A multi-step finite-state automaton for arbitrarily deterministic Tsetlin Machine learning

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Stochastic automata and learning systems

We consider stochastic automata models of learning systems in this article. Such learning automata select the best action out of a finite number of actions by repeated interaction with the unknown random environment in which they operate. The selection of an action at each instant is done on the basis of a probability distribution which is updated according to a learning algorithm. Convergence theorems for the learning algorithms are available. Moreover the automata can be arranged in the form of teams and hierarchies to handle complex learning problems such as pattern recognition. These interconnections of learning automata could be regarded as artificial neural networks

Stability of systems with power-law non-linearities

It is shown that a sufficient condition for the asymptotic stability-in-the-large of an autonomous system containing a linear part with transfer function G(jω) and a non-linearity belonging to a class of power-law non-linearities with slope restriction [0, K] in cascade in a negative feedback loop is ReZ(jω)[G(jω) + 1 K] ≥ 0 for all ω where the multiplier is given by, Z(jω) = 1 + αjω + Y(jω) - Y(-jω) with a real, y(t) = 0 for t < 0 and ∫ 0 ∞ |y(t)|dt < 1 2c2, c2 being a constant associated with the class of non-linearity. Any allowable multiplier can be converted to the above form and this form leads to lesser restrictions on the parameters in many cases. Criteria for the case of odd monotonic non-linearities and of linear gains are obtained as limiting cases of the criterion developed. A striking feature of the present result is that in the linear case it reduces to the necessary and sufficient conditions corresponding to the Nyquist criterion. An inequality of the type |R(T) - R(- T)| ≤ 2c2R(0) where R(T) is the input-output cross-correlation function of the non-linearity, is used in deriving the results

Improved Conditions for the L2L_2-Stability of Nonstationary Feedback Systems

Concerning the $L_2$-stability of feedback systems containing a linear time-varying operator, some of the stringent restrictions imposed on the multiplier as well as the linear part of the system, in the criteria presented earlier, are relaxed

Learning the global maximum with parameterized learning automata

A feedforward network composed of units of teams of parameterized learning automata is considered as a model of a reinforcement teaming system. The internal state vector of each learning automaton is updated using an algorithm consisting of a gradient following term and a random perturbation term. It is shown that the algorithm weakly converges to a solution of the Langevin equation implying that the algorithm globally maximizes an appropriate function. The algorithm is decentralized, and the units do not have any information exchange during updating. Simulation results on common payoff games and pattern recognition problems show that reasonable rates of convergence can be obtained

Time-Varying System Stability-Interchangeability of the Bounds on the Logarithmic Variation of Gain

A frequency-domain criterion for the $L_2$-stability of systems containing a single time-varying gain in an otherwise time-invariant linear feedback loop is given. 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

Time-Domain Criteria For L2-Stability Of Nonstationary Feedback-Systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers