Csaba Szepesvari (1996) Comparing Yardsticks for Cognition . Psycoloquy: 7(26) Optimal Cognition (4)

Versions: ASCII formatted

Commentary on Worden on Optimal-Cognition

Bolyai Institute of Mathematics

Jozsef Attila University

Szeged, 6720 Aradi vrt tere 1.

and

Department of Adaptive Systems,

Institute of Isotopes

Hungarian Academy of Sciences and

Jozsef Attila University

Budapest 1525, Pf. 77. HUNGARY

szepes@math.u-szeged.hu

Worden (1996) has suggested that cognitive science could be built around a model for optimal cognition. He has also proposed an equation, called the Requirement Equation (RE), which should describe the biological requirement brains must meet. Here I analyse the limitations of his equation in detail. The analysis is based on a more general class of models, namely, models of optimal sequential decisions, of which Worden's equation is a special case. It turns out that the RE can describe optimal behaviour if there is no perceptual aliasing. If the RE is able to capture all aspects of cognition then animal cognition is probably modular and thus it is more likely to be suboptimal than optimal. I also show that -- contrary to Worden's suggestion -- the optimisation problem faced by evolution may have many local minima, depending on the genetic encoding. Nevertheless, one can show, purely on the basis of the theory of optimal sequential decisions, that brains of animals probably use internal representations and that cognition has a universal limit when one considers its biological function.

- [Astrom, 1965] K.J. Astrom. Optimal control of Markov decision processes with incomplete state estimation. Journal of Mathematical Analysis and Applications, 1:174-205, 1965.
- [Barto et al., 1991] A.G. Barto, S.J. Bradtke and S.P. Singh. Real-time Learning and Control using Asynchronous Dynamic Programming. Computer Science Department, University of Massachusetts, Technical Report 59:91-57, 1991.
- [Bellman, 1957] R. Bellman. Dynamic Programming, Princeton University Press, Princeton, New Jersey, 1957.
- [Dawkins, 1976] R. Dawkins. The Selfish Gene, Oxford University Press, 1976.
- [Drake, 1962] A.W. Drake. Observation of Markov Process Through a Noisy Channel, PhD thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1962.
- [Kumar, 1985] P.R. Kumar. A survey of some results in stochastic adaptive control. SIAM J. Control and Optimization, 23:329-380, 1985.
- [Lewis et al., 1995] F.L. Lewis, K. Liu and A. Yesildirek. Neural Net Robot Controller with Guaranteed Tracking Performance. IEEE Trans. on Neural Networks, 6:703-715, 1995.
- [Littman 1994] M.L. Littman. Memoryless policies: Theoretical limitations and practical results. In "From Animals to Animats 3: Proc. of the Third International Conf. on Simulation of Adaptive Behaviour", eds D. Cliff, P. Husbands, J.A. Meyer, S.W. Wilson, Cambridge, Massachusetts, 1994, MIT Press.
- [Nowak, 1989] A.S Nowak. Existence of optimal strategies in zero-sum nonstationary stochastic games with lack of information on both sides. SIAM J. Control and Optimization, 27:289-295, 1989.
- [Rawlins, 1991] Foundations of Genetic Algorithms. Edited by Gregory J.E. Rawlins. Morgan Kaufmann Publishers, San Mateo, California, 1991.
- [Shapley, 1953] L.S. Shapley. Stochastic games. Proceedings of the National Academy of Sciences of the United States of America, 39:1095- 1100, 1953.
- [Singh, 1992] S.P. Singh. Transfer of learning by composing solutions for elemental sequential tasks. Machine Learning, 8:323--339, 1992.
- [Worden, 1996] R.P. Worden An Optimal Yardstick for Cognition. PSYCOLOQUY 7(1) optimal-cognition.1.worden, 1996.