# Multi-Agent Machine Learning: A Reinforcement Approach

Language: English

Pages: 256

ISBN: 111836208X

Format: PDF / Kindle (mobi) / ePub

The book begins with a chapter on traditional methods of supervised learning, covering recursive least squares learning, mean square error methods, and stochastic approximation. Chapter 2 covers single agent reinforcement learning. Topics include learning value functions, Markov games, and TD learning with eligibility traces. Chapter 3 discusses two player games including two player matrix games with both pure and mixed strategies. Numerous algorithms and examples are presented. Chapter 4 covers learning in multi-player games, stochastic games, and Markov games, focusing on learning multi-player grid games—two player grid games, Q-learning, and Nash Q-learning. Chapter 5 discusses differential games, including multi player differential games, actor critique structure, adaptive fuzzy control and fuzzy interference systems, the evader pursuit game, and the defending a territory games. Chapter 6 discusses new ideas on learning within robotic swarms and the innovative idea of the evolution of personality traits.

• Framework for understanding a variety of methods and approaches in multi-agent machine learning.

• Discusses methods of reinforcement learning such as a number of forms of multi-agent Q-learning

• Applicable to research professors and graduate students studying electrical and computer engineering, computer science, and mechanical and aerospace engineering

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prediction error. The algorithm takes the following form: We apply this algorithm to the previous grid game. We initialize the action probabilities to be equal in all directions; therefore, as in Section 2.7, π(s,a)=0.25-->. We set the discount factor γ=0.9-->, just as we did in the previous example, and set the learning rate to α=0.001-->. We then run the algorithm for 1,000,000 steps and get the value of the state as VT=8.892.450.042.560.97−0.37−0.13−0.42−1.27.--> Recall that the true value

interpretations of set operations, such as union and intersection, are complicated in fuzzy set theory because of the graded property of MFs. Zadeh [12] proposed the following definitions for union and intersection operations: Union μA∪B(x)=max[μA(x),μB(x)]--> Intersection μA∩B(x)=min[μA(x),μB(x)]--> where A--> and B--> are fuzzy sets. MFs are normally described using graphics. Figure 5-1 shows various types of MFs commonly used in fuzzy set theory. The Gaussian MF, for example, in Fig. 5-1b

(ut′−ut)/σ--> in (5.36). Then, Eq. (5.36) becomes 5.37 wt+1l=wtl+βsignΔut′−utσ∂u∂wl--> where 5.38 ∂u∂wl=∏i=1nμFil(xi)∑l=1M∏i=1nμFil(xi)=Φtl--> The task of the critic is to estimate the value function over a continuous state space. The value function is the expected sum of discounted rewards defined as 5.39 Vt=E∑k=0∞γkrt+k+1--> where t--> is the current time step, rt+k+1--> is the received immediate reward at the time step t+k+1-->, and γ∈[0,1)--> is a discount factor. Equation (5.39) can be

problem of finding the zeros of a function. If one knows the gradient of the function, then one can use the well-known Newton–Raphson method to find the zeros, but in this case one takes the noise-corrupted measurements of the function at different values of θ-->. One then makes small corrections to θ--> in the estimated direction of zero. The method of stochastic approximation and the theoretical proofs of stability are used in the proofs of convergence for several fundamental algorithms in

the robots during the simulation. Reproduced from [21] � S. Givigi and H. M. Schwartz. Another aspect observed in the simulations was the behavior of robots after some of them were shot. Observe that, since the number of active robots decreases, the reward ?2(.)--> for the personality trait γ2-->, “fear,” calculated in step 19 of Algorithm 6.4, and ?3(.)--> for the personality trait γ3-->, “cooperation,” calculated on step 20, decrease. Therefore, the reward ?1(.)--> for the trait of personality