over every POMs
Bytes received by the aggregator: D6.2 Scalability of machine learning algorithms over every POMs
Bytes received by the aggregator: D6.2 Scalability of machine learning algorithms over every POMs
RAM (MB) consumption by master and workers:
RAM (MB) consumption by master and workers:
For large size datasets, we can observe the influence of the POM and dataset size in the memory consumption.
For large size datasets, we can observe the influence of the POM and dataset size in the memory consumption.
Figure 5. Neural networks (multilclass)
Figure 5. Neural networks (multilclass)
Bytes received by the aggregator: D6.2 Scalability of machine learning algorithms over every POMs
Bytes received by the aggregator: D6.2 Scalability of machine learning algorithms over every POMs
RAM (MB) consumption by master and workers: The influence of number of workers and the POM cannot be observed.
RAM (MB) consumption by master and workers: The influence of number of workers and the POM cannot be observed.
input variables to a continuous output variable. A continuous output variable is a real-value,
input variables to a continuous output variable. A continuous output variable is a real-value,
Figure 6. Neural networks (regression)
Figure 6. Neural networks (regression)
Bytes received by the aggregator: D6.2 Scalability of machine learning algorithms over every POMs
Bytes received by the aggregator: D6.2 Scalability of machine learning algorithms over every POMs
RAM (MB) consumption by master and workers:
RAM (MB) consumption by master and workers:
Since POM1 makes not use of encrypted information in memory, we can observe a lowe memory consumption.
Since POM1 makes not use of encrypted information in memory, we can observe a lowe memory consumption.
In the case of SVM implementations. In FBSVM we can appreciate how the accuracy decreases slowly as we increase the number of workers. This training procedure presents some problems in non-iid datasets. This problem is solved in DSVM, that tend to achieve the same solution independently of the number of workers. same solution independently of the number of workers.
In the case of SVM implementations. In FBSVM we can appreciate how the accuracy decreases slowly as we increase the number of workers. This training procedure presents some problems in non-iid datasets. This problem is solved in DSVM, that tend to achieve the same solution independently of the number of workers. same solution independently of the number of workers.
POM1 is the fastest one (see section 5.1). It doesn't need encryption and the master node can broadcast the information to the worker nodes at the same time in every iteration. We can see how the training time increases linearly with the number of workers due to the bottleneck associated to receive the information from every worker after every iteration. Typically, the runtime increases with the number of training samples. However, every dataset is different and has associated a different number of training steps until convergence. For this reason, in some cases such as the Neural Networks for regression, we can observe how the runtime decreases because an increase of input features has motivated a decrease in the training iterations.
POM1 is the fastest one (see section 5.1). It doesn't need encryption and the master node can broadcast the information to the worker nodes at the same time in every iteration. We can see how the training time increases linearly with the number of workers due to the bottleneck associated to receive the information from every worker after every iteration. Typically, the runtime increases with the number of training samples. However, every dataset is different and has associated a different number of training steps until convergence. For this reason, in some cases such as the Neural Networks for regression, we can observe how the runtime decreases because an increase of input features has motivated a decrease in the training iterations.
scalability.
scalability.
Typically, the runtime increases with the number of input features. However, we are working with different datasets and problems and in the case of Neural Networks for regression, we can observe how the runtime decreases because an increase of input features has motivated a decrease in the training iterations. 5.2.3 G1.4: Assessing the computational efficiency of MLA
Typically, the runtime increases with the number of input features. However, we are working with different datasets and problems and in the case of Neural Networks for regression, we can observe how the runtime decreases because an increase of input features has motivated a decrease in the training iterations. 5.2.3 G1.4: Assessing the computational efficiency of MLA
The following pictures belongs to the FBSVM algorithm, but the behaviour is very similar in all of them: We have measured the bytes sent and received by the master node. Section 5.1 contains the complete list of graphics about data transmission in every algorithm.
The following pictures belongs to the FBSVM algorithm, but the behaviour is very similar in all of them: We have measured the bytes sent and received by the master node. Section 5.1 contains the complete list of graphics about data transmission in every algorithm.
(*) We could appreciate that the accuracy decreases as we increase the number of workers. (**) For transmissions over the internet. Table 1. Summary of GQM tests results for algorithms in POM1 5.3.1 Assessment of algorithms under POM1
(*) We could appreciate that the accuracy decreases as we increase the number of workers. (**) For transmissions over the internet. Table 1. Summary of GQM tests results for algorithms in POM1 5.3.1 Assessment of algorithms under POM1
(*) We could appreciate that the accuracy decreases as we increase the number of workers. (**) Neural Networks scale correctly with the number of input features, but we have used a higher number of neurons in the hidden layers as we increase the number of input features. The scalability as we increase the number of neurons in this way is low.
(*) We could appreciate that the accuracy decreases as we increase the number of workers. (**) Neural Networks scale correctly with the number of input features, but we have used a higher number of neurons in the hidden layers as we increase the number of input features. The scalability as we increase the number of neurons in this way is low.
Table 3. Summary of GQM tests results for algorithms in POM3 5.3.3 Assessment of algorithms under POM3 D6.2 Scalability of machine learning algorithms over every POMs
Table 3. Summary of GQM tests results for algorithms in POM3 5.3.3 Assessment of algorithms under POM3 D6.2 Scalability of machine learning algorithms over every POMs
Figure 7. Computational comparison of different confidentiality preserving protocols. Before analysing the results of the GQM assessment we will briefly discuss some of the general aspects concerning the main protocols and techniques used to implement the algori thms under POMs 4, 5 and 6. In the implemented algorithms, two fundamental confidentiality preserving mechanisms have been used. The first one is the Homomorphic Encry ption (HE) used to encrypt the data or the model such that the operations take place in the encrypted domain. This technique has been used in the context of POMs 4 (data is encry algori pted) and 5 (model is encrypted). Another fundamental procedure used to build the thms is the Two-Party Computation protocol used to compute a Secure Dot Product (SDP), as described in [Zhu_2015]. In Figure 7 below, we show, for every dataset used in the assessment of POMs 4, 5 and 6, the computation time of a relatively simple operation: computing the dot product between the input training patterns and a linear model represented by a weight vector w. We observe how the fastest computation takes place when data is locally available and it is non encrypted (dashed line marked as “Unencrypted data”). This could also be the computation time when the data is distributed and we send the model to the participants in plain text (e.g. POM1), such that the operations take place in the unencrypted domain (clear text). When we try to protect the model from the participants, the dot product operation is not so straightforward, and secure protocols are needed. The Two-party computation Secure Dot Product described in [Zhu_2015] has been used in the context of POM6, and it provides
Figure 7. Computational comparison of different confidentiality preserving protocols. Before analysing the results of the GQM assessment we will briefly discuss some of the general aspects concerning the main protocols and techniques used to implement the algori thms under POMs 4, 5 and 6. In the implemented algorithms, two fundamental confidentiality preserving mechanisms have been used. The first one is the Homomorphic Encry ption (HE) used to encrypt the data or the model such that the operations take place in the encrypted domain. This technique has been used in the context of POMs 4 (data is encry algori pted) and 5 (model is encrypted). Another fundamental procedure used to build the thms is the Two-Party Computation protocol used to compute a Secure Dot Product (SDP), as described in [Zhu_2015]. In Figure 7 below, we show, for every dataset used in the assessment of POMs 4, 5 and 6, the computation time of a relatively simple operation: computing the dot product between the input training patterns and a linear model represented by a weight vector w. We observe how the fastest computation takes place when data is locally available and it is non encrypted (dashed line marked as “Unencrypted data”). This could also be the computation time when the data is distributed and we send the model to the participants in plain text (e.g. POM1), such that the operations take place in the unencrypted domain (clear text). When we try to protect the model from the participants, the dot product operation is not so straightforward, and secure protocols are needed. The Two-party computation Secure Dot Product described in [Zhu_2015] has been used in the context of POM6, and it provides
We observe that the size of the encryp alain data. This is also a factor that affects the 9atterns need to be transmitted. We -onditions, t again, the co he transmission rate is about 2.7 mmunication means used by MM ‘rransport ne tworks) if needed for a specific ap ted datasets is between 10-100 times larger than th total training time, when encrypted models o have estimated that, in our particular experimente Mbytes per second on a steady regime. Onc LL could be replaced by faster ones (dedicate plication, but when the Internet is used as th communication platform, rates like this one are expected.
We observe that the size of the encryp alain data. This is also a factor that affects the 9atterns need to be transmitted. We -onditions, t again, the co he transmission rate is about 2.7 mmunication means used by MM ‘rransport ne tworks) if needed for a specific ap ted datasets is between 10-100 times larger than th total training time, when encrypted models o have estimated that, in our particular experimente Mbytes per second on a steady regime. Onc LL could be replaced by faster ones (dedicate plication, but when the Internet is used as th communication platform, rates like this one are expected.
a a a, Dee To address these questions, we have run several training experiments with every algorithm and dataset, for every POM and with different number of workers (250 different trainings, each one repeated several times), and we represent the variation in performance of the collection of resulting performances for both the reference result (batch scikit-learn [scikit]) and MUSKETEER. The results are represented as “box plots” which represent the distribution of the obtained performances (the specific used metric depends on the task at hand). In the next Figure, we depict several examples of those experiments, the rest being included in Section 10 (Appendix 1):
a a a, Dee To address these questions, we have run several training experiments with every algorithm and dataset, for every POM and with different number of workers (250 different trainings, each one repeated several times), and we represent the variation in performance of the collection of resulting performances for both the reference result (batch scikit-learn [scikit]) and MUSKETEER. The results are represented as “box plots” which represent the distribution of the obtained performances (the specific used metric depends on the task at hand). In the next Figure, we depict several examples of those experiments, the rest being included in Section 10 (Appendix 1):
We observe in Figure (a) the typical result for a model with little variance, i.e., those models ‘hat converge to almost the same solution irrespectively of the random initialization (e.g., _R, LC, MLC, etc.). We observe that all of the results, for an increasing number of workers, are within the 5% margin (marked with dashed lines in the figures), and are also very close tc the centralized solution (first plot on the left). In all cases, there is a little variance from one 2xperiment to another. We observe on (b) an example of those methods that are more sensitive to the initialization conditions or that rely on some random parameterization (e.g.
We observe in Figure (a) the typical result for a model with little variance, i.e., those models ‘hat converge to almost the same solution irrespectively of the random initialization (e.g., _R, LC, MLC, etc.). We observe that all of the results, for an increasing number of workers, are within the 5% margin (marked with dashed lines in the figures), and are also very close tc the centralized solution (first plot on the left). In all cases, there is a little variance from one 2xperiment to another. We observe on (b) an example of those methods that are more sensitive to the initialization conditions or that rely on some random parameterization (e.g.
D6.2 Scalability of machine learning algorithms over every POMs
D6.2 Scalability of machine learning algorithms over every POMs
Figure 10. Examples of training time as a function of the No. of training patterns. Although it may seem at first glance that a quadratic growing may be observed, actually the best fit to these measurements is obtained using a polynomial curve which function of both the number of training patterns (P) and the number of inpu is a linear t features, i.e.(F), as in Figure 10 (a) and (b). In these cases the complexity is O(PF) and therefore the behaviour is linear with respect to the number of training patterns. For ins observed large growth in Figure 10 (a) from 26.000 patterns (Income) to 50.000 mainly due to the fact that the number of features grows from 107 to 784. In o tance, the (MNIST) is ther cases, the complexity has a better fit with respect to the model size (number of centroids, C), as in
Figure 10. Examples of training time as a function of the No. of training patterns. Although it may seem at first glance that a quadratic growing may be observed, actually the best fit to these measurements is obtained using a polynomial curve which function of both the number of training patterns (P) and the number of inpu is a linear t features, i.e.(F), as in Figure 10 (a) and (b). In these cases the complexity is O(PF) and therefore the behaviour is linear with respect to the number of training patterns. For ins observed large growth in Figure 10 (a) from 26.000 patterns (Income) to 50.000 mainly due to the fact that the number of features grows from 107 to 784. In o tance, the (MNIST) is ther cases, the complexity has a better fit with respect to the model size (number of centroids, C), as in
The second question Q1.3_Q2 can be answered by plotting the training time of every dataset when an increasing number of workers are used. The machine were we have run the experiment is able to run 20 separate threads/cores, so we have tested the cases with 1, 5, 10 and 15 workers, some of the remaining threads/cores being used for the aggregator (anc cryptonode, in POM 4). Some typical observed evolution of training times is depicted in Figure 11 below: D6.2 Scalability of machine learning algorithms over every POMs
The second question Q1.3_Q2 can be answered by plotting the training time of every dataset when an increasing number of workers are used. The machine were we have run the experiment is able to run 20 separate threads/cores, so we have tested the cases with 1, 5, 10 and 15 workers, some of the remaining threads/cores being used for the aggregator (anc cryptonode, in POM 4). Some typical observed evolution of training times is depicted in Figure 11 below: D6.2 Scalability of machine learning algorithms over every POMs
Figure 11. Typical examples of training time as a function of the No. of workers: POM6G in (a), POM4 in (b), POMS in (c). We observe in Figure 11(a) that, in the case of POM6, the training time grows linearly with the number of workers because the used SDP needs the cooperation between aggregator and the workers to compute the results, and more workers means more serial interactions between aggregator and workers, plus the needed communications. No quadratic dependence is observed with respect to the number of workers, though, so the test is positive in these cases.
Figure 11. Typical examples of training time as a function of the No. of workers: POM6G in (a), POM4 in (b), POMS in (c). We observe in Figure 11(a) that, in the case of POM6, the training time grows linearly with the number of workers because the used SDP needs the cooperation between aggregator and the workers to compute the results, and more workers means more serial interactions between aggregator and workers, plus the needed communications. No quadratic dependence is observed with respect to the number of workers, though, so the test is positive in these cases.
We clearly observe, as already anticipated in Figure 7, that algorithms in POM6 are the most lightweight ones, and those in POM4 are the most computationally demanding, often requiring 2 orders of magnitude more time to complete the training process with respect to POMBE ones. lightweight ones, and those in POM4 are the most computationally demanding, often
We clearly observe, as already anticipated in Figure 7, that algorithms in POM6 are the most lightweight ones, and those in POM4 are the most computationally demanding, often requiring 2 orders of magnitude more time to complete the training process with respect to POMBE ones. lightweight ones, and those in POM4 are the most computationally demanding, often
D6.2 Scalability of machine learning algorithms over every POMs Concerning the first question, it comes out that we have found it difficult to carry out tha comparison since the concept of “competing platform” is very dependent on the underlying; security model and/or on the required security in the communications. We will postpons until Section 6.4 the analysis/discussion of this Question, and we concentrate by now it answering questions No. 2 and 3. To evaluate G1.4_Q2 we have measured the total amoun of transmitted information and the total processing or transmission times, as depicted in the following Figures:
D6.2 Scalability of machine learning algorithms over every POMs Concerning the first question, it comes out that we have found it difficult to carry out tha comparison since the concept of “competing platform” is very dependent on the underlying; security model and/or on the required security in the communications. We will postpons until Section 6.4 the analysis/discussion of this Question, and we concentrate by now it answering questions No. 2 and 3. To evaluate G1.4_Q2 we have measured the total amoun of transmitted information and the total processing or transmission times, as depicted in the following Figures:
In POMs 4 and 5, that operate in the encrypted domain, the reference dataset size is defined using the Ve observe in Figure 14 (a) that for this particular POM and algorithm, the amount o ransmitted information by both the master and workers is below the reference thresholds 10x the dataset size5). In other cases, we have observed that, when the dataset is very mall, the overhead transmission costs dominate and the ratio is higher, but for average o1 arge sized dataset, the test is passed since the amount of transmitted information is mainly ower than 10 times the dataset size.
In POMs 4 and 5, that operate in the encrypted domain, the reference dataset size is defined using the Ve observe in Figure 14 (a) that for this particular POM and algorithm, the amount o ransmitted information by both the master and workers is below the reference thresholds 10x the dataset size5). In other cases, we have observed that, when the dataset is very mall, the overhead transmission costs dominate and the ratio is higher, but for average o1 arge sized dataset, the test is passed since the amount of transmitted information is mainly ower than 10 times the dataset size.
We observe in Figure 15 that the transmission time is superior to the processing time in almost all cases. This is mainly caused by the slow rate of transmission over the internet and the specific network characteristics where the experiments have been run. It is always possible to balance this ratio by providing faster communication conditions to the platform. Anyhow, we will mark this test as NOT PASSED given the current assessment scenario.
We observe in Figure 15 that the transmission time is superior to the processing time in almost all cases. This is mainly caused by the slow rate of transmission over the internet and the specific network characteristics where the experiments have been run. It is always possible to balance this ratio by providing faster communication conditions to the platform. Anyhow, we will mark this test as NOT PASSED given the current assessment scenario.
Table 4. Summary of GQM tests results for algorithms in POM4 As already discussed in the general section POM4 is the most computationally demandin; approach, since the whole dataset is encrypted and both computations and communication are increased accordingly. The main advantage (but also disadvantage) of this POM is tha the training data is outsourced to the aggregator and the workers do not need t contribute/participate/operate during the training process. This may represent a potentic leakage risk but as a positive characteristic the workers do not need to spend computatione power during training, so they can be more lightweight. The cooperation of a non-colludin process (cryptonode) is needed in this POM. Again, this can be seen as a potential —leakage weakness or as an opportunity to speed up computations if the aggregator and cryptonod: are able to count with especially powerful computing resources that can speed y| operations in the encrypted domain by several orders of magnitude. .5.1 Assessment of algorithms under POM4
Table 4. Summary of GQM tests results for algorithms in POM4 As already discussed in the general section POM4 is the most computationally demandin; approach, since the whole dataset is encrypted and both computations and communication are increased accordingly. The main advantage (but also disadvantage) of this POM is tha the training data is outsourced to the aggregator and the workers do not need t contribute/participate/operate during the training process. This may represent a potentic leakage risk but as a positive characteristic the workers do not need to spend computatione power during training, so they can be more lightweight. The cooperation of a non-colludin process (cryptonode) is needed in this POM. Again, this can be seen as a potential —leakage weakness or as an opportunity to speed up computations if the aggregator and cryptonod: are able to count with especially powerful computing resources that can speed y| operations in the encrypted domain by several orders of magnitude. .5.1 Assessment of algorithms under POM4
(*) In this case gradient descent was used and two out of three datasets gave poor performance, hence the NO+. Table 5. Summary of GQM tests results for algorithms in POM5
(*) In this case gradient descent was used and two out of three datasets gave poor performance, hence the NO+. Table 5. Summary of GQM tests results for algorithms in POM5
Table 6. Summary of GQM tests results for algorithms in POM6 We observe in POM6 that the performance tests are always positive, since the used solvers are more efficient than gradient descent and they are able to provide solutions comparable to scikit-learn. Also, scalability is very good. As in the previous cases, the high transmission times force that in this case the metric “communication time less than half the processing time” is not passed either, since the computation times are much reduced with respect tc the previous POMs, but communications overheads do not reduce in the same proportion.
Table 6. Summary of GQM tests results for algorithms in POM6 We observe in POM6 that the performance tests are always positive, since the used solvers are more efficient than gradient descent and they are able to provide solutions comparable to scikit-learn. Also, scalability is very good. As in the previous cases, the high transmission times force that in this case the metric “communication time less than half the processing time” is not passed either, since the computation times are much reduced with respect tc the previous POMs, but communications overheads do not reduce in the same proportion.
Figure 16. MUSKETEER’s graphical guide to select the appropriate POM
Figure 16. MUSKETEER’s graphical guide to select the appropriate POM
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D6.2 Scalability of machine learning algorithms over every POMs
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