CN111950194A - Newton momentum-based distributed acceleration composite optimization method and system - Google Patents

Newton momentum-based distributed acceleration composite optimization method and system Download PDF

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CN111950194A
CN111950194A CN202010709580.7A CN202010709580A CN111950194A CN 111950194 A CN111950194 A CN 111950194A CN 202010709580 A CN202010709580 A CN 202010709580A CN 111950194 A CN111950194 A CN 111950194A
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李华青
郑李逢
夏大文
严羽
吕庆国
王政
胡锦辉
程胡强
冉亮
丁文韬
苏恩冰
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Southwest University
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Abstract

The invention discloses a Newton momentum-based distributed acceleration composite optimization method and system, which are characterized in that on the basis that a plurality of intelligent agents are connected into a non-directional network, a smooth structure and a non-smooth structure are combined to establish an objective function, so that the coverage range of the processed problem is wider, the established model is more accurate, the problem can be converged to a global optimal solution at a linear speed, the convergence speed is higher than that of a similar method by introducing a momentum acceleration item and a gradient tracking item, and the processing speed of large-scale intelligent automation equipment data can be effectively improved.

Description

Newton momentum-based distributed acceleration composite optimization method and system
Technical Field
The invention relates to the technical field of computers, in particular to a Newton momentum-based distributed acceleration composite optimization method and system.
Background
Some optimization problems need to be solved in the fields of machine learning, statistical learning, unmanned aerial vehicle formation navigation, non-inductive sensor networks and the like, and the problems can be solved only through a single intelligent body when the problems are simpler. However, as information technology is continuously developed, in order to obtain more accurate solutions, the size of data to be considered and processed is larger and more accurate problem models need to be established, and the problem models are no longer simple smooth functions capable of representing problems, and may involve problems in a non-smooth form.
Considering that the existing computer has limited computing resources, a single agent cannot easily deal with the optimization problem of the large-scale compound form (smooth + non-smooth), so that the data processing speed of a large amount of intelligent automation equipment is slow.
Disclosure of Invention
The invention aims to solve the technical problem of the prior art, provides a Newton momentum-based distributed acceleration composite optimization method and system, and can effectively improve the data processing speed of large-scale intelligent automation equipment.
The technical scheme for solving the technical problems is as follows: a Newton momentum-based distributed acceleration composite optimization method comprises the following steps:
s1, connecting a plurality of agents into a non-directional communication network, and establishing an objective function combining a smooth structure and a non-smooth structure based on the agents:
Figure BDA0002595805790000021
wherein the content of the first and second substances,
Figure BDA0002595805790000022
is a smooth local objective function known only to agent i,
Figure BDA0002595805790000023
is a non-smooth local function known only to agent i,
Figure BDA0002595805790000024
is the set of feasible solutions, m is the number of agents;
s2, each agent calculates its own local estimation value and sends it to the first neighbor agent, the first neighbor agent is the neighbor agent corresponding to the agent, the neighbor agents are the agents directly communicating between two agents, and each is the neighbor agent;
s3, the first neighbor agent calculates momentum acceleration item according to the received local estimation value and sends the momentum acceleration item to a second neighbor agent, and the second neighbor agent is the neighbor agent of the first neighbor agent;
s4, the second neighbor agent calculates a gradient tracking item according to the momentum acceleration item and sends the gradient tracking item to a third neighbor agent, and the third neighbor agent is an agent of the second neighbor agent;
s5, loop S2 to S4, and terminate the loop until a preset condition is met.
The method has the advantages that on the basis that a plurality of intelligent agents are connected into a non-directional network, the coverage range of the processed problems is wider by establishing the target function combining the smooth structure and the non-smooth structure, the established model is more accurate, the problem can be converged to the global optimal solution at a linear speed, the convergence speed is higher than that of a similar method by introducing the momentum acceleration item and the gradient tracking item, and the processing speed of large-scale intelligent automatic equipment data can be effectively improved.
Further, the calculation process of the local estimation in S2 is:
s201, each agent calculates local optimal solution of each agent
Figure BDA0002595805790000025
The calculation formula is as follows:
Figure BDA0002595805790000026
s202, calculating the local estimation value of the local optimal solution according to the local optimal solution
Figure BDA0002595805790000027
The calculation formula is as follows:
Figure BDA0002595805790000028
wherein the content of the first and second substances,
Figure BDA0002595805790000031
is that
Figure BDA0002595805790000032
In the form of a continuous convex approximation of (a),
Figure BDA0002595805790000033
Figure BDA0002595805790000034
is fiIn that
Figure BDA0002595805790000035
Is a positive constant step.
The method has the advantages that the variable is updated instead of the target function by using the distributed optimization strategy and utilizing the continuous convex approximation replacement of the target function, so that the method can still solve the fixed point for the target problem when the target problem is not convex, and can converge to the global optimal solution at a linear speed for the problem which can be modeled as the convex function when the introduced step length alpha is positive and smaller than a given upper bound.
Further, the calculation process of the momentum acceleration term in S3 is:
s301, carrying out weighted average on the local estimation values to obtain local average estimation values
Figure BDA0002595805790000036
The calculation formula is as follows:
Figure BDA0002595805790000037
s302, estimating according to the local average
Figure BDA0002595805790000038
Calculating the momentum acceleration term according to the following calculation formula:
Figure BDA0002595805790000039
wherein, wijIs weight, w is more than or equal to 0ijIs < 1, and
Figure BDA00025958057900000310
beta is a momentum term parameter.
The method has the advantages that the Newton momentum method is used for calculating the gradient in the steps S301 and S302, and the method has the advantages that under the condition that the updating direction is the same as the previous moment, the convergence speed can be accelerated to a certain extent, the updating direction of the gradient is adjusted, the stability of the distributed optimization method is improved, and the time overhead for solving the global optimal solution is reduced. The similar method also has a common momentum method, but the common momentum method is easy to have the condition of large fluctuation of variable values in the iteration process, and the system is unstable.
Further, the specific calculation formula of the gradient tracking term in S4 is as follows:
Figure BDA00025958057900000311
wherein the content of the first and second substances,
Figure BDA00025958057900000312
is a function fiGradient of (. cndot.).
The beneficial effect of adopting the above further scheme is that by carrying out gradient tracing, the local agent can also trace the global gradient value, and the situation that the agent falls into solving the local optimal solution because the agent can only master the local information is avoided. Further, w isijThe value rule is as follows:
defining an undirected graph
Figure BDA0002595805790000041
Wherein
Figure BDA0002595805790000042
Is a set of agents that are intelligent agents,
Figure BDA0002595805790000043
is a set of edges that are to be considered,
Figure BDA0002595805790000044
is a weighted adjacency matrix in which the weights w for the edges (i, j)ijThe following conditions are satisfied: if (i, j) ∈ then wij> 0, otherwise wij＝0，
Figure BDA0002595805790000045
Wherein d isiIs the number of neighbor agents for agent i.
A Newton momentum-based distributed acceleration composite optimization system comprises an objective function establishing module and a plurality of intelligent agents which are connected into a non-directional communication network;
the objective function establishing module is used for establishing an objective function combining a smooth structure and a non-smooth structure according to the plurality of agents:
Figure BDA0002595805790000046
wherein the content of the first and second substances,
Figure BDA0002595805790000047
is a smooth local objective function known only to agent i,
Figure BDA0002595805790000048
is a non-smooth local function known only to agent i,
Figure BDA0002595805790000049
is the set of feasible solutions, m is the number of agents;
the intelligent agents are used for calculating local estimation values of the intelligent agents and sending the local estimation values to a first neighbor intelligent agent, the first neighbor intelligent agent is a neighbor intelligent agent corresponding to the intelligent agent, the neighbor intelligent agents are intelligent agents which directly communicate between the two intelligent agents, and the neighbor intelligent agents are neighbor intelligent agents;
the first neighbor agent is used for calculating momentum acceleration items according to the received local estimation values and sending the momentum acceleration items to a second neighbor agent, and the second neighbor agent is a neighbor agent of the first neighbor agent;
the second neighbor agent is used for calculating a gradient tracking item according to the momentum acceleration item and sending the gradient tracking item to a third neighbor agent, and the third neighbor agent is an agent of the second neighbor agent;
the plurality of agents are further configured to loop the local estimates, the momentum acceleration term, the gradient tracking term until a predetermined condition is met and terminate the loop.
Further, the calculation process of the local estimation is as follows:
s201, each agent calculates local optimal solution of each agent
Figure BDA0002595805790000051
The calculation formula is as follows
Figure BDA0002595805790000053
S202, calculating the local estimation value of the local optimal solution according to the local optimal solution
Figure BDA0002595805790000054
The calculation formula is as follows:
Figure BDA0002595805790000055
wherein the content of the first and second substances,
Figure BDA0002595805790000056
is that
Figure BDA0002595805790000057
In the form of a continuous convex approximation of (a),
Figure BDA0002595805790000058
Figure BDA0002595805790000059
is fiIn that
Figure BDA00025958057900000510
Is a positive constant step.
The method has the advantages that on the basis that a plurality of intelligent agents are connected into a non-directional network, the coverage range of the processed problems is wider by establishing the target function combining the smooth structure and the non-smooth structure, the established model is more accurate, the problem can be converged to the global optimal solution at a linear speed, the convergence speed is higher than that of a similar method by introducing the momentum acceleration item and the gradient tracking item, and the processing speed of large-scale intelligent automatic equipment data can be effectively improved.
Further, the calculation process of the momentum acceleration term is as follows:
s301, carrying out weighted average on the local estimation values to obtain local average estimation values
Figure BDA00025958057900000511
The calculation formula is as follows:
Figure BDA00025958057900000512
s302, estimating according to the local average
Figure BDA00025958057900000513
Calculating the momentum acceleration term according to the following calculation formula:
Figure BDA00025958057900000514
wherein, wijIs weight, w is more than or equal to 0ijIs < 1, and
Figure BDA00025958057900000515
beta is a momentum term parameter.
The method has the advantages that the variable is updated instead of the target function by using the distributed optimization strategy and utilizing the continuous convex approximation replacement of the target function, so that the method can still solve the fixed point for the target problem when the target problem is not convex, and can converge to the global optimal solution at a linear speed for the problem which can be modeled as the convex function when the introduced step length alpha is positive and smaller than a given upper bound.
Further, the specific calculation formula of the gradient tracking term is as follows:
Figure BDA0002595805790000061
wherein the content of the first and second substances,
Figure BDA0002595805790000062
is a function fiGradient of (. cndot.).
The beneficial effect of adopting the above further scheme is that by carrying out gradient tracing, the local agent can also trace the global gradient value, and the situation that the agent falls into solving the local optimal solution because the agent can only master the local information is avoided.
Further, w isijThe value rule is as follows:
defining an undirected graph
Figure BDA0002595805790000063
Wherein
Figure BDA0002595805790000064
Is a set of agents that are intelligent agents,
Figure BDA0002595805790000065
is a set of edges that are to be considered,
Figure BDA0002595805790000066
is a weighted adjacency matrix in which the weights w for the edges (i, j)ijThe following conditions are satisfied: if (i, j) ∈ then wij> 0, otherwise wij＝0，
Figure BDA0002595805790000067
Wherein d isiIs the number of neighbor agents for agent i.
Reference 1: W.Shi, Q.Ling, G.Wu, and W.yin, "A formal gradient for centralized composition optimization," IEEE Transactions on Signal Processing, vol.63, No.22, pp.6013-6023,2015.
Drawings
FIG. 1 is a graph comparing the convergence of PG-EXTRA according to the present invention;
FIG. 2 is a graph comparing the test accuracy of the present invention with PG-EXTRA;
FIG. 3 is a block diagram of four types of networks in one embodiment;
fig. 4 is a graph comparing the performance of four types of networks using the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments that can be derived by one of ordinary skill in the art from the embodiments given herein are intended to be within the scope of the present invention.
Example 1
A Newton momentum-based distributed acceleration composite optimization method comprises the following steps:
s1, connecting a plurality of agents into a non-directional communication network, and establishing an objective function combining a smooth structure and a non-smooth structure based on the plurality of agents:
Figure BDA0002595805790000071
wherein the content of the first and second substances,
Figure BDA0002595805790000072
is a smooth local objective function known only to agent i,
Figure BDA0002595805790000073
is a non-smooth local function known only to agent i,
Figure BDA0002595805790000074
is the set of feasible solutions, m is the number of agents;
s2, each agent calculates its own local estimation value and sends it to the first neighbor agent, the first neighbor agent is the neighbor agent corresponding to the agent, the neighbor agents are the agents directly communicating between two agents, and each is the neighbor agent;
s3, the first neighbor agent calculates momentum acceleration item according to the received local estimation value and sends the momentum acceleration item to the second neighbor agent, and the second neighbor agent is the neighbor agent of the first neighbor agent;
s4, the second neighbor agent calculates a gradient tracking item according to the momentum acceleration item and sends the gradient tracking item to a third neighbor agent, and the third neighbor agent is an agent of the second neighbor agent;
s5, loop S2 to S4, and terminate the loop until a preset condition is met.
On the basis that a plurality of agents are connected into a non-directional network, a smooth structure and a non-smooth structure are combined to form an objective function, so that the coverage range of the processed problems is wider, the established model is more accurate, the problem can be converged to a global optimal solution at a linear speed, the convergence speed is higher than that of a similar method by introducing a momentum acceleration item and a gradient tracking item, and the processing speed of large-scale intelligent automatic equipment data can be effectively improved. The intelligent agent is a device with computing capability, storage capability and communication capability, and can be a computer, a server, an unmanned aerial vehicle, an automobile and the like. The corresponding neighbor agent should be understood as: since each agent is calculating its own local estimate in S2, each agent is transmitting the local estimate at the same time, and each agent has its own neighbor agent, i.e., the first neighbor agent. Undirected networks should be understood as: and a connection mode for enabling a plurality of agents to mutually transmit and receive information. The preset conditions include: the iteration number, the running time or the value of the target problem are within a preset interval and the like. A smooth function is a function of infinite order, continuously derivable within its domain of definition. A non-smooth function is a function that is not infinitely derivable within its domain of definition. The calculation process of the local estimation in S2 is:
s201, each agent calculates local optimal solution of each agent
Figure BDA0002595805790000081
The calculation formula is as follows:
Figure BDA0002595805790000082
s202, calculating local estimation value of the local optimal solution according to the local optimal solution
Figure BDA0002595805790000083
The calculation formula is as follows:
Figure BDA0002595805790000084
wherein the content of the first and second substances,
Figure BDA0002595805790000085
is that
Figure BDA0002595805790000086
In the form of a continuous convex approximation of (a),
Figure BDA0002595805790000087
Figure BDA0002595805790000088
is fiIn that
Figure BDA0002595805790000089
Is a positive constant step.
The variable updating is carried out by using a distributed optimization strategy and using continuous convex approximation replacement of the objective function instead of the objective function, so that the advantage that when the objective problem is not convex, the immobile point can still be solved for the objective problem, and when the introduced step length alpha is positive and smaller than a given upper bound, the problem which can be modeled as a convex function can be converged to the global optimal solution at a linear speed.
The calculation process of the momentum acceleration term in the S3 is as follows:
s301, carrying out weighted average on the local estimation to obtain local average estimation
Figure BDA00025958057900000810
The calculation formula is as follows:
Figure BDA00025958057900000811
s302, estimating according to local average
Figure BDA00025958057900000812
And calculating a momentum acceleration term, wherein the calculation formula is as follows:
Figure BDA00025958057900000813
wherein, wijIs weight, w is more than or equal to 0ijIs < 1, and
Figure BDA00025958057900000814
beta is a momentum term parameter.
In the steps S301 and S302, the gradient is calculated by using a Newton momentum method, and the method has the advantages that under the condition that the updating direction is the same as the previous moment, the convergence speed can be accelerated to a certain extent, the updating direction of the gradient is adjusted, the stability of the distributed optimization method is improved, and the time overhead for solving the global optimal solution is reduced. The similar method also has a common momentum method, but the common momentum method is easy to have the condition of large fluctuation of variable values in the iteration process, and the system is unstable.
In this embodiment, an undirected graph is defined
Figure BDA0002595805790000091
Wherein
Figure BDA0002595805790000092
Is a set of agents that are intelligent agents,
Figure BDA0002595805790000093
is a set of edges that are to be considered,
Figure BDA0002595805790000094
is a weighted adjacency matrix in which the weights w for the edges (i, j)ijThe following conditions are satisfied: if (i, j) ∈ then wij> 0, otherwise wij＝0，
Figure BDA0002595805790000095
Wherein d isiIs the number of neighbor agents to agent i, let self-loops exist, i.e. (i, i) ∈, and let
Figure BDA0002595805790000096
Agents i and j can communicate directly if and only if there is an edge (i, j) e.
The specific calculation formula of the gradient tracking term in the S4 is as follows:
Figure BDA0002595805790000097
wherein the content of the first and second substances,
Figure BDA0002595805790000098
is a function fiGradient of (. cndot.).
By carrying out gradient tracking, the local agent can also track the global gradient value, and the situation that the local optimal solution is solved because the agent can only master local information is avoided.
To verify the convergence of the present invention, the following assumptions are made:
assume that 1: (i) collection
Figure BDA0002595805790000099
Is a closed and convex set; (ii) local objective function
Figure BDA00025958057900000910
In the first order of the gradient of (1), wherein
Figure BDA00025958057900000911
Is an open set; gradient of gradient
Figure BDA00025958057900000912
In the collection
Figure BDA00025958057900000913
Upper LiLiphoz continuous; (iii) function(s)
Figure BDA00025958057900000914
Is convex and may be non-smooth; (iv) function U is in
Figure BDA00025958057900000915
The upper boundary is lower boundary.
Assume 2: function F in set
Figure BDA00025958057900000916
The method is characterized in that the method mainly comprises the following steps of (1) performing optimization on a high-degree mu-strong convex, wherein the high convexity is used for optimization, and particularly one of the conditions for ensuring the linear convergence rate of a plurality of algorithms based on a gradient descent method is defined as follows:
Figure BDA00025958057900000917
it is noted that strong convexity does not require that the function be differentiable from place to place, and when the function is not smooth, the gradient is replaced by a sub-gradient in which strong convexity is more strictly a quadratic term than a normal convex function
Figure BDA0002595805790000101
This strongly convex nature is important. Intuitive from a one-dimensional function, a convex function only requires that the function curve be above its tangent, and there is little requirement for "up", meaning that the curve can "follow" the tangent indefinitely, as long as it remains above it. It goes without saying that in optimization, in particular in gradient optimization, such weak gradient changes make it difficult to achieve fast optimization, possibly with a limited number of times that convergence has not yet been reached. This is also difficult if we take a solution close to the minimum. "very" close is only a qualitative understanding, in which case a bad situation occurs where the optimal solution is very similar but the decision variables differ greatly. At this time, a secondary term is added, so that a secondary lower bound is ensured, the condition of 'clinging' to a tangent line is avoided, and the optimization is simpler.
Assume that 3: undirected graph G is connected.
Definition 1: for a function with continuous first order gradient
Figure BDA0002595805790000102
Wherein
Figure BDA0002595805790000103
And aggregate
Figure BDA0002595805790000104
Is a closed and convex set. If it is not
Figure BDA0002595805790000105
Is continuous and satisfies the condition that (i) for all
Figure BDA0002595805790000106
(ii) Gradient of gradient
Figure BDA0002595805790000107
Is that
Figure BDA0002595805790000108
-rishoz continuous; (iii) function(s)
Figure BDA0002595805790000109
In the collection
Figure BDA00025958057900001010
Is that
Figure BDA00025958057900001011
And (4) strong convex. Then function
Figure BDA00025958057900001012
Is fiOf functions
Figure BDA00025958057900001013
-the smoothness of the film is improved,
Figure BDA00025958057900001014
successive convex approximation replacement of strong convex, wherein
Figure BDA00025958057900001015
Refers to
Figure BDA00025958057900001016
Partial derivatives in the parameters (x, y).
Assume 4: function(s)
Figure BDA00025958057900001017
Is fiIs/are as follows
Figure BDA00025958057900001018
Is smooth and
Figure BDA00025958057900001019
strongly convex successive convex approximation to the substitution function.
And (3) convergence analysis:
introduction 1: let 1-4 be true, for all k ≧ 0 available,
pk+1≤σ(α，β)pk+η(α，β)||k||2 (4)
wherein the parameters σ (α, β) and η (α, β) are defined as follows
Figure BDA0002595805790000111
Figure BDA0002595805790000112
Note that 0 < beta < 1,
Figure BDA0002595805790000113
and
Figure BDA0002595805790000114
and (3) proving that: according to the proposed method and pkDefinition of (1), to know
Figure BDA0002595805790000115
Wherein beta is more than 0 and less than 1.
By utilizing the continuous property of the Lipruztz,
Figure BDA0002595805790000116
by using
Figure BDA0002595805790000117
The first-order optimal condition of (1) is derived
Figure BDA0002595805790000118
The combined formulas (8) and (9) are obtained,
Figure BDA0002595805790000119
this means that
Figure BDA0002595805790000121
And can be derived from (7) and (11)
Figure BDA0002595805790000122
Wherein the content of the first and second substances,
Figure BDA0002595805790000123
the next step will be to determine
Figure BDA0002595805790000124
The lower bound of (c). Review of
Figure BDA0002595805790000125
Can be defined by
Figure BDA0002595805790000126
Using the mu-strong convex nature of the function F, it can be shown that the following holds
Figure BDA0002595805790000131
An arrangement formula (13) can be found
Figure BDA0002595805790000132
It is thus possible to obtain,
Figure BDA0002595805790000133
Figure BDA0002595805790000134
to determine pk+1Upper bound of (1), analysis
Figure BDA0002595805790000135
And obtain
Figure BDA0002595805790000136
The combination of formulas (15) and (16) can be found
Figure BDA0002595805790000141
This is equivalent to
pk+1≤σ(α，β)pk+η(α，β)||k||2 (17)
And finishing the guiding certification.
2, leading: let 1-3 hold, for all k ≧ 0, the following holds
Figure BDA0002595805790000142
Wherein L ismax＝max{Li}，，
Figure BDA0002595805790000143
And (3) proving that: according to |k||2By definition in Lesion 1, it is understood that
Figure BDA0002595805790000144
Because of the gradient of the magnetic field, the gradient,
Figure BDA0002595805790000145
is Li --Liphoz continuous, analytically available
Figure BDA0002595805790000146
And finishing the guiding certification.
And 3, introduction: let hypothesis 3 be true, for all k ≧ 0, the following holds
Figure BDA0002595805790000151
Wherein the content of the first and second substances,
Figure BDA0002595805790000152
and (3) proving that: review of
Figure BDA0002595805790000153
Can be given by
Figure BDA0002595805790000154
Thus, it is known that
Figure BDA0002595805790000155
Wherein the content of the first and second substances,sis greater than 0. And finishing the guiding certification.
And (4) introduction: the following equation holds under the condition that 1 to 4 hold
Figure BDA0002595805790000156
Wherein the content of the first and second substances,y＞0。
prove that consider
Figure BDA0002595805790000157
Definition of (1), to know
Figure BDA0002595805790000158
Thus, it is possible to obtain
Figure BDA0002595805790000161
WhereinyIs greater than 0. And finishing the guiding certification.
And (5) introduction: let assumption 1-4 be true, then the following equation holds
Figure BDA0002595805790000162
And (3) proving that: according to
Figure BDA0002595805790000163
Is/are as follows
Figure BDA0002595805790000164
Strength properties, obtainable
Figure BDA0002595805790000165
Thus, the analysis can be found
Figure BDA0002595805790000166
Using x*Global of (2)Optimality and convexity of G (-) can be obtained
Figure BDA0002595805790000167
The combination of formulas (26) and (27) is known
Figure BDA0002595805790000171
Further, utilize
Figure BDA0002595805790000172
Is/are as follows
Figure BDA0002595805790000173
Strong convexity and according to
Figure BDA0002595805790000174
Is that
Figure BDA0002595805790000175
To obtain an optimal solution
Figure BDA0002595805790000176
Thus, the analysis can be found
Figure BDA0002595805790000177
This means that
Figure BDA0002595805790000178
Thus, it is possible to obtain
Figure BDA0002595805790000179
And finishing the guiding certification.
And (6) introduction: according to the sequence skFor all k ≧ 0, define
Figure BDA00025958057900001710
And
Figure BDA00025958057900001711
wherein
Figure BDA00025958057900001712
If it is not
Figure BDA00025958057900001713
Is bounded, then
Figure BDA00025958057900001714
To analyze the linear convergence speed of the present invention using lemma 6, the following variables were defined:
Figure BDA0002595805790000181
Figure BDA0002595805790000182
the next step will be to process the sequence { p using the lemmas 1, 3-6k}，
Figure BDA0002595805790000183
Figure BDA0002595805790000184
And { | | dkAnd thus demonstrates linear convergence.
The main results are:
proposition 1: let assumptions 1-4 hold. Considering sigma (alpha), eta (alpha) and two free variabless> 0 and omegay> 0, for arbitrary
Figure BDA0002595805790000185
The following inequality holds
Figure BDA0002595805790000186
Figure BDA0002595805790000187
Figure BDA0002595805790000188
Figure BDA0002595805790000189
Wherein the content of the first and second substances,
Figure BDA00025958057900001810
Figure BDA00025958057900001811
Figure BDA00025958057900001812
Figure BDA00025958057900001813
Figure BDA00025958057900001814
Figure BDA00025958057900001815
Figure BDA00025958057900001816
Figure BDA00025958057900001817
and (3) proving that: using theorem 1 and considering s for positive sequenceskAnd
Figure BDA0002595805790000191
is provided with
Figure BDA0002595805790000192
Can obtain the product
Figure BDA0002595805790000193
A finishing formula (42) when
Figure BDA0002595805790000194
Then, it is found that the expression (30) holds. Similar to the analysis process for equation (30), equations (31) and (32) hold.
Consider the lemmas 5.3.5 and
Figure BDA0002595805790000195
and
Figure BDA0002595805790000196
definition of (1), to know
Figure BDA0002595805790000197
And finishing the guiding certification.
Theorem 1: let assumptions 1-4 hold if α and β satisfy
Figure BDA0002595805790000198
And 0 < beta < 1, objective function
Figure BDA0002595805790000199
Will be at speed
Figure BDA00025958057900001910
Linear convergence when α ∈ [ min { α, α)max}，αmax) When the temperature of the water is higher than the set temperature,
Figure BDA00025958057900001911
and when alpha is epsilon (0, min { alpha, alpha)max}) of the two or more,
Figure BDA00025958057900001912
and (3) proving that: according to proposition 1, it can be known
Figure BDA00025958057900001913
Wherein the content of the first and second substances,
Figure BDA00025958057900001914
and is
Figure BDA0002595805790000201
Using lemma 6, it can be seen that if some parameters exist, then
Figure BDA0002595805790000202
I.e. omega (alpha, beta, z) < 1, then
Figure BDA0002595805790000203
Will be at a linear rate
Figure BDA0002595805790000204
Converge to 0. For this purpose, the selection of suitable parameters is minimized
Figure BDA0002595805790000205
And
Figure BDA0002595805790000206
consider that
Figure BDA0002595805790000207
There is therefore a parameter θ > 0' such that
Figure BDA0002595805790000208
Further analysis revealed that if
Figure BDA0002595805790000209
Then
Figure BDA00025958057900002010
In that
Figure BDA00025958057900002011
The minimum value is obtained. In other words, it is possible to provide a high-quality image
Figure BDA00025958057900002012
If step size is selected
Figure BDA00025958057900002013
Derived from the above
Figure BDA00025958057900002014
Selecting
Figure BDA00025958057900002015
It can be known that
Figure BDA00025958057900002016
Wherein
Figure BDA00025958057900002017
By similar analysis it can be seen
Figure BDA0002595805790000211
And is
Figure BDA0002595805790000212
Based on the previous analysis, the appropriate 3 variables ω were selectedopt，s，ySo that
Figure BDA0002595805790000213
Become sufficient conditions of
Figure BDA0002595805790000214
Wherein the content of the first and second substances,
Figure BDA0002595805790000215
in addition, due to
Figure BDA0002595805790000216
Can obtain the product
Figure BDA0002595805790000217
Wherein the content of the first and second substances,
Figure BDA0002595805790000218
summarize the above analysis
Figure BDA0002595805790000219
It can be known that
Figure BDA00025958057900002110
Wherein the content of the first and second substances,
Figure BDA00025958057900002111
to ensure
Figure BDA00025958057900002112
The value range of (a) is not null, alpha should satisfy
Figure BDA00025958057900002113
Analysis of
Figure BDA00025958057900002114
The value range of (1) can be found if
Figure BDA00025958057900002115
Then
Figure BDA0002595805790000221
Therefore, if α ∈ [ min { α, α [ ], α is knownmax}，αmax) Then
Figure BDA0002595805790000222
If α ∈ (0, min { α)*，αmax}) then
Figure BDA0002595805790000223
And (5) finishing the certification.
In this embodiment, a logistic regression simulation experiment is performed based on breast cancer data provided by the UCI machine learning database to verify the effectiveness of the method. Features of this data include Radius (Radius), Texture (Texture), circumference (Perimeter), Area (Area), and Smoothness (Smoothness) of the nucleus, etc., as calculated from digitized images of breast masses. The experiment is intended to predict whether a patient's condition is malignant based on the sample values given in the data set. The prediction probability can be expressed as
Figure BDA0002595805790000224
Where c and l are the data and label, respectively, for the sample. From 683 data in the data set, 200 samples of N are distributed to m networked intelligent agents for training
Figure BDA0002595805790000225
The remaining 483 samples were used for testing. The j-th data and sample of agent i are respectively
Figure BDA0002595805790000226
And li，hE { -1, 1}, wherein
Figure BDA0002595805790000227
h＝1，...，qi。
Based on the model, classifier
Figure BDA0002595805790000228
About sample data (c)i，h，li，h) The maximum log-likelihood estimate of (c) is the optimal solution to the following optimization problem:
wherein the regularization term
Figure BDA00025958057900002210
For the purpose of avoiding over-fitting,
Figure BDA00025958057900002211
for increasing the sparsity of the solution. The residual error is defined as in the following simulation
Figure BDA00025958057900002212
In this example, the convergence of the PG-EXTRA method and the proposed method is compared in reference 1. Defining initial values
Figure BDA00025958057900002213
And
Figure BDA00025958057900002214
setting the step length α to 0.01, the momentum term coefficient β to 0.5, and setting the preset condition to be the number of iterations to 70, it should be understood that the number of iterations is different for different data samples, and the setting is here according to actual requirements. A undirected network of m-10 agents is randomly generated with a 70% probability of direct communication between each pair of agents. The evolution of the residual with respect to the different methods is shown in fig. 1, and the test accuracy is shown in fig. 2. As can be seen from fig. 1, when α is 0.01, the convergence rate of the proposed method is faster than that of reference 1, and the data processing speed is greatly increased.
It should be noted that the disclosure in reference 1 is mainly used for comparison with the present invention, and does not disclose the technical contents of the present invention, nor suggest the technical problems and technical solutions solved by the present invention.
In the present embodiment, a network including a star network a, a ring network b, a tree network c, and a fully connected network d as shown in fig. 3 is also studied. Setting an initial value to
Figure BDA0002595805790000231
And
Figure BDA0002595805790000232
and sets the step size alpha to 0.01 and the momentum parameter beta to 0.5. The performance of the proposed method under each type of network is shown in fig. 4, and the result shows that the convergence speed is higher and the data processing speed is higher when the network is dense.
Example 2
On the basis of the embodiment 1, the Newton momentum-based distributed acceleration composite optimization system comprises an objective function establishing module and a plurality of intelligent agents which are connected into a non-directional communication network;
the target function establishing module is used for establishing a target function combining a smooth structure and a non-smooth structure according to a plurality of agents:
Figure BDA0002595805790000233
wherein the content of the first and second substances,
Figure BDA0002595805790000234
is a smooth local objective function known only to agent i,
Figure BDA0002595805790000235
is a non-smooth local function known only to agent i,
Figure BDA0002595805790000236
is the set of feasible solutions, m is the number of agents;
the system comprises a plurality of intelligent agents, a first neighbor intelligent agent and a second neighbor intelligent agent, wherein the plurality of intelligent agents are used for calculating local estimated values of the intelligent agents and sending the local estimated values to the first neighbor intelligent agent;
the first neighbor agent is used for calculating momentum acceleration terms according to the received local estimated values and sending the momentum acceleration terms to the second neighbor agent, and the second neighbor agent is a neighbor agent of the first neighbor agent;
the second neighbor agent is used for calculating a gradient tracking item according to the momentum acceleration item and sending the gradient tracking item to a third neighbor agent, and the third neighbor agent is an agent of the second neighbor agent;
the plurality of agents are further configured to loop the local estimates, the momentum acceleration term, and the gradient tracking term until a predetermined condition is met.
In this embodiment, a single agent is a drone with traffic capacity, computing capacity and storage capacity, and a undirected network connected by a plurality of agents means that the agents can communicate with each other. The first neighbor agent, the second neighbor agent and the third neighbor agent are all contained in a plurality of agents, and the target function is solved by the cooperation of the plurality of agents; the preset conditions include: the iteration number, the running time or the value of the target problem are within a preset interval and the like.
The calculation process of the local estimation is as follows:
s201, each agent calculates local optimal solution of each agent
Figure BDA0002595805790000241
The calculation formula is as follows:
Figure BDA0002595805790000242
s202, calculating local estimation value of the local optimal solution according to the local optimal solution
Figure BDA0002595805790000243
The calculation formula is as follows:
Figure BDA0002595805790000244
wherein the content of the first and second substances,
Figure BDA0002595805790000245
is that
Figure BDA0002595805790000246
In the form of a continuous convex approximation of (a),
Figure BDA0002595805790000247
Figure BDA0002595805790000248
is fiIn that
Figure BDA0002595805790000249
Is a positive constant step.
On the basis that a plurality of agents are connected into a non-directional network, a smooth structure and a non-smooth structure are combined to form an objective function, so that the coverage range of the processed problems is wider, the established model is more accurate, the problem can be converged to a global optimal solution at a linear speed, the convergence speed is higher than that of a similar method by introducing a momentum acceleration item and a gradient tracking item, and the processing speed of large-scale intelligent automatic equipment data can be effectively improved.
The momentum acceleration term is calculated as follows:
s301, carrying out weighted average on the local estimation to obtain local average estimation
Figure BDA00025958057900002410
The calculation formula is as follows:
Figure BDA0002595805790000251
s302, estimating according to local average
Figure BDA0002595805790000252
And calculating a momentum acceleration term, wherein the calculation formula is as follows:
Figure BDA0002595805790000253
wherein, wijIs weight, w is more than or equal to 0ijIs < 1, and
Figure BDA0002595805790000254
beta is a momentum term parameter.
The variable updating is carried out by using a distributed optimization strategy and using continuous convex approximation replacement of the objective function instead of the objective function, so that the advantage that when the objective problem is not convex, the immobile point can still be solved for the objective problem, and when the introduced step length alpha is positive and smaller than a given upper bound, the problem which can be modeled as a convex function can be converged to the global optimal solution at a linear speed.
The specific calculation formula of the gradient tracking term is as follows:
Figure BDA0002595805790000255
wherein the content of the first and second substances,
Figure BDA0002595805790000256
is a function fiGradient of (. cndot.).
By carrying out gradient tracking, the local agent can also track the global gradient value, and the situation that the local optimal solution is solved because the agent can only master local information is avoided.
wijThe value rule is as follows:
defining an undirected graph
Figure BDA0002595805790000257
Wherein
Figure BDA0002595805790000258
Is a set of agents that are intelligent agents,
Figure BDA0002595805790000259
is a set of edges that are to be considered,
Figure BDA00025958057900002510
is a weighted adjacency matrix in which the weights w for the edges (i, j)ijThe following conditions are satisfied: if (i, j) ∈ then wij> 0, otherwise wij＝0，
Figure BDA00025958057900002511
Wherein d isiIs the number of neighbor agents for agent i.
In this embodiment, adopt a plurality of unmanned aerial vehicles to solve the problem of target location, every unmanned aerial vehicle can all be regarded as an agent, and specific implementation process is as follows:
firstly, a sound source/energy source is planned to continuously send signals outwards, as the propagation of the volume is gradually attenuated along with the increase of the distance, a plurality of unmanned aerial vehicles establish an objective function related to the distance and the information intensity according to the received intensity, the communication and the information calculation are carried out among the unmanned aerial vehicles, and finally, the target position is obtained, and the rapid positioning is realized.
Example 3
On the basis of embodiment 1, solve the resource allocation problem with the intelligent generator of many microprocessor control, be intelligent agent at every microprocessor:
for example, assuming that there are several different power generators, the power generator generates power with coal, the relationship between the amount of coal used and the amount of power generated is positively correlated, and the utilization rate of coal is different for each power generator, some are high, and some are low. How to effectively utilize limited coal is the problem solved by the case.
Aiming at the performances of different generators, a mathematical model between the generated energy and the coal consumption is established, an objective function related to the generated energy is obtained, and a function value is the coal consumption. The microprocessors are combined with the specific conditions of the corresponding generators, communication and information calculation are carried out among the microprocessors, and finally the coal consumption of each generator is obtained.
The technical solutions provided by the embodiments of the present invention are described in detail above, and the principles and embodiments of the present invention are explained herein by using specific examples, and the descriptions of the embodiments are only used to help understanding the principles of the embodiments of the present invention; also, while the present invention has been described with respect to particular embodiments and with reference to certain preferred embodiments thereof, it will be understood by those skilled in the art that the foregoing descriptions of the present invention are provided for illustration and not for the purpose of limiting the invention as defined by the appended claims.

Claims (10)

1. A Newton momentum-based distributed acceleration composite optimization method is characterized by comprising the following steps:
s1, connecting a plurality of agents into a non-directional communication network, and establishing an objective function combining a smooth structure and a non-smooth structure based on the agents:
Figure FDA0002595805780000011
Figure FDA0002595805780000012
wherein the content of the first and second substances,
Figure FDA0002595805780000013
is a smooth local objective function known only to agent i,
Figure FDA0002595805780000014
is a non-smooth local function known only to agent i,
Figure FDA0002595805780000015
is the set of feasible solutions, m is the number of agents;
s2, each agent calculates its own local estimation value and sends it to the first neighbor agent, the first neighbor agent is the neighbor agent corresponding to the agent, the neighbor agents are the agents directly communicating between two agents, and each is the neighbor agent;
s3, the first neighbor agent calculates momentum acceleration item according to the received local estimation value and sends the momentum acceleration item to a second neighbor agent, and the second neighbor agent is the neighbor agent of the first neighbor agent;
s4, the second neighbor agent calculates a gradient tracking item according to the momentum acceleration item and sends the gradient tracking item to a third neighbor agent, and the third neighbor agent is an agent of the second neighbor agent;
s5, loop S2 to S4, and terminate the loop until a preset condition is met.
2. The method of claim 1, wherein the local estimation in S2 is calculated by:
s201, each agent calculates local optimal solution of each agent
Figure FDA0002595805780000016
The calculation formula is as follows:
Figure FDA0002595805780000017
s202, calculating the local estimation value of the local optimal solution according to the local optimal solution
Figure FDA0002595805780000018
The calculation formula is as follows:
Figure FDA0002595805780000019
wherein the content of the first and second substances,
Figure FDA0002595805780000021
is that
Figure FDA0002595805780000022
In the form of a continuous convex approximation of (a),
Figure FDA0002595805780000023
Figure FDA0002595805780000024
is fiIn that
Figure FDA0002595805780000025
Is a positive constant step.
3. The method according to claim 2, wherein the calculation process of the momentum acceleration term in S3 is as follows:
s301, the local estimation is carried outWeighted averaging to obtain a locally averaged estimate
Figure FDA0002595805780000026
The calculation formula is as follows:
Figure FDA0002595805780000027
s302, estimating according to the local average
Figure FDA0002595805780000028
Calculating the momentum acceleration term according to the following calculation formula:
Figure FDA0002595805780000029
wherein, wijIs weight, w is more than or equal to 0ijIs < 1, and
Figure FDA00025958057800000210
beta is a momentum term parameter.
4. The method according to any one of claims 1 to 3, wherein the specific calculation formula of the gradient pursuit term in S4 is as follows:
Figure FDA00025958057800000211
wherein the content of the first and second substances,
Figure FDA00025958057800000212
is a function fiGradient of (. cndot.).
5. The method of claim 4, wherein w isijThe value rule is as follows: defining an undirected graph
Figure FDA00025958057800000213
Wherein
Figure FDA00025958057800000214
Is a set of agents that are intelligent agents,
Figure FDA00025958057800000215
is a set of edges that are to be considered,
Figure FDA00025958057800000216
is a weighted adjacency matrix in which the weights w for the edges (i, j)ijThe following conditions are satisfied: if (i, j) ∈ then wij> 0, otherwise wij＝0，
Figure FDA00025958057800000217
Wherein d isiIs the number of neighbor agents for agent i.
6. A Newton momentum-based distributed acceleration composite optimization system is characterized by comprising an objective function establishing module and a plurality of intelligent agents which are connected into a non-directional communication network;
the objective function establishing module is used for establishing an objective function combining a smooth structure and a non-smooth structure according to the plurality of agents:
Figure FDA0002595805780000031
Figure FDA0002595805780000032
wherein the content of the first and second substances,
Figure FDA0002595805780000033
is a smooth local objective function known only to agent i,
Figure FDA0002595805780000034
is a non-smooth local function known only to agent i,
Figure FDA0002595805780000035
is the set of feasible solutions, m is the number of agents;
the intelligent agents are used for calculating local estimation values of the intelligent agents and sending the local estimation values to a first neighbor intelligent agent, the first neighbor intelligent agent is a neighbor intelligent agent corresponding to the intelligent agent, the neighbor intelligent agents are intelligent agents which directly communicate between the two intelligent agents, and the neighbor intelligent agents are neighbor intelligent agents;
the first neighbor agent is used for calculating momentum acceleration items according to the received local estimation values and sending the momentum acceleration items to a second neighbor agent, and the second neighbor agent is a neighbor agent of the first neighbor agent;
the second neighbor agent is used for calculating a gradient tracking item according to the momentum acceleration item and sending the gradient tracking item to a third neighbor agent, and the third neighbor agent is an agent of the second neighbor agent;
the plurality of agents are further configured to loop the local estimates, the momentum acceleration term, the gradient tracking term until a predetermined condition is met and terminate the loop.
7. The system of claim 6, wherein the local estimate is calculated by:
s201, each agent calculates local optimal solution of each agent
Figure FDA0002595805780000036
The calculation formula is as follows:
Figure FDA0002595805780000037
s202, calculating the local estimation value of the local optimal solution according to the local optimal solution
Figure FDA0002595805780000038
The calculation formula is as follows:
Figure FDA0002595805780000039
wherein the content of the first and second substances,
Figure FDA00025958057800000310
is that
Figure FDA00025958057800000311
In the form of a continuous convex approximation of (a),
Figure FDA00025958057800000312
Figure FDA00025958057800000313
is fiIn that
Figure FDA00025958057800000314
Is a positive constant step.
8. The system of claim 7, wherein the momentum acceleration term is calculated by:
s301, carrying out weighted average on the local estimation values to obtain local average estimation values
Figure FDA0002595805780000041
The calculation formula is as follows:
Figure FDA0002595805780000042
s302, estimating according to the local average
Figure FDA0002595805780000043
Calculating the momentum acceleration term according to the following calculation formula:
Figure FDA0002595805780000044
wherein, wijIs weight, w is more than or equal to 0ijIs < 1, and
Figure FDA0002595805780000045
beta is a momentum term parameter.
9. The system according to any one of claims 6 to 8, wherein the gradient tracking term is calculated by the following formula:
Figure FDA0002595805780000046
wherein the content of the first and second substances,
Figure FDA0002595805780000047
is a function fiGradient of (. cndot.).
10. The system of claim 9, wherein w isijThe value rule is as follows: defining an undirected graph
Figure FDA0002595805780000048
Wherein
Figure FDA0002595805780000049
Is a set of agents that are intelligent agents,
Figure FDA00025958057800000410
is a set of edges that are to be considered,
Figure FDA00025958057800000411
is a weighted adjacency matrix in which the weights w for the edges (i, j)ijThe following conditions are satisfied: if (i, j) ∈ then wij> 0, otherwise wij＝0，
Figure FDA00025958057800000412
Wherein d isiIs the number of neighbor agents for agent i.
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Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102393709A (en) * 2011-10-27 2012-03-28 上海交通大学 Optimization method of multi-agent synchronization problem
US20170337682A1 (en) * 2016-05-18 2017-11-23 Siemens Healthcare Gmbh Method and System for Image Registration Using an Intelligent Artificial Agent
US20180164835A1 (en) * 2016-09-27 2018-06-14 Arizona Board Of Regents On Behalf Of Arizona State University Systems and methods for dynamics, modeling, simulation and control of mid-flight coupling of quadrotors
AU2020100078A4 (en) * 2020-01-16 2020-02-13 Southwest University A Distributed Generalization and Acceleration Strategy for Convex Optimization Problem
CN110933056A (en) * 2019-11-21 2020-03-27 博智安全科技股份有限公司 Anti-attack multi-agent control system and method thereof
CN111259327A (en) * 2020-01-15 2020-06-09 桂林电子科技大学 Subgraph processing-based optimization method for consistency problem of multi-agent system
AU2020100842A4 (en) * 2020-05-26 2020-07-02 Southwest University An efficient and accelerated distributed algorithm for smart grids

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102393709A (en) * 2011-10-27 2012-03-28 上海交通大学 Optimization method of multi-agent synchronization problem
US20170337682A1 (en) * 2016-05-18 2017-11-23 Siemens Healthcare Gmbh Method and System for Image Registration Using an Intelligent Artificial Agent
US20180164835A1 (en) * 2016-09-27 2018-06-14 Arizona Board Of Regents On Behalf Of Arizona State University Systems and methods for dynamics, modeling, simulation and control of mid-flight coupling of quadrotors
CN110933056A (en) * 2019-11-21 2020-03-27 博智安全科技股份有限公司 Anti-attack multi-agent control system and method thereof
CN111259327A (en) * 2020-01-15 2020-06-09 桂林电子科技大学 Subgraph processing-based optimization method for consistency problem of multi-agent system
AU2020100078A4 (en) * 2020-01-16 2020-02-13 Southwest University A Distributed Generalization and Acceleration Strategy for Convex Optimization Problem
AU2020100842A4 (en) * 2020-05-26 2020-07-02 Southwest University An efficient and accelerated distributed algorithm for smart grids

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
ZHENG WANG,LIFENG ZHENG,HUAQING LI: ""Distributed Optimization over General Directed Networks with Rando Sleep Scheme"", 《INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS》 *
郑李逢: ""基于多智能体系统的快速分布式优化算法研究"", 《中国优秀硕士学位论文全文数据库信息科技辑》 *

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