Imperial College London > Talks@ee.imperial > Featured talks > Risk-sensitivity, Path Integrals and Stochastic Maximum Principles

Risk-sensitivity, Path Integrals and Stochastic Maximum Principles

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The LQG model of observation and control and the optimisation of its policy are complete and familiar to the point of satiety. However, it is worth emphasising that the Riccati formalism associated with a recursive approach to optimisation is both uglier and less penetrating than the canonical operator factorisation associated with a path-integral approach. This assertion gains in point if one follows the line first proposed by D. Jacobson and generalises the LQG model to the LEQG model, in which the expectation to be minimised is that of the exponential of a quadratic cost function C rather than of C itself. This has the effect of bringing the path integral C into the exponent, and adding a multiple of it to the path integral D associated with the stochastics of the problem. It has many consequences: e.g. the incorporation of risk-sensitivity and the unexpected linking with H-infinity models. If one wishes to escape the constraints of the LQG assumptions then the path integrals are no longer quadratic in form, and the slickness and explicitness associated with a quadratic structure are lost. However, under appropriate assumptions one can apply large-deviation methods to obtain a stochastic maximum principle, with useful conclusions.

Hosted by Professor Erol Gelenbe

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