Watkins, C. J. C. H. and Dayan, P.: "Technical Note: Q-Learning," Machine Learning, Vol. 8, pp. 55--68, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....scheme estimates the reward accumulation which is called the value function. In order to make a good prediction, it is important to know the dynamics of the environment, i.e. how the current state changes by an action. Model free RL methods like the actor critic learning [3] and the Q learning [64] require no model of the environmental dynamics; instead, they try to directly estimate the value function. In contrast, model based RL methods [54, 34, 13, 15, 14, 32] try to model the environmental dynamics and the value function is approximated using the model. Especially when the environment ....

....problems, however, the state transition probability is unknown. Temporal difference (TD) learning [53] tries to approximate the value function based on the agent s experiences without directly modeling the environment; it is a model free approach. The actor critic learning [3] and the Q learning [64] are model free TD learning. TD learning makes use of the so called TD error: ffi = r(s; a) flV (s ) 0 V (s) 2) The second term is the value of state s based on the present prediction, while the first term is the value of state action pair (s; a) using one ply actual state transition to ....

Watkins, C.J.C.H., and Dayan, P. (1992). Technical note: Q-learning. Machine Learning, 8, 279-292.

....we take the simplest reinforcement learning method. The control policy is a mapping of re: Q A, from a state q Q, into an action a A, and an agent decides an action a t as a t = re(qt ) at time t. Table 1 shows an outline algorithm of reinforcement learning. Profit sharing [12] and Q learning [13] are wellknown reinforcement learning methods, which choose actions (line 4bi) and update policies (line 4c) in different ways. 1.3 Concept Learning Concept learning is to infer a Boolean value function from the training of examples of its input and output [9] The Boolean value function ....

C. J. C. H. Watkins and P. Dayan, "Technical Note: QLearning, " Machine Learning, 8:279-292, 1992.

....to be placed on the amount of links added. An other difference is that the number of possible system actions at each state is much higher than the number of states, since the system action is in fact the selection of a combination of possible next states. A model free RL approach like Q Learning [21] in which values are estimated for each state and action combination can become infeasible because the number of actions is so high. 5 THE EXPLORATION EXPLOITATION DILEMMA One important aspect of RL is exploration. In order to accurately estimate the value of states to be able to improve the ....

C.J.C.H. Watkins and P. Dayan. Technical note: Q learning. Machine Learning, 8:279592, 1992.

....of gradient based methods is given in Werbos [29] Sofge White [30] have successfully applied a gradient method to optimizing a manufacturing process. 3.5. 3 Q Learning This method was first introduced by Watkins [27] For a more detailed discussion of Q learning see also Watkins Dayan [28]. In Q Learning unlike the adaptive critic approach we learn only one function. This function is called Q, or action value function. For a given state and action the optimal Q function gives the estimated future cost when that action is performed and the same policy is used in the future. Using ....

C.J.C.H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8:279 292, 1992.

....of control tasks with general action spaces. Furthermore, convergence to the optimal policy has been shown for this algorithm under a set of restricted circumstances, requiring that the problem is purely Markovian and that the value function is represented in the form of a state action table [113]. In addition, convergence in stochastic domains requires that each state action pair is updated in nitely often, illustrating the importance of exploration in this framework in order to acquire good control policies. 75 A number of control systems employing reinforcement learning techniques ....

Watkins, C.J., and Dayan, P. Technical note: Q-learning. Machine Learning 8 (1992), 279-292.

....r t (x t , u t , X t 1 ) #r t 1 # . where probabilistic variables are capitalised; and # is the discount factor, between 0 and 1, that makes rewards that are earned later exponentially less valuable. The action values are updated through the one step Q update equation [10]: x t , u t ) # r (x t , u t , x t 1 ) # max (x t 1 , u t 1 ) where # is a learning rate (or step size) between 0 and 1, that controls convergence. Accurate pursuit of a moving target requires continuously variable actuator commands, and the ability to respond to smooth changes in ....

C. J. C. H. Watkins and P. Dayan, "Technical note: Q learning," Machine Learning, vol. 8(3/4):pp. 279--292, 1992.

....are still in flux. Nevertheless, the overall trend in the policies is clear. The graphs in Figures 8 and 9 show the performance of the algorithms over time, and Table 1 summarises the policies developed by the learning algorithms. 4. 1 is an algorithm for solving reinforcement learning tasks [11]. stores the expected value, x, u) of performing each action in each state, assuming that the actions with the highest expected values will be performed thereafter. The action values are updated according to: r (x t , u t , x t 1 ) # max (x t 1 , u t 1 ) 1) where # is the ....

C. J. C. H. Watkins and P. Dayan, "Technical note: Q learning," Machine Learning, vol. 8(3/4):pp. 279--292, 1992.

....extensively employed for signal analog to digital conversion and compression, which have common characteristics to MDP problems. We have applied this technique for compacting the set of states that an agent perceives, thus dramatically reducing the reinforcement table size. We have used Q learning [18] as the reinforcement learning technique, though we believe this can be made extensible to any other technique relying on a state action table. In this paper, we have used the combination of vector quantization and reinforcement learning for acquiring the ball interception skill for agents playing ....

....2 Reinforcement Learning The main objective of reinforcement learning is to automatically acquire knowledge to better decide what action an agent should perform at any moment to optimally achieve a goal. Among many di erent reinforcement learning techniques, Q learning has been very widely used [18]. The Q learning algorithm for deterministic Markov decision processes is described in table 1. It needs a de nition of the possible states, S, the actions that the agent can perform in the environment, A, and the rewards that it receives at any moment for the states it arrives to after applying ....

C. J. C. H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8(3/4):279-292, May 1992.

....targets. Instead, incidental positive (reward) or negative (punishment) reinforcement signals constitute the teaching signal. The network must be trained to maximize the sum of the reinforcements for a complete sequence of actions. An appropriate reinforcement learning method is Q learning [8]. Q learning is a method for learning state action values. A state action value, or Q value, is the maximum expected sum of reinforcements that can be obtained from a given state when performing the associated action. For neural networks this means that for each possible action, the network has ....

....of the optimal Qvalue (which is unknown) Although the targets calculated by formula (2) give reasonable results, convergence is usually quite slow. The reason is that long chains of actions delay learning from distant rein forcement signals. To overcome this problem Q( learning [4] 6] [8] can be used. The target function for Q( learning can be defined recursively as . 8 66120 2 2 99 99 7 A # B4 ( 6 140 2 9 7 6 A # . 6 0 140 2 (3) in which is a weighting factor between 0 and 1 that determines the ....

C.J.C.H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8:279-292, 1992.

....few samples, so the average of them will be highly influenced by the current sample. When we are in a well visited area of state space, the learning rate is low. We have taken lots of samples, so the single current sample can t make much difference to the average of all of them (the Q value) [Watkins and Dayan, 1992] proved that the discrete case of Q learning will converge to an optimal policy under the following conditions. The learning rate c, where 0 c l, should take decreasing (with each update) successive values o1, o2, o3. such that oo 2 4:1 oq = oo and i 1 oq oo. The typical scheme ....

....each update) successive values o1, o2, o3. such that oo 2 4:1 oq = oo and i 1 oq oo. The typical scheme (and the one used in this work) is, where n(x, a) 1, 2, 3, is the number of times Q(x, a) has been visited: If each pair (x, a) is visited an infinite number of times, then [Watkins and Dayan, 1992] shows that for lookup tables Q learning converges to a unique set of values Q(x,a) Q (x,a) which define a stationary de terministic optimal policy. Q learning is asynchronous and sampled each Q(x, a) is updated one at a time, and the control policy may visit them in any order, so long as it ....

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Watkins, Christopher J.C.H. and Dayan, Peter (1992), Tech- nical Note: Q-Learning, Machine Learning 8:279-292.

....of gradient based methods is given in Werbos [29] Sofge White [30] have successfully applied a gradient method to optimizing a manufacturing process. 3.5. 3 Q Learning This method was first introduced by Watkins [27] For a more detailed discussion of Q learning see also Watkins : Dayan [28]. In Q Learning unlike the adaptive critic approach we learn only one function. This function is called Q, or action value function. For a given state and action the optimal Q function gives the estimated future cost when that action is performed and the same policy is used in the future. Using ....

C.J.C.H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8:279-292, 1992.

....of the robot through its real sensors. As a learning algorithm, Q learning is often utilized since it dose not require any domain knowledge. Mahadevan and Cornel [6] have demonstrated that a robot can obtain its programs for finding a box, push ing it, unwedging in a real world by Q learning [10]. The important point of their work is how to reduce the huge size of the state space represented with discrete sensor inputs. They have proposed a method to reduce the size based on similarities between states. Nakamura and Asada [2] have recently proposed a method using a motion sketch which ....

C.H. Watkins and P. Dayan, Technical note: Q- learning, Machine Learning 82, pp. 39-46, 1992.

....robots. Size reduction with similarities between states A more autonomous method have been proposed by Mahadevan and others [3] in advance of Nakamura s work. They demonstrated that a robot can obtain its programs for finding a box, pushing it, and unwedging in a simple environment by Q learning [8]. One of the important points of their work is in the size reduction of the state space represented with the discrete sensor inputs. They proposed a method to reduce the size based on similarities between states themselves and propagated rewards by the Q learning. Autonomous state space ....

C.H. Watkins and P. Dayan, Technical note: Q-learning, Machine Learning 82, pp. 39-46, 1992.

....to look for the best out of a set of similar EOs to be employed in that context. The task on this level can therefore be stated as Given: A context C requiring the execution of an EO of a specific class. Determine: The EO e that maximizes a given evaluation criterion related to C. Q Learning [80, 81] is an appropriate technique for solving this learning task. If r denotes the feedback obtained after the execution of the EO e in the context C, the value Q that estimates r a priori can be updated through Q(C, e) t = 1 a)Q(C, e) t at, where c is the learning rate. It should be noted that ....

C. J. C. H. Watkins. A technical note on Q-Learning. Machine Learning, 8, 1992.

.... strategy for learning, such as SteppingStone [17] that learns cases for achieving good solutions, EvoCK [1] that uses genetic programming to improve hamlet output, or reinforcement learning systems that acquire numerical information about the expected values of applying actions to states [20]. Another related work is the one on reinforcement learning, since they also try to acquire an optimal policy for achieving the goals [20] However, reinforcement handles planning in a di erent way, since usually there is no explicit declarative representation of operators. Learning relates to ....

.... to improve hamlet output, or reinforcement learning systems that acquire numerical information about the expected values of applying actions to states [20] Another related work is the one on reinforcement learning, since they also try to acquire an optimal policy for achieving the goals [20]. However, reinforcement handles planning in a di erent way, since usually there is no explicit declarative representation of operators. Learning relates to modifying numerical quantities associated to expected values of applying actions to states. There has also been some work on planning using ....

C. J. C. H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8(3/4):279-292, May 1992.

....of the robot through its real sensors. As a learning algorithm, Q learning is often utilized since it dose not require any domain knowledge. Mahadevan and Cornel [6] have demonstrated that a robot can obtain its programs for finding a box, push ing it, unwedging in a real world by Q learning [10]. The important point of their work is how to reduce the huge size of the state space represented with discrete sensor inputs. They have proposed a method to reduce the size based on similarities between states. Nakamura and Asada [2] have recently proposed a method using a motion sketch which ....

C.H. Watkins and P. Dayan, Technical note: Q- learning, Machine Learning 82, pp. 39-46, 1992.

....well enough, the action with the highest probability of bringing the system in the preferred next state can be selected as control action. A system model is required for this. Because such a model is not always available, model free RL techniques were developed. Q Learning is model free RL [18] [19]. In Q learning the sum of future reinforcements is approx imated as a function of the state and the action. This function is called the Q function and it has a value for each state and action combination. The function can be implemented in a lookup table, such that the optimal action can be ....

....correctly then the greedy policy will be an improvement compared to the policy used to generate the data. The policy can be further improved by repeating the whole process of approximating the Q function for the greedy policy and deriving the new greedy policy. It has been be proven [18] [19] that this will eventually converge to the optimal policy. 1Note that we use the same notation for discrete and continuous state action spaces. In case of a discrete state action spaces often the symbols s, a and axe used for the state, action and policy. 2Note that this is the policy iteration ....

C.J.C.H. Watkins and P. Dayan, "Technical note: Q learning," Machine Learning, 1992.

....(average points) for each cluster just created. The new codebook, Cm 1 will be composed of those centroids. Iterating these two steps several times, a new codebook that minimizes the average distortion of quantifying the vectors of T is obtained. 3 VQQL Model The VQQL model uses Q Learning [2] as a reinforcement learning technique and the vector quantization as a generalization technique in continuous domains. The use of both techniques requires two consecutive phases: Learning the quantizer, designing the N levels vector quantizer from the input data obtained from the environment, ....

C. J. C. H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8(3/4):279-292, May 1992.

....evaluations, that can be seen as punishments or rewards. The policy or feedback is the function that maps the state of the system to control actions. By estimating the sum of future reinforcements, the policy can be improved. For systems with a discrete state and action space, Q Learning [13][14] can be applied. For each state and action combination the estimated sum of future reinforcements is stored in a look up table. The estimations are based on data generated by controlling the system using some initial policy. The look up table can be used to select for each state the best action, ....

C.J.C.H. Watkins and P. Dayan. Technical note: Q learning. Machine Learning, 1992.

....(9) Although it is possible to nd exact solutions to equations 5, 7, 8 and 9 using methods from the eld of dynamic programming (e.g. value iteration [7] these require that a model of the environment (r a s and p a ss 0 ) is known in advance. Alternatively, the algorithm, 1 step Q learning [14], uses a modi ed form of temporal di erence learning [12] to learn the Q function for the optimal policy using only observations gained from experience. After making a transition from state s to s 0 using action a, the following update is made: Q(s; a) Q(s; a) target return estimate z ....

....2 2 Q(s , a ) 10 2 k Figure 1: A simple process in which optimistic initial Q values slows learning. are observed (i.e. after each action) In e ect, Q learning is performing a stochastic form of dynamic programming. Convergence proofs for Q learning rely upon establishing this relationship [14, 4]. The purpose of learning these estimates of return is to transform the initial problem of learning an optimal policy, into the trivial one of simply deciding which action leads to the highest expected return: s) arg max a Q(s; a) 11) Finally we note that RL methods may be ....

Christopher Watkins and P. Dayan. Technical note: Q-Learning. Machine Learning, 8:279-292, 1992.

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Watkins, C. J. C. H. and Dayan, P.: "Technical Note: Q-Learning," Machine Learning, Vol. 8, pp. 55--68, 1992.

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C. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8(3-4):279--292, 1992.

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C. J. Watkins, P. Dayan, Technical note Q-learning, Machine Learning 8 (1992) 279.

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C. J. C. H. Watkins, , and P. Dayan". "Technical note: Q-learning". PhD thesis, 1992.

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Watkins, C.J.C.H., Dayan, P.D.: Technical note: Q-learning. Machine Learning 8 (1992) 279--292

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C. J. C. H. Watkins and P. D. Dayan. Technical note: Qlearning. Machine Learning, 8(3):279--292, 1992.

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C. J. C. H. Watkins and P. D. Dayan. Technical note: Qlearning. Machine Learning, 8(3):279--292, 1992.

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C. J. C. H. Watkins and P. Dayan. Technical note: Q- learning. Machine Learning, 8:279--292, 1992.

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C. J. C. H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8(3):279--292, 1992.

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C. J. Watkins and P. Dayan, "Technical note: Q-Learning," Machine Learning, vol. 8, no. 3, pp. 279--292, 1992.

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C. J. C. H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8(3/4):279--292, May 1992.

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C.J.C.H. Watkins and P. Dayan. Technical note: Q-learning. Machin Learning, 8:39--46, 1992. 14

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C. J. C. H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8(3/4):279--292, May 1992.

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C. Watkins and P. Dayan. Technical note: Q learning. Machine Learning, 8:279--292, 1992.

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C. J. C. H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8(3/4):279-292, May 1992.

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C. J. C. H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8(3/4):279-292, May 1992.

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C.J.C.H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8(3/4):279-292, 1992.

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C. J. C. H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8(3/4), May 1992.

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C. J. C. H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8:279--292, 1992.

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C. J. C. H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8(3/4), May 1992.

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C. J. C. H. Watkins, P. Dayan (1992) Technical note: Q-learning. Machine Learning 8, 279-292. E-mail: der@informatik.uni-leipzig.de, michael@zoo.riken.go.jp, mherrma@gwdg.de New address of MH: MPI SF, Postfach 2853, 37018 Gottingen, Germany

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C. J. C. H. Watkins, , and P. Dayan". "Technical note: Q-learning". PhD thesis, 1992.

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C. J. C. H. Watkins and P. Dayan. Technical note: Q- learning. Machine Learning, 8:279--292, 1992.

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C.J.C.H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8:279--292, 1992.

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WATKINS, C.J. & DAYAN, P. "Technical note : Q-learning." Machine Learning. Vol. 8(3-4), pp. 279-292. 1992.

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C. J. C. H. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8:279--292, 1992. 20

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C. J. C. H. Watkins and P. Dayan. Technical note: Q- learning. Machine Learning, 8:279-292, 1992.

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C. Watkins and P. Dayan. Technical note: Q-learning. Machine Learning, 8(3-4):279--292, 1992.

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C.J.C.H. Watkins and P. Dayan. Technical note: Q-Learning. Machine Learning, 8:279-292, 1992.

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