By David S. Touretzky, Jeffrey L. Elman, Terrence J. Sejnowski
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Extra info for Connectionist Models. Proceedings of the 1990 Summer School
This approach was discussed by W e r b o s (1977) in relation to the dif ferential dynamic programming method of Jacobson and Mayne (1970), and Jordan and Jacobs (1990) il lustrated it using a version o f the pole-balancing task with continuous control actions. , El-Fattah, 1981; Sutton, 1990). Werbos (1987, 1988, 1989) discusses gradient methods that make use of system models. Although direct reinforcement learning methods d o not use state-transit ion models, they can use value function models, which we call value models in what follows.
L where a is a positive constant. T h e fractions in (3) cause the controller t o sometimes prefer over u* an action that has not been been performed for a long time. Sato et al. (1988) show that if 0 satisfies the condi tions given by ( 2 ) , then in the limit all actions are performed infinitely often for each state, as needed for convergence o f the state-transition m o d e l , and that the policy converges t o an optimal policy. Specifically, they define the relative frequency coefficient t o be (4) n o At each time t, an estimated optimal policy, i / * ( t ) , is c o m p u t e d using the policy iteration method o f D P based o n the current state-transition model and the payoff array.
T h e policy can then b e adjusted via gradient ascent. Using an artificial neural network to repre sent the value model makes this approach attractive because the value model's gradient can be computed efficiently by error back-propagation. This approach was discussed by W e r b o s (1977) in relation to the dif ferential dynamic programming method of Jacobson and Mayne (1970), and Jordan and Jacobs (1990) il lustrated it using a version o f the pole-balancing task with continuous control actions.