CN114385272B - Ocean task oriented online adaptive computing unloading method and system - Google Patents

Ocean task oriented online adaptive computing unloading method and system Download PDF

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CN114385272B
CN114385272B CN202210291802.7A CN202210291802A CN114385272B CN 114385272 B CN114385272 B CN 114385272B CN 202210291802 A CN202210291802 A CN 202210291802A CN 114385272 B CN114385272 B CN 114385272B
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王英龙
张玮
杨美红
吴晓明
郝昊
史慧玲
刘礼彬
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Shandong Computer Science Center National Super Computing Center in Jinan
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    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00Arrangements for program control, e.g. control units
    • G06F9/06Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/44Arrangements for executing specific programs
    • G06F9/445Program loading or initiating
    • G06F9/44594Unloading
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02DCLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
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Abstract

The invention belongs to the technical field of network communication, and provides an online adaptive computation unloading method and system for ocean tasks, which can acquire environmental information and user information in real time and establish an accurate model to describe a current system, thereby realizing efficient task allocation and ensuring time delay. Therefore, unlike traditional off-line methods, we build an offloading model and optimize in real-time to achieve efficient offloading of device tasks based on reinforcement learning by learning from historical allocation strategies to provide current decisions without the need for future information. The scheme of the invention not only can fully utilize energy, but also can effectively reduce task delay and ensure QoS.

Description

Ocean task oriented online self-adaptive computing unloading method and system
Technical Field
The invention belongs to the technical field of network communication, and particularly relates to an online adaptive computing unloading method and system for ocean tasks.
Background
The ocean buoy plays an important role in the aspects of ocean hydrology and water quality, meteorological monitoring and the like, but generates a data processing task which is intensive in calculation and sensitive in delay during work, and therefore great challenge is brought to the calculation delay of the ocean service task.
The mobile edge computing can effectively enhance the computing capability of the mobile equipment, the mobile equipment unloads the computing task of the mobile equipment to the edge server, the edge server completes the computing processing of the unloading task and feeds back the computing result to the mobile equipment, and therefore the time delay requirement of the task execution of the mobile equipment is met.
The maritime edge computing network faces challenges such as changing wireless channel conditions and dynamic changes of computing resources provided by large ships, and meanwhile, the energy limit of a single unmanned ship and the computing delay of unloading services possibly influenced by the environmental changes of unmanned ship movement are considered.
In recent years, machine learning methods, particularly reinforcement learning, have been highly successful in the fields of computer vision, speech recognition, and natural language processing as a method for analyzing inter-relationships in complex systems. However, if reinforcement learning is used in the ocean-oriented computing task, due to the lack of information in the aspect of users, the complex and dynamic ocean environment and difficulty in determining reward information, the model is difficult to accurately train, the effectiveness of computing unloading is influenced, and the ocean task is difficult to quickly complete with high quality.
Disclosure of Invention
In order to solve at least one technical problem in the background art, the invention provides an online adaptive computing unloading method and system for ocean tasks, which are different from the traditional offline method, and based on reinforcement learning, the current decision is provided by learning from a historical allocation strategy without future information, an unloading model is constructed and real-time optimization is carried out, so that efficient unloading of equipment tasks is realized.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides an online self-adaptive computing unloading method for ocean tasks, which comprises the following steps:
acquiring maritime affair edge network information and equipment calculation task request information;
obtaining a marine task calculation unloading decision based on the marine marginal network information, the equipment calculation task request information and the constructed calculation unloading decision system model;
wherein, the construction process of the unloading decision system model comprises the following steps: constructing an unloading decision system model by taking average task completion delay of minimum equipment energy budget constraint as a target and taking QoS (quality of service) requirements and total energy consumption of equipment as constraints;
and calculating and unloading decision execution equipment calculation tasks based on the ocean tasks and feeding back calculation results to the equipment.
A second aspect of the present invention provides an online adaptive computing offloading system to a marine mission, comprising:
an information acquisition module configured to: acquiring maritime affair edge network information and equipment calculation task request information;
an offload decision computation module configured to: obtaining a marine task calculation unloading decision based on the marine marginal network information, the equipment calculation task request information and the constructed calculation unloading decision system model;
wherein, the construction process of the unloading decision system model comprises the following steps: constructing an unloading decision system model by taking average task completion delay of minimum equipment energy budget constraint as a target and taking QoS (quality of service) requirements and total energy consumption of equipment as constraints;
a task execution result output module configured to: and calculating and unloading decision execution equipment calculation tasks based on the ocean tasks and feeding back calculation results to the equipment.
Compared with the prior art, the invention has the beneficial effects that:
according to the invention, the user information vector is analyzed through interaction of the node gateway and the equipment, an accurate system model is established, an energy loss variable is introduced, the energy is fully utilized under the ocean scene with limited energy consumption, the rapid allocation of tasks is realized, and then the allocation strategy is optimized in real time according to historical information through an online optimization algorithm based on reinforcement learning. The scheme of the invention not only can fully utilize energy, but also can effectively reduce task delay and ensure QoS.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.
FIG. 1 is a flow chart of adaptive online learning offload decision making according to a first embodiment of the present invention;
fig. 2 is a diagram illustrating an example of a reinforcement learning model according to a first embodiment of the present invention.
Detailed Description
The invention is further described with reference to the following figures and examples.
It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
Interpretation of terms:
reinforcement learning is a special class of machine learning algorithms, which takes into account behavioral psychology. Unlike the goals of supervised and unsupervised learning, the problem to be solved by the algorithm is how the agent (i.e. the entity running the reinforcement learning algorithm) performs actions in the environment to obtain the maximum accumulated reward. Reinforcement learning is widely applied and is considered as one of core technologies leading to strong artificial intelligence/general artificial intelligence. All places needing decision making and control have the shadow of the person. MAB is a typical reinforcement learning problem. In a MAB, there are multiple gambling machines, each with an arm. A player pulls one arm in each turn in succession to obtain an unknown prize. In each round of distribution, the collected rewards should be used to the maximum extent to determine the distribution goals of each round.
Example one
As shown in fig. 1, the present embodiment provides an online adaptive computing unloading method for ocean tasks, which includes the following steps:
s101, acquiring maritime affair edge network information and equipment calculation task request information;
s102, obtaining a marine task calculation unloading decision based on the marine marginal network information, the equipment calculation task request information and the constructed calculation unloading decision system model;
wherein, the construction process of the unloading decision system model comprises the following steps: constructing an objective function by taking average task completion delay of minimizing equipment energy budget constraint as a target, and constructing an unloading decision system model based on the objective function and constraint by taking QoS (quality of service) requirements and total energy consumption of equipment as constraints;
and S103, calculating unloading decisions based on the ocean tasks, executing the calculation tasks and feeding back the calculation results to the equipment.
As one or more embodiments, in S101, the maritime edge network information includes: a transmission network constructed by ocean buoys, in-sea sensors, ships and related network facilities along the shore;
the device computing task request information comprises: the calculation tasks are brought by tide, weather and other information detected by the ocean buoy, hydrological information detected by the ocean sensor and the like.
As one or more embodiments, in S102, the average task completion delay of the device energy budget constraint is:
Figure 317087DEST_PATH_IMAGE001
(1)
the objective function is therefore:
Figure 724410DEST_PATH_IMAGE002
(2)
wherein, α and qiRespectively the task completion delay and the weight of energy consumption,ioriginal position (node) representing task generation andjindicating the target location (edge server node) to offload,v ik indicating the amount of computation required per unit of input data,K i is shown at each positioniThe number of tasks to be offloaded,r ij which indicates the rate of the uplink transmission,l ik representing the input data size in bits; x ijk the expression of the number of the boolean variables,Ncalculating the number of nodes of an edge server existing in the network for the maritime edge;
wherein, the uplink transmission rate can be expressed as:
Figure 837860DEST_PATH_IMAGE003
(3)
in the formula (I), the compound is shown in the specification,Wrepresenting infinite bandwidthH ij Indicating a locationiThe wireless channel gain between the device and the gateway,N 0the power spectral density of the noise is represented,P ij indicating a locationiThe wireless transmission power of the device at (a).
Because of power limitations of mobile devices, energy consumption at each location is coupled to each other, providing more energy to a task at a current location will reduce the energy budget for other tasks at future locations.
Weight q of said energy consumptioniThe remaining energy of the device at the previous location, the energy consumption of the device for all tasks at the current location, and the energy budget of the device may be expressed as:
Figure 763090DEST_PATH_IMAGE004
(4)
the energy budget may reflect how the energy consumption at each location deviates from the total energy budget when q isiWhen larger, indicating insufficient energy, a greater weight may be applied to the energy consumption, and therefore the computational offloading decision should consume the least energy as possible.
qiIndicating an energy deficit at the previous location,
Figure 190660DEST_PATH_IMAGE005
the average energy budget for each location is represented,Ewhich represents the battery capacity of the device and,Mthe total number of tasks sent by the mobile device to the marine network at different locations,
Figure 252157DEST_PATH_IMAGE006
indicating the task allocation decision of the previous location.
In the constraint of the QoS requirement and the total energy consumption of the device, the expression of the QoS requirement is as follows:
Figure 474191DEST_PATH_IMAGE007
(5)
f j representing the computing power allocated by the edge server node j,D ik which represents QoS requirements and is in seconds.
The expression of the total energy consumption constraint of the device is:
Figure 886718DEST_PATH_IMAGE008
(6)
the derivation process of the calculation unloading decision system model is constructed according to the definition of the task model, the QoS constraint stipulated task completion delay constraint and the energy consumption model of the equipment, and specifically comprises the following steps:
(1) the delay model comprises two parts of uplink wireless transmission delay and task processing delay for unloading, and is represented as follows:
the uplink radio transmission delay for offloading is represented by:
Figure 914717DEST_PATH_IMAGE009
(7)
r ij which indicates the rate of the uplink transmission,l ik representing the input data size in bits;x ijk the expression of the number of the boolean variables,Ncomputing the number of nodes of an edge server present in a network for a maritime edge,jIndicating the target location (edge server node) to offload.
x ijk Represents a boolean variable expressed as: x is the number of ijk <l ik ,v ik ,D ik >The Boolean variable is a three-parameter model when task k is in placeiOffloading to a nodejIt is equal to 1.
Wherein, the uplink transmission rate can be expressed as:
Figure 768403DEST_PATH_IMAGE010
(8)
in the formula (I), the compound is shown in the specification,Wrepresenting infinite bandwidthH ij Indicating a locationiThe wireless channel gain between the device and the gateway,N 0the power spectral density of the noise is represented,P ij indicating a positioniThe wireless transmission power of the device at (a).
The task processing latency is expressed as:
Figure 958076DEST_PATH_IMAGE011
(9)
in the formula (I), the compound is shown in the specification,v ik representing the calculation intensity, and the unit is CPU period;l ik representing the input data size in bits;f ij representing edge server nodesjIs assigned to a position fromiComputing power of a devicex ijk The expression of the number of the boolean variables,Nthe number of edge server nodes present in the network is calculated for the edge of the maritime.
Thus, the delay model can be expressed as:
Figure 857899DEST_PATH_IMAGE012
(10)
(2) the QoS constraint specifies that the task completion delay constraint should not exceed the QoS requirement and can be expressed as:
Figure 627272DEST_PATH_IMAGE013
(11)
D ik which represents QoS requirements and is in seconds.
(3) The energy consumption model of the equipment is as follows: due to the limited battery capacity of the device, the total energy consumption of the device should not exceed the capacity after the device has passed through multiple locations, which can be expressed as:
Figure 928940DEST_PATH_IMAGE014
(12)
Msending the total number of tasks to the marine network for the mobile device at different locations, at each locationiThe number of unloaded tasks is K i ERepresenting the battery capacity of the device.
Whereine ik Represents the energy consumed by task k at location i, expressed as:
Figure 289515DEST_PATH_IMAGE015
(13)
when solving, firstly, initializing the energy deficiency q1=0, solving for each position i according to an optimization algorithm
Figure 348738DEST_PATH_IMAGE016
Then, then
Figure 718539DEST_PATH_IMAGE017
For line update, the detailed pseudo code of the online task allocation algorithm flow based on energy constraint is shown as algorithm 1.
Algorithm 1: online task allocation algorithm based on energy constraint
Input: M,N,K i ,l ik ,v ik ,D ik ,f j ,r ij ,E;
Output: task allocation decision x ijk
Initialize energy deficit q1 = 0
for each location i do
Calculate
Figure 609135DEST_PATH_IMAGE018
by solving
Figure 343872DEST_PATH_IMAGE019
Update energy deficit q1+1
end
return
Figure 952708DEST_PATH_IMAGE020
;
Inputting current information including wireless channel condition, node computing power, task information and the like, and realizing on-line task distribution by on-line operation and the like.
As shown in fig. 2, in the current reinforcement learning mentioned in the background art, since the player makes a decision based on the previously obtained award due to lack of the award information of the current round, a lower arm may be selected, but remorse may be generated; meanwhile, the information on the aspect of users is lacked, the reward is an unknown defect, in the marine task calculation unloading decision, the reward value corresponding to the unloading decision action is estimated based on the marine marginal network information, the equipment calculation task request information and the constructed calculation unloading decision system model, the reward value corresponding to the unloading decision action is estimated, the goal of maximizing the system reward is achieved, the unloading decision information training model is calculated through historical marine tasks, and the task calculation unloading decision is achieved based on a reinforcement learning mode.
The training model for calculating unloading decision information through historical marine tasks and realizing task calculation unloading decisions based on reinforcement learning comprises the following steps:
the first step is as follows: establishing a reward function for evaluating unloading decision actions, and defining through two aspects of energy constraint and task time delay;
the second step is that: calculating the reward value of each decision through a reward function, and adding a revised value through a confidence upper limit strategy to form a final reward value;
the third step: and selecting the decision with the maximum final reward in each round to execute, and updating the calculation state of the edge node in the system according to the selected decision action to obtain the optimal decision.
Wherein in the first step the reward function
Figure 329463DEST_PATH_IMAGE021
Is defined as follows:
Figure 340144DEST_PATH_IMAGE022
(14)
Figure 308100DEST_PATH_IMAGE023
representing tasks with respect tokFrom the home positioniUnloading to a target locationjThe corresponding reward function.
In the second step, the confidence limit strategy forms a revised value of
Figure 73407DEST_PATH_IMAGE024
The method is used for ensuring that the model can select the computation interrupt which is not selected or is selected for a few times for unloading.
Therefore, the final reward value is the reward value corresponding to the reward function plus the revised value, namely:
Figure 785011DEST_PATH_IMAGE025
(15)
wherein the content of the first and second substances,T ij indicating the current assignment to a nodejThe number of tasks.
In the third step, the decision with the maximum final reward is selected, and the optimal strategy is generated, namely selection
Figure 650198DEST_PATH_IMAGE026
To carry outUnloading:
Figure 992318DEST_PATH_IMAGE027
(16)
the detailed pseudo code of the reinforcement learning based node optimization algorithm is shown as algorithm 2.
Algorithm 2, namely node optimization algorithm based on reinforcement learning
Input: M,N,K i ,l ik ,v ik ,D ik ,f j ,r ij ,E;
Output: task allocation decision x ijk
Initialize x ijk = 0
for task k = 1 to N do
Assign each task k to GW k;
Initialize
Figure 575746DEST_PATH_IMAGE028
Initialize T ik = 1;
Update x ikk = 1;
end
for task k =N+ 1 to Ki do
Assign task k to GW
Figure 825462DEST_PATH_IMAGE029
;
Update
Figure 748419DEST_PATH_IMAGE030
;
Calculate
Figure 58177DEST_PATH_IMAGE031
Update
Figure 128901DEST_PATH_IMAGE032
Update
Figure 854412DEST_PATH_IMAGE033
end
for task k = 1 to N do
if
Figure 694192DEST_PATH_IMAGE034
then
UpdateT ik =T ik -1
Update
Figure 174852DEST_PATH_IMAGE035
Assign task k to GW
Figure 670555DEST_PATH_IMAGE036
Update
Figure 527653DEST_PATH_IMAGE037
;
Calculate
Figure 894043DEST_PATH_IMAGE031
Update
Figure 545604DEST_PATH_IMAGE032
Update
Figure 590921DEST_PATH_IMAGE033
end
Example two
The embodiment provides an online adaptive computing unloading system for ocean tasks, which comprises:
an information acquisition module configured to: acquiring maritime affair edge network information and equipment calculation task request information;
an offload decision computation module configured to: obtaining a marine task calculation unloading decision based on the marine marginal network information, the equipment calculation task request information and the constructed calculation unloading decision system model;
wherein, the construction process of the unloading decision system model comprises the following steps: constructing an unloading decision system model by taking average task completion delay of minimum equipment energy budget constraint as a target and taking QoS (quality of service) requirements and total energy consumption of equipment as constraints;
a task execution result output module configured to: and calculating and unloading decision execution equipment calculation tasks based on the ocean tasks and feeding back calculation results to the equipment.
In the marine task calculation unloading decision obtained based on the maritime affair edge network information, the equipment calculation task request information and the constructed calculation unloading decision system model, the reward value corresponding to the unloading decision action is estimated, the maximum system reward is taken as the target, the unloading decision information training model is calculated through historical marine tasks, and the task calculation unloading decision is realized based on reinforcement learning.
The training model for calculating unloading decision information through historical marine tasks and realizing task calculation unloading decisions based on reinforcement learning comprises the following steps:
establishing a reward function for evaluating unloading decision actions, and defining through two aspects of energy constraint and task time delay;
calculating the reward value of each decision through a reward function, and adding a revised value through a confidence upper limit strategy to form a final reward value;
and selecting the decision with the maximum final reward in each round to execute, and updating the calculation state of the edge node in the system according to the selected decision action to obtain the optimal decision.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (7)

1. The ocean task oriented online self-adaptive computing unloading method is characterized by comprising the following steps:
acquiring maritime affair edge network information and equipment calculation task request information;
the device computing task request information comprises: the tide and weather information detected by the ocean buoy and the calculation task brought by the hydrological information detected by the ocean sensor; obtaining a marine task calculation unloading decision based on the marine marginal network information, the equipment calculation task request information and the constructed calculation unloading decision system model, taking the maximum system reward as a target by estimating a reward value corresponding to an unloading decision action, calculating an unloading decision information training model through a historical marine task, and realizing the task calculation unloading decision based on reinforcement learning;
wherein, the construction process of the unloading decision system model comprises the following steps: constructing an unloading decision system model by taking average task completion delay of minimum equipment energy budget constraint as a target and taking QoS (quality of service) requirements and total energy consumption of equipment as constraints;
the average task completion delay for the equipment energy budget constraint is:
Figure 358898DEST_PATH_IMAGE001
in the formula, alpha and qiRespectively the task completion delay and the weight of energy consumption,irepresenting the home position of the task generation,jthe edge server node is represented as an edge server node, K i is shown at each positioniThe number of tasks to be offloaded,r ij which indicates the rate of the uplink transmission,l ik representing the input data size in bits; x ijk the expression of the number of the boolean variables,Nthe number of nodes of the edge server present in the network is calculated for the maritime edge,P ij indicating a locationiThe wireless transmission power of the device at (a),v ik the intensity of the calculation is represented by,f j representing edge server nodesj(ii) the allocated computing power;
and calculating and unloading decision execution equipment calculation tasks based on the ocean tasks and feeding back calculation results to the equipment.
2. The ocean task oriented online adaptive computing offloading method of claim 1 wherein the maritime edge network information comprises: ocean buoys, in-sea sensors, ships, and shore related network facilities.
3. The ocean task oriented online adaptive computing offloading method of claim 1, wherein the QoS requirement expression is:
Figure 907691DEST_PATH_IMAGE002
in the formula (I), the compound is shown in the specification, D ik indicating the QoS requirements.
4. The ocean task oriented online adaptive computing offloading method of claim 1, wherein the total energy consumption constraint of the device is expressed as:
Figure 261312DEST_PATH_IMAGE003
in the formula (I), the compound is shown in the specification,Erepresenting the battery capacity of the device.
5. The ocean task oriented online adaptive computing unloading method according to claim 1, wherein the training of the model through historical ocean task computing unloading decision information, and the implementation of the task computing unloading decision based on reinforcement learning comprises:
establishing a reward function for evaluating unloading decision actions, and defining through two aspects of energy constraint and task time delay;
calculating the reward value of each decision through a reward function, and adding a revised value through a confidence upper limit strategy to form a final reward value;
and selecting the decision with the maximum final reward in each round to execute, and updating the calculation state of the edge node in the system according to the selected decision action to obtain the optimal decision.
6. The on-line self-adaptive computing unloading system facing the ocean task is characterized by comprising the following steps:
an information acquisition module configured to: acquiring maritime affair edge network information and equipment calculation task request information;
the device computing task request information comprises: the tide and weather information detected by the ocean buoy and the calculation task brought by the hydrological information detected by the ocean sensor;
an offload decision computation module configured to: obtaining a marine task calculation unloading decision based on the marine marginal network information, the equipment calculation task request information and the constructed calculation unloading decision system model;
wherein, the construction process of the unloading decision system model comprises the following steps: the method comprises the steps of constructing an unloading decision system model by taking average task completion delay of minimum equipment energy budget constraint as a target and taking QoS (quality of service) requirements and total energy consumption of equipment as constraints, calculating an unloading decision information training model by historical marine tasks by estimating reward values corresponding to unloading decision actions and taking maximum system reward as a target, and realizing task calculation unloading decisions based on reinforcement learning;
the average task completion delay of the equipment energy budget constraint is as follows:
Figure 325083DEST_PATH_IMAGE001
in the formula, alpha and qiRespectively the task completion delay and the weight of energy consumption,irepresenting the home position of the task generation,jwhich represents the edge server node(s) of the edge server node, K i is shown at each positioniUnloadedThe number of tasks is increased, and the task scheduling process,r ij which indicates the rate of the uplink transmission,l ik representing the input data size in bits; x ijk it is shown that the variables of the boolean type,Nthe number of nodes of the edge server present in the network is calculated for the edge of the maritime,P ij indicating a locationiThe wireless transmission power of the device at (a),v ik the intensity of the calculation is represented by,f j representing edge server nodesj(ii) the allocated computing power;
a task execution result output module configured to: and calculating and unloading decision execution equipment calculation tasks based on the ocean tasks and feeding back calculation results to the equipment.
7. The ocean task oriented online adaptive computing offloading system of claim 6, wherein the training of the model through historical ocean task computing offloading decision information, the implementation of the task computing offloading decision based on reinforcement learning comprises:
establishing a reward function for evaluating unloading decision actions, and defining through two aspects of energy constraint and task time delay;
calculating the reward value of each decision through a reward function, and adding a revised value through a confidence upper limit strategy to form a final reward value;
and selecting the decision with the maximum final reward in each round to execute, and updating the calculation state of the edge node in the system according to the selected decision action to obtain the optimal decision.
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