Risk Sensitive Markov Decision Processes

Risk-sensitive control is an area of significant current interest in stochastic control theory. It is a generalization of the classical, risk-neutral approach, whereby we seek to minimize an exponential of the sum of costs that depends not only on the expected cost, but on higher order moments as well.

[1]  R. Howard,et al.  Risk-Sensitive Markov Decision Processes , 1972 .

[2]  Edward J. Sondik,et al.  The Optimal Control of Partially Observable Markov Processes over a Finite Horizon , 1973, Oper. Res..

[3]  Rhodes,et al.  Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games , 1973 .

[4]  Chelsea C. White,et al.  A Markov Quality Control Process Subject to Partial Observation , 1977 .

[5]  Evan L. Porteus,et al.  Temporal Resolution of Uncertainty and Dynamic Choice Theory , 1978 .

[6]  A. Bensoussan,et al.  Optimal control of partially observable stochastic systems with an exponential-of-integral performance index , 1985 .

[7]  V. Borkar On Minimum Cost Per Unit Time Control of Markov Chains , 1984 .

[8]  Pravin Varaiya,et al.  Stochastic Systems: Estimation, Identification, and Adaptive Control , 1986 .

[9]  Dimitri P. Bertsekas,et al.  Dynamic Programming: Deterministic and Stochastic Models , 1987 .

[10]  M. J. Sobel,et al.  Discounted MDP's: distribution functions and exponential utility maximization , 1987 .

[11]  William S. Lovejoy Technical Note - On the Convexity of Policy Regions in Partially Observed Systems , 1987, Oper. Res..

[12]  K. Glover,et al.  State-space formulae for all stabilizing controllers that satisfy and H ∞ norm bound and relations to risk sensitivity , 1988 .

[13]  Rolando Cavazos-Cadena,et al.  Weak conditions for the existence of optimal stationary policies in average Markov decision chains with unbounded costs , 1989, Kybernetika.

[14]  P. Whittle Risk-Sensitive Optimal Control , 1990 .

[15]  Ari Arapostathis,et al.  On the average cost optimality equation and the structure of optimal policies for partially observable Markov decision processes , 1991, Ann. Oper. Res..

[16]  W. Fleming,et al.  Risk sensitive optimal control and differential games , 1992 .

[17]  Rolando Cavazos-Cadena,et al.  Comparing recent assumptions for the existence of average optimal stationary policies , 1992, Oper. Res. Lett..

[18]  Ari Arapostathis,et al.  Analysis of an adaptive control scheme for a partially observed controlled Markov chain , 1990 .

[19]  M. K. Ghosh,et al.  Discrete-time controlled Markov processes with average cost criterion: a survey , 1993 .

[20]  M. James,et al.  Risk-sensitive control and dynamic games for partially observed discrete-time nonlinear systems , 1994, IEEE Trans. Autom. Control..

[21]  T. Runolfsson The equivalence between infinite-horizon optimal control of stochastic systems with exponential-of-integral performance index and stochastic differential games , 1994, IEEE Trans. Autom. Control..

[22]  J. Speyer,et al.  Centralized and decentralized solutions of the linear-exponential-Gaussian problem , 1994, IEEE Trans. Autom. Control..

[23]  M. James,et al.  Robust and Risk-Sensitive Output Feedback Control for Finite State Machines and Hidden Markov Models , 1994 .

[24]  T. Sargent,et al.  Discounted linear exponential quadratic Gaussian control , 1995, IEEE Trans. Autom. Control..

[25]  W. Fleming,et al.  Risk-Sensitive Control on an Infinite Time Horizon , 1995 .

[26]  S. Marcus,et al.  Risk sensitive control of Markov processes in countable state space , 1996 .

[27]  W. Fleming,et al.  Risk-Sensitive Control of Finite State Machines on an Infinite Horizon I , 1997 .

[28]  J. Lynch,et al.  A weak convergence approach to the theory of large deviations , 1997 .

[29]  E. Fernández-Gaucherand,et al.  Risk-sensitive optimal control of hidden Markov models: structural results , 1997, IEEE Trans. Autom. Control..

[30]  S. Marcus,et al.  Existence of Risk-Sensitive Optimal Stationary Policies for Controlled Markov Processes , 1999 .