Interesting stability criteria are developed by exploiting this characteristic. It is hoped that a study of this kind will aid in understanding some aspects of the mechanisms subserving human visual pattern recognition. A few examples are given to illustrate the method. A learning algorithm for the game based on a decentralized team of learning automata is presented. A class of model reference adaptive control system which make use of an augmented error signal has been introduced by Monopoli. No knowledge of the statistics of the pattern classes is assumed and the given classified sample may be noisy.
The only available information is the noise corrupted value of the objective function at any chosen point in the parameter space. This paper introduces a new model, i. Using weak convergence concepts it is shown that for large time and small values of parameters in the algorithm, the evolution of the action probability can be represented by Gauss-Markov diffusion. The reinforcement learning model is used to pose the goal of the system as a constrained optimization problem. Necessary and sufficient conditions on the functions in the reinforcement scheme are given for the expected payoff to be monotonically increasing in any arbitrary environment. An algorithm for updating the action probabilities of the automata, taking into account environmental reactions at all the levels, is proposed. Any allowable multiplier can be converted to the above form and this form leads to lesser restrictions on the parameters in many cases.
It considers synthesis of complex learning structures from simple building blocks and uses stochastic algorithms for refining probabilities of selecting actions. These schemes are compared with the already existing optimal linear schemes in the light of average variance and average rate of learning. The algorithm is analyzed to show that it converges weakly to global optimum of Kullback measure for that model. These interconnections of learning automata could be regarded as artificial neural networks. It turns out that the transfer function of the linear part shifted in argument has to satisfy the same conditions as for stability in order to ensure exponential boundedness. This is an improvement upon the earlier criteria presented by the authors in permitting an interchangeability of the allowable bounds on the logarithmic variation of the gain. A frequency-domain criterion for the asymptotic stability-in-the-large of systems containing many non-linearities is derived in terms of the positive realness of the product of a diagonal multiplier matrix and the transfer function matrix of the linear part.
This essentially results in a probabilistic search through the space of classifiers. A class of nonlinear learning algorithms for the Q-and S-model stochastic automaton-random environment setup are described. It is shown that, if updating is done in sufficiently small steps, the group will converge to the policy that maximizes the long-term expected reward per step. This transfer function dependent on the structure of the system with respect to the parameters. These are sufficient conditions for the system stability and involve conditions on the shifted imaginary-axis behavior of the multipliers. A new result on convergence in identical payoff games with a unique equilibrium point is also presented. It is shown that none of the existing algorithms can perform in the most general type of hierarchical problem.
The algorithm is approximated by the Langevin equation. Parallel algorithms are presented for modules of learning automata with the objective of improving their speed of convergence without compromising accuracy. By using Intermediate Rewards instead of Monte Carlo rewards, the hierarchical learning automata are shown both empirically and theoretically to have a faster and more accurate convergence by even using less information. A few computer-based methods by which this problem can be solved are indicated and it is shown that this constitutes a stop-by-step procedure for testing the stability properties of a given system. He is currently pursuing his Ph. Simulation results are presented to illustrate the effectiveness of these techniques based on learning automata.
The problem is that once you have gotten your nifty new product, the networks of learning automata thathachar m a l sastry p s gets a brief glance, maybe a once over, but it often tends to get discarded or lost with the original packaging. The modified algorithm is shown to exhibit local optimization properties. The automata update the probabilities according to whether the environment responds with a reward or a penalty. A particular case when the system matrices can be simultaneously transformed to normal matrices is shown to correspond to the existence of a common quadratic Lyapunov function. In this paper we continue this analysis but we assume here that our agents are fully ignorant about the other agents in the environment, i.
A learning algorithm is presented for the team and convergence is established. A sequence of increasingly complex empirical tests verifies the efficacy of this technique. When the number of actions is large the automaton becomes slow because there are too many updatings to be made at each instant. Multiaction learning automata which update their action probabilities on the basis of the responses they get from an environment are considered in this paper. The learning algorithm for the hierarchical system turns out to be a simple modification of the absolutely expedient algorithm known in the literature. It is also shown that under some additional constraints on the game, the team will always converge to a Nash equilibrium. The analysis reveals that the automaton tends to equalize the penalty probabilities.
In Chapter 3 we have seen how we can build much more powerful models by combining such teams of automata into networks. A cooperative game played in a sequential manner by a pair of learning automata is investigated in this paper. It is shown that the condition on the linear part of the system has to be stronger than the one given earlier. The automaton's environment, in turn, reads the action and sends the next input to the automaton. The automaton uses the feedback to update its action probability vector set. Mathematical analysis of the behavior of games and feedforward networks is provided. Learning Automata for Pattern Classification.
In Chapter 4 we have discussed at length one generic application area, namely, pattern classification. The algorithm selects the optimal threshold asymptotically with probability one. Simulation results on a pattern recognition problem show that reasonable rates of convergence can be obtained A model made of units of teams of learning automata is developed for the three layer pattern classifier. In episodic multi-stage learning problems agents were designed as tree-structured hierarchies of automata, mimicking the structure of the environment. The problem of learning correct decision rules to minimize the probability of misclassification is a long-standing problem of supervised learning in pattern recognition. Additionally, Tsetlin worked on reasonable and collective automata behaviour, and on automata games.