Task caching method based on multi-arm selection algorithm in edge computing scenario

Abstract

The application discloses a task caching method based on a multi-arm selection algorithm in an edge computing scene and belongs to the technical field of edge computing technology. In the application, F tasks to be cached in a scene are regarded as swing arms, and the size of the demand of the cached tasks is maximized as a target. The optimal caching decision problem of the tasks under the two constraint conditions that the storage capacity of a MEC server is limited and the switching cost of newly added tasks in a unit round cannot exceed the upper threshold is solved. The Gomory cutting plane algorithm is innovatively introduced into the combined multi-arm selection algorithm, and the solution of the task caching decision under multiple constraint conditions is realized.

Description

Technical Field

[0001] This invention relates to the field of edge computing technology, and in particular to a task caching method based on a multi-arm selection algorithm in edge computing scenarios. Background Technology

[0002] In recent years, the emergence of massive numbers of end users has led to an explosive growth in data residing at the network edge. Installing multiple Mobile Edge Computing (MEC) servers within or near base stations can meet business demands at the hardware level. MEC is a new computing paradigm where a large amount of computing and storage resources are placed at the network edge, close to mobile devices or sensors, to meet the service quality requirements of low latency, low power consumption, and high bandwidth. However, how to optimize the allocation of these server cache resources to multiple services in real time, while ensuring that the switching cost of newly added tasks per unit round does not exceed a specified threshold, remains a pressing problem to be solved.

[0003] Xu et al. studied the learning-based caching problem in small cellular networks with unknown user preferences, and modeled the caching decision problem from the perspective of a multi-agent multi-armed gambling machine, realizing online learning caching strategies in stationary and non-stationary environments. Blasco et al. inferred task popularity by observing the immediate demand for content stored in the cache, maximizing the utilization of limited cache capacity by transforming the caching decision problem into a multi-armed gambling machine problem with switching costs. Bitaghsir et al. considered a cellular network overlaid on a vehicle social network and proposed a center-driven algorithm that found the optimal traversal path to maximize cache hit rate. Zhou et al. proposed a tree- and context-based multi-armed gambling cooperation theory for efficient content caching, and simulation results proved that the algorithm has a sublinear range of cumulative regret. Han et al. studied the cache placement problem in real-world MEC networks with unknown user behavior and proposed a joint cache placement scheme for collaborative edge server scenarios with overlapping service areas. Dai et al. proposed a context-based multi-armed problem when the network state is an unknown random variable, and simulation results verified the feasibility and superiority of the proposed method through comparison. Han et al. proposed an improved UCB-AC (Upper Confidence Bound-Adaptive Caching) algorithm to solve the caching decision problem for unknown task popularity. Simulation results show that the algorithm can reduce user service latency with less learning cost.

[0004] However, previous studies have largely failed to consider the impact of task data size on caching decisions. For example, Xu et al. assumed that all tasks had the same data size, which was assumed to be 1; Bitaghsir et al. assumed that all files were divided into blocks of the same size; Han et al. also divided files into blocks of the same size and treated each block as an independent file; Dai et al. assumed that each file had the same size f. s These assumptions can greatly simplify the complexity of the problem, but they have limitations in some practical applications.

[0005] Furthermore, most current work only considers the single constraint of limited MEC server cache capacity, which cannot be applied to real-world scenarios with multiple constraints. For example, Blasco et al. designed the objective function as the sum of cache task demands minus task switching costs, with the constraint that the sum of cache task data sizes cannot exceed the MEC server's cache capacity; Zhou et al. defined the objective function as maximizing global cache benefits, with the constraint that user cache benefits are in the [0,1] interval; Han et al. defined the objective function as minimizing task request latency in the scenario, also considering only a single constraint: limited MEC server cache capacity.

[0006] In view of the shortcomings of the prior art, the improvements made by the present invention are as follows: (1) It considers the caching decision problem under different task data size, which is closer to the real scenario of task caching; (2) It takes into account the update cost of adding new tasks to the cache. At this time, the constraints of task caching become multiple, including: the MEC server cache capacity is limited and the switching cost of adding new tasks in a unit round cannot exceed the upper limit of the threshold. The present invention realizes the solution of the multi-constraint combination multi-armed gambling machine problem. This model can be better transferred to other applications of multi-constraint combination multi-armed gambling machine problems, and is more universal. Summary of the Invention

[0007] The purpose of this invention is to solve the above-mentioned problems by providing a task caching method based on a multi-arm selection algorithm in edge computing scenarios.

[0008] To achieve the above objectives, the technical solution adopted by this invention is: a task caching method based on a multi-arm selection algorithm in edge computing scenarios, comprising the following steps:

[0009] Step 1: First, construct the system's objective function P1 with the goal of maximizing the demand for cached tasks:

[0010]

[0011]

[0012]

[0013]

[0014]

[0015] C1 indicates that the total size of the cached task data cannot exceed the cache capacity of the MEC server. C2 indicates that the switching cost of a newly added task in a unit round cannot exceed the threshold limit C; C3 and C4 represent cached decision variables. It is an integer between 0 and 1. A value of 0 indicates that task f was not cached on MEC server n at time t, and vice versa.

[0016] Step Two: For the objective function P1, first solve the integer linear programming problem using the Gomory cutting plane method. Then, based on the solution results from the Gomory cutting plane method, shake the rocker arms and sample and update the selected rocker arms. Specifically, first shake each arm once, and each arm returns a random reward within its corresponding distribution. This random reward is then assigned to... This represents the estimated demand distribution for task f in the initial round. The algorithm then proceeds to update for T rounds. At each time step t, the estimated demand for the task at the current time is... Substituting the objective function P1, the optimization objective now becomes:

[0017]

[0018] stC1,C2,C3,C4

[0019] Step 3: Next, use the Gomory cutting plane method to solve P2. First, add slack variables to transform the inequality constraints into equality constraints, and then cache the decision variables. The combination of slack variables and unknown variables is a combination of unknown variables. Let C be the coefficient before x in the equality constraint, A be the variable on the right side of the equation, and b be the variable. The optimal basic feasible solution of the objective function is obtained using the simplex method. If the i-th element b in the optimal basic feasible solution... i If it is not an integer, then the equation of the cutting plane is introduced:

[0020]

[0021] Where, x n+1 To introduce the remaining variables, we add the equation of the cutting plane to the simplex tableau to obtain a new standard form of linear programming problem. Then we continue to solve it using the simplex method, repeating the above process until the optimal basic feasible solution satisfies the integer constraints.

[0022] Furthermore, the algorithm flow of the multi-arm selection algorithm based on the Gomory cutting plane is as follows:

[0023]

[0024]

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] (1) Multi-arm selection algorithm based on Gomory cut plane: This invention treats the F tasks to be cached in the scene as a rocker arm, aiming to maximize the demand of cached tasks. It solves the problem of optimal task caching decision under the constraints of limited MEC server storage capacity and the switching cost of newly added tasks in a unit round not exceeding the upper limit of the threshold. Innovatively, the Gomory cut plane algorithm is introduced into the combined multi-arm selection algorithm, realizing the solution of task caching decision under multiple constraints.

[0027] (2) Proof of the upper bound of regret in the GMAS algorithm: This invention completes the proof of the logarithmic property of the upper bound of regret in the multi-armed selection algorithm based on the Gomory cut plane. First, starting from Hoeffding's inequality, the long-term cumulative regret of algorithms for high-probability events and low-probability events is discussed. From the proof, it can be concluded that the cumulative regret of the GMAS algorithm is less than 1 / 3. Attached Figure Description

[0028] Figure 1 This is a flowchart of the multi-arm selection algorithm based on the Gomory cut plane of the present invention;

[0029] Figure 2 This is a long-term accumulated regret for the different cache capacities in different scenarios with different task data volumes in this invention. Detailed Implementation

[0030] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0031] In scenarios with varying task data sizes, this paper sets the number of tasks in each scenario to 10, with task data sizes of [2KB, 3KB, 4KB, 2KB, 1KB, 2KB, 2KB, 3KB, 1KB, 2KB]. The paper varies the MEC server's cache capacity from 7KB to 12KB and observes the performance of the GMAS algorithm and the baseline algorithm. In the baseline algorithm, this paper selects the Greedy algorithm and sets ε to 0.9 and 0.99, preserving a certain exploration factor. This means the baseline algorithm can explore the demand for other tasks in the scenario when low-probability events occur. In the Greedy algorithm, this paper redefines the reward for each task as... In other words, the Greedy algorithm prioritizes tasks with higher popularity per unit of data volume.

[0032] like Figure 1 As shown, the GMAS algorithm proposed in this paper has significant advantages over the Greedy algorithm. After the first N rounds of random exploration, the GMAS algorithm can quickly select a better decision, and the long-term accumulated regret increases slowly. This invention first constructs the system's objective function P1 with the goal of maximizing the demand of cached tasks:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] C1 indicates that the total size of the cached task data cannot exceed the cache capacity of the MEC server. C2 indicates that the switching cost of a newly added task in a unit round cannot exceed the threshold limit C; C3 and C4 represent cached decision variables. It is an integer between 0 and 1. A value of 0 indicates that task f was not cached on MEC server n at time t, and vice versa.

[0039] For the objective function P1, this invention first uses the Gomory cutting plane method to solve the integer linear programming problem. Then, based on the solution results from the Gomory cutting plane method, the rocker arms are shaken, and the selected rocker arms are sampled and updated. Specifically, each arm is shaken once, and each arm returns a random reward within its corresponding distribution. This random reward is then assigned to... This represents the estimated demand distribution corresponding to task f in the initial round. The algorithm then proceeds to update for T rounds. At each time step t, the estimated demand for the task at the current time is... Substituting the objective function P1, the optimization objective now becomes:

[0040]

[0041] stC1,C2,C3,C4

[0042] Next, the Gomory cutting plane method is used to solve P2. First, slack variables are added to transform the inequality constraints into equality constraints. Then, the decision variables are cached. The combination of slack variables and unknown variables is a combination of unknown variables. Let C be the coefficient before x in the equality constraint, A be the coefficient, and b be the variable on the right side of the equation. The optimal basic feasible solution of the objective function is obtained using the simplex method. If the i-th element b in the optimal basic feasible solution... i If it is not an integer, then the equation of the cutting plane is introduced:

[0043]

[0044] Where, x n+1 The remaining variables are introduced here. Adding the equation of the cutting plane to the simplex tableau yields a new standard form of linear programming problem, which is then solved using the simplex method. This process is repeated until the optimal basic feasible solution satisfies the integer constraints.

[0045] The algorithm flow of the Gomory Based Multi-Arm Selection (GMAS) algorithm is as follows:

[0046] The algorithm is based on the Gomory cutting plane multi-arm selection algorithm.

[0047]

[0048]

[0049] Next, this invention analyzes the upper bound of regret in the GMAS algorithm. The cumulative regret of the algorithm is analyzed from the perspective of high-probability events "hp" and low-probability events "lp". In the high-probability event "hp", the cumulative regret of the algorithm consists of the regret generated in the first N rounds of exploration and the regret generated in the TN rounds of update. In the TN round update phase, the algorithm estimates the current task requirement. Substituting the objective function, we can select the rocker arm. Then, according to Hoeffding's inequality, we obtain:

[0050]

[0051]

[0052] We define f opt f is the set of rocker arms corresponding to the optimal caching decision. com This represents the set of rocker arms corresponding to the suboptimal caching decision. According to formula 3.15, u(f) can be obtained. opt There is a high probability that it is located in Between, u(f) com There is a high probability that it is located in between.

[0053] when Regret arises at this time, and at this time: It is easy to deduce that:

[0054] u(f opt )-r(f)≤u(f com )+r(f)

[0055] u(f opt )-u(f com )≤2r(f)

[0056] Therefore, the maximum regret value during the TN-round update phase is The maximum number of regrets occurring in the first t rounds is (tN). The number of regrets during the update phase in the first t rounds is:

[0057]

[0058] In the N-round exploration phase, the maximum number of regrets occurring in the first t rounds is N (assuming t > N), and the maximum upper bound of regret is d (corresponding to the difference between the reward obtained by the optimal set of rocker arms with the best buffer decision and the reward obtained by the worst combination of rocker arms). Therefore, regret is defined as:

[0059] R(t|t=N)=d×N

[0060] The regret of the first t under a high-probability event is:

[0061]

[0062] The function decreases as N increases, while d×N increases as N increases. Treating N as the independent variable, the derivative yields the extreme points of the function: Substituting E[R(t)|hp], we get:

[0063] Taking into account the cumulative regret of the low-probability event "lp" in the algorithm, the expected value of R(t) can be obtained as follows:

[0064]

[0065] In summary, the logarithmic property of the upper bound of the GMAS algorithm has been proven.

[0066] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0067] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A task caching method based on a multi-arm selection algorithm in edge computing scenarios, characterized in that, Its features are, Includes the following steps, Step 1: First, construct the system's objective function with the goal of maximizing the demand for cached tasks. : ： ( ) ( ) in This means that the total size of the cached task data cannot exceed the cache capacity of the MEC server. ; This means that the switching cost of a newly added task in a unit of round cannot exceed the upper limit of the threshold. ; and Represents cached decision variables are integers of 0 and 1, where A value of 0 indicates a task exist t Not cached on MEC server n Conversely, cache; Step 2: For the objective function First, the Gomory cutting plane method is used to solve the integer linear programming problem. Then, based on the solution results of the Gomory cutting plane method, the rocker arms are shaken. The selected rocker arms are sampled and updated. Specifically, each arm is shaken once, and each arm returns a random reward within its corresponding distribution. This random reward is then assigned to... , indicating the tasks in the initial round The algorithm then proceeds to obtain the estimated value of the corresponding demand distribution. T Each round of updates, entering each time step. t Then, the estimated task demand at the current moment is... Substitute into the objective function The optimization objective then becomes: ： Step 3: Next, use the Gomory cutting plane method to... To solve this problem, we first add slack variables to transform the inequality constraints into equality constraints, thus caching the decision variables. The combination of slack variables and unknown variables is a combination of unknown variables. , for In the equality constraints The coefficient before is A The variable on the right side of the equals sign is b The optimal basic feasible solution of the objective function is obtained through the simplex method. If the optimal basic feasible solution contains the th... i element If it is not an integer, then the equation of the cutting plane is introduced: in, To introduce the remaining variables, we add the equation of the cutting plane to the simplex tableau to obtain a new standard form of linear programming problem. We then continue to solve the problem using the simplex method, repeating the above process until the optimal basic feasible solution satisfies the integer constraints.

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