EP1116172A2 - Procede et systeme pour determiner une suite d'actions pour un systeme presentant des etats et selon lequel le passage d'un etat a l'autre intervient suite a une action - Google Patents

Procede et systeme pour determiner une suite d'actions pour un systeme presentant des etats et selon lequel le passage d'un etat a l'autre intervient suite a une action

Info

Publication number
EP1116172A2
EP1116172A2 EP99953714A EP99953714A EP1116172A2 EP 1116172 A2 EP1116172 A2 EP 1116172A2 EP 99953714 A EP99953714 A EP 99953714A EP 99953714 A EP99953714 A EP 99953714A EP 1116172 A2 EP1116172 A2 EP 1116172A2
Authority
EP
European Patent Office
Prior art keywords
sequence
state
action
actions
states
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP99953714A
Other languages
German (de)
English (en)
Inventor
Ralf Neuneier
Oliver Mihatsch
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Siemens AG
Siemens Corp
Original Assignee
Siemens AG
Siemens Corp
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Siemens AG, Siemens Corp filed Critical Siemens AG
Publication of EP1116172A2 publication Critical patent/EP1116172A2/fr
Withdrawn legal-status Critical Current

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Classifications

    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management

Definitions

  • the invention relates to a method and an arrangement for determining a sequence of actions for a system which has states, a state transition between two states taking place as a result of an action.
  • Markov decision problem MDP
  • MDP Markov decision problem
  • the system 201 is in a state x ⁇ .
  • the state x ⁇ can be observed by an observer of the system.
  • the system Based on an action a - j - from a set of possible actions in the state Xt, a ⁇ e A (x ⁇ ), the system goes with a certain probability into a subsequent state xt + i at a subsequent time t + 1.
  • An observer 200 takes observable quantities about the state x - (- true 202 and makes a decision about an action 203 with which he acts on the system 201.
  • the system 201 is usually subject to a fault 205.
  • the profit r- ⁇ can assume a positive or negative scalar value, depending on whether the decision leads to a system development which is positive or negative with regard to a predefinable criterion, in [1] to an increase in capital or to a loss.
  • the observer 200 of the system 201 decides on a new action a - ⁇ + i etc. based on the observable variables 202, 204 of the subsequent state xt + i.
  • future states of system 201 do not depend on states and actions that are further than a time step in the past.
  • the goal is to determine a strategy based on observable variables, the variables referred to hereinafter as training data, i.e. a series of functions
  • Such a strategy is evaluated by an optimization function.
  • the optimization function specifies the expected value of the gains accumulated over time for a given strategy ⁇ and a starting state xn.
  • V (x) max V ⁇ (x) Vx e X (5) ⁇
  • V ⁇ (x) ⁇ t * x t + l)
  • 0 x (6)
  • ⁇ denotes a predefinable reduction factor, which is formed in accordance with the following regulation:
  • a Q evaluation function Q (xt, at) is formed for each pair (state xt, action at) in accordance with the following rule:
  • the so-called Q values Q * (x, a) are approximated for different actions a by a function approximator, for example a neural network or also a polynomial classifier, with a weight vector w which contains the weights of the function approximator.
  • a function approximator for example a neural network or also a polynomial classifier
  • a function approximator is understood to mean, for example, a neural network, a polynomial classifier or also a combination of a neural network with a polynomial classifier.
  • the neural network which represents the financial market system as described in [1], is trained using the training data, which describe information about previous price developments of a financial market as time series values.
  • TD ( ⁇ ) learning method Another approximate dynamic programming method, the so-called TD ( ⁇ ) learning method, is known from [2] and is explained in more detail in connection with an exemplary embodiment.
  • the extended Q function Q ⁇ (xt, t) describes the worst case if the action at is carried out in the state xt and the strategy ⁇ is then followed.
  • the invention is therefore based on the problem of specifying a method and an arrangement for determining a sequence of actions for a system in which or in which an increased flexibility in determining the strategy is achieved.
  • the sequence of actions is determined in such a way that a sequence of states resulting from the sequence of actions takes place a given optimization function is optimized, the optimization function contains a variable parameter with which a risk which has the resulting sequence of states with respect to a predetermined state of the system can be set.
  • An arrangement for determining a sequence of actions for a system which has states, a state transition between two states taking place as a result of an action has a processor which is set up in such a way that the sequence of actions can be determined in such a way that a a sequence of states resulting from the sequence of actions is optimized with regard to a predetermined optimization function, the optimization function containing a variable parameter with which a risk which the resulting sequence of states has with respect to a predetermined state of the system can be set.
  • the invention makes it possible for the first time to specify a method for determining a sequence of actions with freely definable accuracy as part of a strategy for a possible regulation or control, in general influencing the system.
  • a method of approximate dynamic programming is used for the determination, for example a method based on Q learning or also a method based on TD ( ⁇ ) learning.
  • the OFQ optimization function is preferably formed in accordance with the following regulation:
  • the following adaptation step is carried out to determine the optimal weight w of the function approximator:
  • the optimization function is preferably formed in accordance with the following regulation:
  • A an action from an action area A
  • the system is preferably a technical system, from which measured variables are measured before the determination, which are used in determining the sequence of actions.
  • the technical system can be controlled or regulated using the determined sequence of actions.
  • the system is preferably modeled as a Markov decision problem.
  • the method or the arrangement are preferably used in a traffic control system or in a communication system, the sequence of actions for carrying out access control or routing, that is to say path assignment, being used in a communication network in the communication system.
  • the system can be a financial market which is modeled by a Markov decision problem and where the course of the financial market, for example a course of a Stock index or a price trend of a foreign exchange market can be analyzed using the methods or the arrangement and can be intervened in the market in accordance with the sequence of determined actions.
  • the course of the financial market for example a course of a Stock index or a price trend of a foreign exchange market can be analyzed using the methods or the arrangement and can be intervened in the market in accordance with the sequence of determined actions.
  • Figure 1 is a flowchart showing individual process steps of the first embodiment
  • FIG. 2 shows a sketch of a system which can be modeled as a Markov decision problem
  • FIG. 3 shows a sketch of a communication network in which access control is carried out in a switching unit
  • FIG. 4 shows a symbolic sketch of a function approximator with which a method of approximate dynamic programming is implemented
  • FIG. 5 shows a further sketch of a number of function approximators, with which an approximate dynamic programming is implemented
  • Figure 6 is a sketch of a traffic control system, which is controlled according to an embodiment.
  • First embodiment access control and routing.
  • FIG. 3 shows a communication network 300 which has a multiplicity of switching units 301a, 301b, ..., 301i, ... 301n which are connected to one another via connections 302a, 302b, 302j, ... 302m.
  • a first terminal 303 is connected to a first switching unit 301a.
  • a request message 304 is sent from the first terminal 303 to the first switching unit 301a, with which a reservation of a predetermined bandwidth within the communication network 300 for the transmission of data (video data, textual data) is requested.
  • a strategy described below is used to determine whether the requested bandwidth is available in the communication network 300 on a specified, requested connection (step 305).
  • the request is rejected (step 306).
  • a further check step (step 307) checks whether the bandwidth can be reserved.
  • the request is rejected (step 308).
  • the first switching unit 301a selects a route from the first switching unit 301a via further switching units 301i to a second terminal 309 with which the first terminal 303 wants to communicate, and a connection is initialized (step 310).
  • a communication network 300 is assumed which comprises a set of switching units
  • N ⁇ l, K, n, K, N ⁇ (17) and a set of physical connections
  • a physical connection 1 has a capacity of B (l) bandwidth units.
  • the profit c (m) is given by the amount of money that a network operator of the communication network 300 charges a subscriber for a connection of the service type.
  • the profit c (m) clearly reflects different priorities which can be specified by the network operator and which he associates with different services.
  • a physical connection 1 can simultaneously provide any combination of communication connections as long as the bandwidth used for the communication connections does not exceed the total available bandwidth of the physical connection. If a new communication connection of type m is requested between a first node i and a second node j (terminals are also referred to as nodes), the requested communication connection can, as shown above, either be accepted or rejected.
  • a route is selected from a set of predefined routes. This selection is called routing.
  • b (m) bandwidth units are used for each physical connection along the selected route for the connection duration.
  • a route within the communication network 300 can therefore only be selected as part of the access control (call admission control) if the selected route has sufficient bandwidth available.
  • the goal of access control and routing is to maximize long-term gain that is obtained by accepting the requested connections.
  • the technical system communication network 300 is in a state xt at a point in time t, which is described by a list of routes via existing connections, by means of which lists it is shown how many connections and which service type use the respective route at the point in time t.
  • Events w through which a state xt could be converted into a subsequent state xt + i, are the arrival of new connection request messages or the termination of a connection existing in the communication network 300.
  • an action at at a time t based on a connection request is the a decision as to whether to accept or reject a connection request and, if the connection is accepted, to select the route through the communications network 300.
  • the aim is to determine a sequence of actions, i.e. vividly determining the learning of a strategy with actions for a state x in such a way that the following rule is maximized:
  • the goal is to maximize the expected value of total profit G according to the following regulation J:
  • a risk that the total profit G of a special implementation of an access control and a routing strategy falls below the expected value can be set.
  • the TD ( ⁇ ) learning method is used to perform access control and routing.
  • An approximated value of the target value J * (xt) is learned and stored using a function approximator 400 (see FIG. 4) using training data.
  • Training data are previously measured data in the communication network 300 about the behavior of the communication network 300 when incoming connection requests 304 and when messages are terminated. This chronological sequence of states is stored and the functional approximator 400 is trained using this training data in accordance with the learning method described below.
  • a number of connections each of a service type m on a route of the communication network 300 are used as the input variable of the function approximator 400 for each input 401, 402, 403 of the function approximator 400. These are represented symbolically in FIG. 4 by blocks 404, 405, 406.
  • the output variable of the function approximator 400 is an approximated target value J of the target value J.
  • An output variable is the approximated target value J, which is formed in accordance with the following regulation:
  • the input variables of the subfunction approximators 510, 520 which are present at inputs 511, 512, 513 of the first subfunction approximator 510 or at inputs 521, 522 and 523 of the second subfunction approximator 520, are each a number of service types of a type m in each case in a physical connection r, symbolized by blocks 514, 515, 516 for the first partial function approximator and 524, 525 and 526 for the second partial function approximator 520.
  • Partial output variables 530, 531, 532, 533 are supplied to an adding unit 540 and the approximated target variable J is formed as the output variable of the adding unit.
  • Service type m of class m for a connection between two Node i, j is requested arrives at the first connection unit 301a.
  • R (i, j) a list of permitted routes between the nodes i and j is designated and with
  • a list of all possible routes is referred to as a subset of the routes R (i, j) that could implement a possible connection with regard to the available and requested bandwidth.
  • a subsequent state xt k + l ( x t ⁇ ⁇ r ' ⁇ k' r ) is determined, which results from the connection request 304 being accepted and the connection being opened the route r is made available to the requesting first terminal 303.
  • step 102 This is shown in FIG. 1 as a second step (step 102), the state of the system and the respective event being ascertained in a first step (step 101).
  • a route r * to be selected is determined in accordance with the following rule:
  • step 1014 it is checked whether the following requirement is met:
  • connection request 304 is rejected (step 105), otherwise the connection is accepted and "switched through” to the node j along the selected route r * (step 106).
  • weights of the functional approximators 400, 500 are stored for a time t, which are adapted to the training data as part of the TD ( ⁇ ) learning method, so that an optimized access control and an optimized routing is achieved.
  • the weight parameters are adapted to the training data created in the function approximator.
  • a risk parameter K is defined, by means of which a desired risk, which is due to a sequence of actions and states with regard to a predetermined state of the system, can be set, in accordance with the following regulations:
  • a specifiable parameter 0 ⁇ ⁇ 1 and a step size sequence ⁇ k are specified as part of the learning process.
  • the weight values of the weight vector ⁇ are adapted to the training data based on each event ⁇ t k in accordance with the following adaptation rule:
  • d k e ßO tk - 1 ) (g (x tk , ⁇ k , a t] ) + j (x tk . ®kl)) " 5 ( x t k _ ⁇ kl)
  • FIG. 6 shows a street 600 which is used by cars 601, 602, 603, 604, 605 and 606.
  • Conductor loops 610, 611 integrated in the street 600 receive electrical signals in a known manner and feed the electrical signals 615, 616 to a computer 620 via an input / output interface 621.
  • the electrical signals are digitized in a time series and in a memory 623, which is connected via a bus
  • a traffic control system 650 is supplied with control signals 651, from which a predefined speed setting 652 can be set in the traffic control system 650 or also further information from traffic regulations which is transmitted to the drivers 601, 602, 603, 604, via the traffic control system 650. 605 and 606 are shown.
  • the local state variables are measured as described above using the conductor loops 610, 611. These variables (v (t), p (t), q (t)) thus represent a state of the technical system "traffic" at a specific time t.
  • the system is thus a traffic system which is regulated using the traffic control system 650.
  • an extended Q learning method is described as a method of approximate dynamic programming.
  • the state xt is described by a state vector
  • the gain r (xt, at, xt + l) describes the quality of the traffic flow that was measured by the conductor loops 610 and 611 between the times t and t + 1.
  • r denotes (xt, at, xt + l)
  • a value of the optimization function OFQ is determined, with an estimated value of the optimization function OFQ being implemented as a neural network.
  • the adaptation rule known from the Q learning method for calculating the optimization function OFQ is expanded according to this exemplary embodiment by a risk control function K Q, which takes the risk into account.
  • the risk control parameter K is specified according to the strategy from the first exemplary embodiment in the interval of [-1 ⁇ K ⁇ 1] and represents the risk that a user wants to take in the context of the application with regard to the control strategy to be determined.
  • A a speed limit from the action space A of all speed limits that can be displayed by the traffic control system 650,
  • the following adaptation step is carried out to determine the optimum weights w of the neural network:
  • an action at can be chosen at random from the possible actions at. It is not necessary to choose the action at which has led to the largest assessment variable.
  • the weights have to be adapted in such a way that not only is a regulation of the traffic optimized in the expected value of the optimization function is achieved, but also a variance of the regulation results is taken into account.
  • a regulation phase on the real system according to the traffic control system takes place according to the following steps:
  • a value of the optimization function is determined for all possible actions at and the action at with the highest rating is selected in the optimization function.

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Abstract

L'invention concerne un procédé selon lequel pour déterminer une suite d'actions, on optimise une suite d'états résultant de la suite d'actions quant à une fonction d'optimisation prédéfinie. Cette fonction d'optimisation comprend un paramètre variable qui permet d'ajuster un risque qui présente la suite d'états obtenue quant à un état prédéfini du système.
EP99953714A 1998-09-23 1999-09-08 Procede et systeme pour determiner une suite d'actions pour un systeme presentant des etats et selon lequel le passage d'un etat a l'autre intervient suite a une action Withdrawn EP1116172A2 (fr)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
DE19843620 1998-09-23
DE19843620 1998-09-23
PCT/DE1999/002846 WO2000017811A2 (fr) 1998-09-23 1999-09-08 Procede et systeme pour determiner une suite d'actions pour un systeme presentant des etats et selon lequel le passage d'un etat a l'autre intervient suite a une action

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EP1116172A2 true EP1116172A2 (fr) 2001-07-18

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US (1) US7047224B1 (fr)
EP (1) EP1116172A2 (fr)
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US7363378B2 (en) * 2003-07-01 2008-04-22 Microsoft Corporation Transport system for instant messaging
US7930564B2 (en) * 2006-07-31 2011-04-19 Intel Corporation System and method for controlling processor low power states
DE102008007700A1 (de) * 2007-10-31 2009-05-07 Siemens Aktiengesellschaft Verfahren zur rechnergestützten Exploration von Zuständen eines technischen Systems
GB201009974D0 (en) 2010-06-15 2010-07-21 Trinity College Dublin Decentralised autonomic system and method for use inan urban traffic control environment
DE102011075337A1 (de) * 2011-05-05 2012-11-08 Siemens Ag Verfahren und Vorrichtung zur Ansteuerung einer Anlage
US8615962B1 (en) * 2013-01-14 2013-12-31 GM Global Technology Operations LLC Retention feature for automotive deco trim
CN103217899B (zh) * 2013-01-30 2016-05-18 中国科学院自动化研究所 基于数据的q函数自适应动态规划方法
WO2014148564A1 (fr) * 2013-03-19 2014-09-25 株式会社イシダ Système de pesage quantitatif et procédé de pesage quantitatif
US9679258B2 (en) * 2013-10-08 2017-06-13 Google Inc. Methods and apparatus for reinforcement learning
US10871585B2 (en) * 2016-08-03 2020-12-22 Harris Corporation System for processing seismic data based upon linear optimization and related methods
CN109870992B (zh) * 2019-03-26 2021-09-07 合肥工业大学 一种不考虑延时等待的csps系统控制方法
CN110758382B (zh) * 2019-10-21 2021-04-20 南京航空航天大学 一种基于驾驶意图的周围车辆运动状态预测系统及方法
US20220108412A1 (en) * 2020-10-07 2022-04-07 Nec Corporation Adaptive autonomous negotiation method and system of using
US12265592B2 (en) * 2021-12-09 2025-04-01 International Business Machines Corporation Model aggregation for fitted Q-evaluation

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EP0565992A2 (fr) * 1992-04-13 1993-10-20 Pietzsch Aktiengesellschaft Procédé et système pour surveiller le trafic et informer les usagers de la voie publique
DE4441356A1 (de) * 1993-11-24 1995-06-01 Siemens Ag Oesterreich Verfahren und Anordnung zum Routen von Verbindungen in einem vermittelnden Kommunikationsnetz

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WO2007036003A1 (fr) * 2005-09-30 2007-04-05 University Of South Australia Apprentissage par renforcement pour attribution de ressources dans un systeme de telecommunications

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US7047224B1 (en) 2006-05-16
WO2000017811A3 (fr) 2000-12-07
JP2002525763A (ja) 2002-08-13

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