Field of the Invention

The present invention relates to a method and apparatus for consolidating an algorithm.

Background

An algorithm in a computing system is a set of rules characterising a particular computation. Traditionally, an algorithm is defined by a computer programmer to define how one or more inputs in a given situation should map to one or more outputs based on a particular goal. The skill involved in defining the set of rules thus scales with the complexity of the given problem. Furthermore, any changes in the inputs, outputs, or goals requires the computer programmer to revisit the algorithm and update the rules.

The field of machine learning emerged to automate the development of an algorithm, and is used in many areas of computing (such as autonomic computing systems).

Typically, a machine learning process takes an example data set (the "training data") relating to an environment. The machine learning process uses one or more statistical techniques on the training data set to define the set of rules (i.e. the algorithm) which transform an input to an output (usually based on a performance goal). The machine learning process may then subsequently develop the algorithm over time by reevaluating the set of rules based on any new data and/or performance goal. However, this may lead to the algorithm become increasingly more complex if it encompasses a greater number of rules, increasing its computational burden on the computing system. This problem is particularly acute in a scenario whereby an algorithm is developed by a machine learning process such that execution of a new version of the algorithm requires execution of all previous versions of the algorithm. In this situation, the computational burden increases with every new version of the algorithm.

In supervised learning scenarios, a supervisor may periodically review the algorithm which has been developed by a machine learning process to determine whether or not a consolidation operation should be performed. The consolidation operation acts to reduce the computational burden of the algorithm (such as by reducing the number of rules in the algorithm) whilst trying to minimise the impact on its performance. Summary of the Invention

According to a first aspect of the invention, there is provided a computer-implemented method of controlling an algorithm, the method comprising the steps of: developing the algorithm from a first state to a second state by a machine learning process; determining a (second) computational cost of executing the algorithm in its second state; determining if the (second) computational cost satisfies a trigger condition; and, if so, developing the algorithm from the second state to a third state, wherein a further (third) computational cost of executing the algorithm in its third state is less than the (second) computational cost.

Embodiments of the present invention provide the benefits that an overly complicated algorithm that has been developed by a machine learning process may be automatically consolidated into a simpler algorithm following a trigger based on the computational resources required to execute the algorithm. This may be particularly useful for algorithms that are susceptible to developing redundant elements over time, such as when the algorithm relates to a highly variable environment, has a very short time delay between iterations, or the performance goal of the algorithm is configured such that it is relatively agile (e.g. low acceptance criteria). The method may further comprise the steps of: executing the algorithm in its second state on a first set of inputs relating to a computing system so as to produce a second set of outputs, wherein each of the second set of outputs is one of a first and second possible outputs; executing the algorithm in its third state on the first set of inputs so as to produce a third set of outputs, wherein each of the third set of outputs is one of the first and second possible outputs; determining a first matching value between the second and third sets of outputs.

The method may further comprise the step of: determining whether the first matching value satisfies a threshold.

The method may further comprise the step of: developing the algorithm from the third state to a fourth state, wherein if the first matching value satisfies the threshold then the algorithm is developed at a first learning rate, and if the first matching value does not satisfy the threshold then the algorithm is developed at a second learning rate. The algorithm may be a decision tree having a plurality of branch nodes and a plurality of leaf nodes, and the computational cost may be determined based on a count of the plurality of branch nodes. The step of developing the algorithm from the second state to the third state may include developing a new algorithm. Alternatively, the step of developing the algorithm from the second state to the third state may include modifying the algorithm from its second state.

According to a second aspect of the invention, there is provided a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method of the first aspect of the invention. The computer program may be stored on a computer-readable data carrier.

According to a third aspect of the invention, there is provided a device for controlling an algorithm, the device comprising memory for storing data relating to a computing system, and a processor configured to carry out the steps of the method of the first aspect of the invention.

Brief Description of the Figures

In order that the present invention may be better understood, embodiments thereof will now be described, by way of example only, with reference to the accompanying drawings in which:

Figure 1 is a schematic diagram of an embodiment of a computing system of the present invention;

Figure 2 is a schematic diagram of an example telecommunications system including the computing system of Figure 1 ;

Figure 3 is a diagram of an embodiment of a decision tree algorithm of the present invention; and

Figure 4 is a flow diagram illustrating an embodiment of a method of the present invention.

Detailed Description of Embodiments

Figure 1 is a block diagram of a computer system 100 suitable for the operation of embodiments of the present invention. A central processor unit (CPU) 102 is communicatively connected to storage 104 and an input/output (I/O) interface 106 via a data bus 108. The storage 104 can be any read/write storage device such as a random access memory (RAM) or a non-volatile storage device. An example of a non-volatile storage device includes a disk or tape storage device. The I/O interface 106 is an interface to devices for the input or output of data, or for both input and output of data.

Examples of I/O devices connectable to I/O interface 106 include a keyboard, a mouse, a display (such as a monitor) and a network connection.

Figure 2 illustrates the computer system 100 in a telecommunications system 1 of an embodiment of the present invention. The telecommunications system 1 includes a plurality of Customer Premises Equipment (CPE) 1 10a...1 1 On connected to an exchange 120, each via a copper pair 130a...130n. The copper pair may use any one of the family of xDSL protocols, such as ADSL, VDSL, VDSL2, G.fast, etc, and may also pass through a further DSL element such as a street cabinet and/or distribution point. Furthermore, the connection between the CPEs and the exchange may be carried in part or in full by an optical fibre connection. To cover all scenarios, the term "line" will hereinafter be used to describe any suitable connection between the CPEs 1 10a...1 1 On and the exchange 120. In the exchange, the lines 130a...130n terminate at an aggregation transceiver device, in this example a Digital Subscriber Line Access Multiplier (DSLAM) 140, which is configured to provide Internet and telephony services to each CPE via each copper pair. The DSLAM thus provides onward connections to the Internet, to a PSTN, and to a Network Management System (NMS).

The CPEs 1 10a...1 1 On and DSLAM 140 all include a control unit 1 15a...1 15n, 145, which are configured to measure certain properties of a modem located in the CPE or

DSLAM, or the associated line, and store them in memory. In this embodiment, the control units 1 15a...1 15n, 145 are configured to store DSL-related parameters such as Signal to Noise Ratio (SNR), SNR margin, error counts, retrain counts, etc., which are stored in 15-minute bins in the Management Information Base (MIB). In this embodiment, the control units 1 15a...1 15n, 145 are also configured to store non-DSL- related parameters such as the line's resistance, moisture levels, etc., which are also stored in memory. Furthermore, each line 130a...130n may include a further control unit (not shown), provided at any point along its length, which is also configured to perform measurements of the various DSL-related and non-DSL-related parameters noted above. The various control units 1 15a...1 15n, 145, 160a...160n are all configured to report their stored DSL-related and non-DSL-related parameters to the NMS. In this embodiment, the NMS receives this data once per day and each day's data is stored, creating a timeline of operational data for subsequent analysis.

In an embodiment of the present invention, the computer system 100 is configured to retrieve this data from the NMS and store it as a vector of quantities, hereinafter designated 'x'. The computer system 100 uses data x in an autonomic process to control the telecommunications system 1. A detailed example of one such autonomic process will now be described in detail. The skilled person will note, however, that the telecommunications system 1 is just one example of a computing system and the various aspects and embodiments of the invention described hereinafter are applicable to any computing system.

In the telecommunications system 1 , a user of one CPE may terminate their service with the Network Operator such that the user's line becomes inactive. After some time has passed, the user requests that their service be restarted, and the Network Operator must decide whether to a) automatically restart the service without sending out an engineer, or b) send an engineer out to inspect the line and associated infrastructure, perform any necessary engineering work to restore the line to full working condition, and manually restart it. There is a greater chance of developing a fault with option a) over option b), and such a fault would have a negative impact on the customer experience. However, there is a greater financial cost associated with option b) over option a). Accordingly, the Network Operator must make a decision on which lines it would be beneficial to use option a) over option b).

In this embodiment, an algorithm is used to decide whether the Network Operator should automatically restart the service or send an engineer to manually restart it. This algorithm may take into account, for example, the amount of time that has passed since the Network Operator terminated service to that user, DSL fault statistics of neighbouring lines, and the various DSL-related and non-DSL-related data noted above. The algorithm thus takes the stored diagnostic data x as an input and outputs either option a) or option b). The Network Operator may then act upon this output. With either option a) or option b), there are two possible outcomes. One option is a success, which in this example means that the service is successfully restarted without a fault occurring in the near future. The second option is a failure, in which the service does not successfully restart and enters a fault state either immediately or shortly after restarting.

An embodiment of a method of present invention will now be described with reference to Figures 3 to 4. In this embodiment, the autonomic process involves the development of a decision tree algorithm which classifies each line as either option a) or option b) based on its input data, x. The algorithm Vo is initially in the form as illustrated in Figure 3, in which a line may be classified as either option a) or option b) based on a single data point indicating the amount of time that has passed since the Network Operator terminated service to that user. Thus, the decision tree incorporates a single decision node m, which implements test function f _m (x) on the input data x, and there are two leaf nodes for option a) and option b) respectively. In this example, the algorithm in its initial form (VO) was defined by a human operative, but the skilled person will understand that it may have been defined by a data mining technique acting upon training data for the telecommunication system 1 . In a first step (S1 ) of this embodiment as shown in the flow diagram of Figure 4, the computing system 100 uses a machine learning process to develop the decision tree algorithm from its first state to a second state. In this embodiment, the machine learning process operates by developing a number of candidate decision tree modifications (e.g. splitting a leaf node into a branch node with the addition of a new test function, or by modifying a criterion of a test function of an existing branch node), and evaluating the prediction accuracy of each candidate decision tree modification against a recent data set. The recent data set includes data for each line including the input data, x, and the real-world outcome on whether an automatic or manual restart for that line - options a) or b) - were successful or not. This analysis therefore gives an objective measurement of each candidate decision tree modification's prediction accuracy by comparing its predicted outputs for each line (using the input data, x, from the recent data set) to the real-world outcomes from the recent data set. The most accurate candidate decision tree modification is then selected as the new state of the algorithm. In step S3, the computing system 100 measures the computational resources required to execute the algorithm in its new state. There are many methods available for performing such a measurement, which may be as simple as a count of the number of test functions (i.e. branch nodes) in the decision tree, or may be based on the application of the decision tree algorithm in its current form to an evaluation data set (which should be representative of the current operating environment) and monitoring the performance of the processor 102 (e.g. run-time, utilisation, etc.).

In step S5, the computing system 100 determines whether the computational resources required to execute the algorithm in its new state satisfy a condition, which in this embodiment is a first resource threshold predetermined by an operator. If not, then the method of this embodiment loops back to step S1 such that the algorithm is developed to a further new state. As shown in Figure 4, the loop between steps S1 and S5 includes a timer (step S19) to implement a timestep between each iteration, which may be adjusted in step S6 in order to modify the learning rate of the algorihtm. Furthermore, the computing system 100 implements a counter in step S18 to distinguish between iterations of the loop between steps S1 and S5. In this example, the computational resources required to execute the algorithm in its new state, V,, exceed the first resource threshold and the method proceeds to step S7.

The aim of the following steps of this process is to produce a new algorithm which is computationally less expensive than the previous algorithm, V, (hereinafter the "pre- consolidation algorithm") whilst producing the same or similar results. These steps will now be explained.

In step S7, the computing system 100 creates a candidate new algorithm, Vc, which is developed using a machine learning process whereby the performance goal is to match the output of the candidate new algorithm, Vc, to the output of the pre-consolidation algorithm, V.

In step S9, the computing system 100 measures the computational resources required to execute the candidate new algorithm, Vc, and in step S10, evaluates whether the candidate new algorithm, Vc, is less computationally expensive than the pre- consolidation algorithm, V. This is achieved by using the techniques outlined in step S3 for both the pre-consolidation algorithm, V, and the candidate new algorithm, Vc, and then comparing the two measurements. If the candidate new algorithm, Vc, is less computationally expensive then it is accepted and the method proceeds to step S1 1 . If the candidate new algorithm, Vc, is as computationally expensive or more computationally expensive than the pre-consolidation algorithm, V, then it is rejected and the algorithm remains as the pre-consolidated algorithm, V (step S12), and the method loops back to step S1 via steps S18 and S19. In this example, the method proceeds to step S1 1 .

In step S1 1 , the computing system 100 evaluates the prediction similarity performance of the candidate new algorithm, Vc, compared to the pre-consolidation algorithm, V. In this embodiment, this is achieved by executing the algorithm in both its new state, Vc, and in its pre-consolidated state, V, using a recent data set (including the input data, x) which outputs a first set of predictions for the candidate new algorithm, Vc, and a second set of predictions for the pre-consolidated algorithm, V. The computing system 100 may then compare a count of instances in which the pre-consolidated algorithm, V, and the candidate new algorithm, Vc, give the same or different predictions based on the same input data. In this manner, the computing system 100 is therefore evaluating the similarity of predictions (i.e. the "closeness") of the candidate new algorithm, Vc, to the pre-consolidated algorithm, V. In this embodiment, this is achieved using a confusion matrix to determine the distance, d, between the pre-consolidation algorithm V and the candidate new algorithm, Vc:

Where:

doo = count of instances in which the pre-consolidation algorithm outputs option a) for a line in the input data and the candidate new algorithm outputs option a) for the same line in the input data;

doi = count of instances in which the pre-consolidation algorithm outputs option b) for a line in the input data but the candidate new algorithm outputs option a) for the same line in the input data; dio = count of instances in which the pre-consolidation algorithm outputs option a) for a line in the input data but the candidate new algorithm outputs option b) for the same line in the input data;

dn = count of instances in which the pre-consolidation algorithm outputs option b) for a line in the input data and the candidate new algorithm outputs option b) for the same line in the input data; and d ₀₁ + d ₁₀

a =

^oo + d ₀₁ + d ₁₀ + d _l

The distance metric, d, is therefore a ratio of misclassifications to the total number of classifications between the two algorithms, Vc, V,. Although not essential, the distance matrix may also apply different weightings to the two types of misclassifications in order to penalise misclassifications of one kind more than the other. This is advantageous when the operator determines that it is more important to keep one class of misclassifications to a minimum (e.g. at the expense of the other misclassification).

In step S13, the computing system 100 compares the distance metric to a matching threshold to determine if the performance of the candidate new algorithm, Vc, is acceptable. In this embodiment, the prediction similarity threshold is set at 5%, such that the candidate new algorithm may only misclassify up to 5% of lines in the recent data set in order to satisfy the threshold. If the matching threshold is met, then the candidate new algorithm, Vc, is accepted to replace the pre-consolidated algorithm, V, (step S15) and the method loops back to step S1 (via steps S18 and S19).

This embodiment of the invention therefore has the advantage that the algorithm's development may be analysed to determine whether the computational resources required to execute the algorithm become greater than a threshold. If so, then the computing system 100 may automatically consolidate the algorithm to one that requires fewer resources to execute and that produces the same or similar results to the pre- consolidated algorithm, V. In this manner, the consolidated algorithm retains some or all of the cumulative learning acquired up to that point (which was embodied in the previous mapping between inputs and outputs by the pre-consolidated algorithm) but is now less burdensome on the computational resources of the computing system 100. In an alternative scenario of step S13, the prediction similarity performance does not satisfy the matching threshold. In this case, the candidate new algorithm, Vc, is accepted to replace the pre-consolidated algorithm, V,, (step S17) but the method then loops back to step S1 via steps S6, S18 and S19, in which the first timer is adjusted to adopt a new, shorter, timestep between subsequent iterations of steps S1 to S5. In this manner, the algorithm is consolidated in order to decrease the computational burden on the computing system 100, but the learning rate of the new algorithm, V,+i , is increased by virtue of the shorter timestep such that any predictive performance degradation is shortlived. After several iterations, the first timer may be re-adjusted in step S6 to adopt longer timesteps between iterations (e.g. the same as the original timestep).

The above embodiment of the invention is applied to a decision tree algorithm being used in an example scenario for determining whether a DSL in a telecommunications system should be automatically or manually restarted. However, the skilled person will understand that, firstly, the invention may be applied in any computing system scenario. For example, a data centre may comprise a number of resources which are either operational or dormant. The data centre operator may then decide on whether to automatically deploy the dormant resource to a user, or whether to manually review and configure the resource for deployment. Data may be collected for the data centre (covering, for example, the length of time since the resource was last used and/or operational data) and a decision tree algorithm may be used to make the above decision, which may also be developed using a machine learning process. This algorithm may therefore benefit from the advantages of the present invention, in which the computational resources required to execute the decision tree algorithm may be reviewed and, if the resource usage is above a threshold, then the decision tree algorithm may be consolidated.

Furthermore, the invention may be applied to other forms of algorithms that may be developed by machine learning processes. For example, the algorithm may be based on any one of the following (non-exhaustive list of) algorithm types that may be developed by machine learning processes: neural networks, binary regression, Hidden Markov Models (HMM), random forests, or support vector machines. Using any one of these algorithm types, the computing system 100 may be configured to periodically measure the computational resources required to execute the algorithm and compare this to a criterion for triggering a consolidation process. The consolidation process may then act to reduce the computational burden of the algorithm (e.g. by creating a new, less computationally complex, algorithm, or by modifying the existing algorithm to reduce its computational burden). Furthermore, the skilled person will understand that it is not essential that the consolidated algorithm be based on the same form as the pre-consolidated algorithm. That is, the computing system 100 may utilise a completely different form of algorithm (e.g. a neural network) to replace the pre-consolidated algorithm (e.g. a decision tree), so long as the computational resources required to execute the new algorithm are less than the pre-consolidated algorithm. The computing system 100 may also determine the

'closeness' of the algorithm of a different form to the pre-consolidation algorithm in order to determine if the learning rate of its future development rate should be adjusted. Furthermore, the machine learning process may operate to produce an additional algorithm which operates in sequence to all previous versions of the algorithm (such that performance of the new algorithm requires performance of all previous versions of the algorithm), and these additional algorithms may be of the same or different form to those used in previous versions. It is noted that the present invention is particularly applicable to these algorithms having a sequential nature, as the computational resources required to execute each new version of the algorithm increases with each development.

The skilled person will also understand that it is not essential for the computing system 100 to evaluate the prediction similarity performance of the candidate new algorithm (i.e. the "closeness" of the candidate new algorithm to the pre-consolidated algorithm) and compare it to a threshold. However, in doing so, the computing system 100 ensures that any cumulative learning of the pre-consolidated algorithm is maintained following the consolidation process.

In the above embodiments, the computing system 100 measures the computational resources required to execute the algorithm upon each iterative development of the algorithm. However, the skilled person will understand that this is non-essential, and the method may also be implemented by monitoring the computational resources following other triggers, such as:

• After a particular number of iterations of the machine learning process since the last consolidation;

· After a particular time period has elapsed since the last consolidation. In all cases, the trigger may be specified as an absolute threshold appropriate to the metric, or as a relative change since the last consolidation function. In the above embodiments, the computing system 100 executes the algorithm but the inputs/outputs of algorithm relate to another computing system (the telecommunications system 1 ). However, the skilled person will understand that the algorithm may be implemented in the same computing system which the algorithm is acting upon. Insofar as embodiments of the invention described are implementable, at least in part, using a software-controlled programmable processing device, such as a microprocessor, digital signal processor or other processing device, data processing apparatus or system, it will be appreciated that a computer program for configuring a programmable device, apparatus or system to implement the foregoing described methods is envisaged as an aspect of the present invention. The computer program may be embodied as source code or undergo compilation for implementation on a processing device, apparatus or system or may be embodied as object code, for example.

Suitably, the computer program is stored on a carrier medium in machine or device readable form, for example in solid-state memory, magnetic memory such as disk or tape, optically or magneto-optically readable memory such as compact disk or digital versatile disk etc., and the processing device utilises the program or a part thereof to configure it for operation. The computer program may be supplied from a remote source embodied in a communications medium such as an electronic signal, radio frequency carrier wave or optical carrier wave. Such carrier media are also envisaged as aspects of the present invention.

It will be understood by those skilled in the art that, although the present invention has been described in relation to the above described example embodiments, the invention is not limited thereto and that there are many possible variations and modifications which fall within the scope of the invention.

The scope of the present invention includes any novel features or combination of features disclosed herein. The applicant hereby gives notice that new claims may be formulated to such features or combination of features during prosecution of this application or of any such further applications derived therefrom. In particular, with reference to the appended claims, features from dependent claims may be combined with those of the independent claims and features from respective independent claims may be combined in any appropriate manner and not merely in the specific combinations enumerated in the claims.