6,024 research outputs found
Controlled diffusion processes
This article gives an overview of the developments in controlled diffusion
processes, emphasizing key results regarding existence of optimal controls and
their characterization via dynamic programming for a variety of cost criteria
and structural assumptions. Stochastic maximum principle and control under
partial observations (equivalently, control of nonlinear filters) are also
discussed. Several other related topics are briefly sketched.Comment: Published at http://dx.doi.org/10.1214/154957805100000131 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Continuous-time Markov decision processes under the risk-sensitive average cost criterion
This paper studies continuous-time Markov decision processes under the
risk-sensitive average cost criterion. The state space is a finite set, the
action space is a Borel space, the cost and transition rates are bounded, and
the risk-sensitivity coefficient can take arbitrary positive real numbers.
Under the mild conditions, we develop a new approach to establish the existence
of a solution to the risk-sensitive average cost optimality equation and obtain
the existence of an optimal deterministic stationary policy.Comment: 14 page
Risk-sensitive Inverse Reinforcement Learning via Semi- and Non-Parametric Methods
The literature on Inverse Reinforcement Learning (IRL) typically assumes that
humans take actions in order to minimize the expected value of a cost function,
i.e., that humans are risk neutral. Yet, in practice, humans are often far from
being risk neutral. To fill this gap, the objective of this paper is to devise
a framework for risk-sensitive IRL in order to explicitly account for a human's
risk sensitivity. To this end, we propose a flexible class of models based on
coherent risk measures, which allow us to capture an entire spectrum of risk
preferences from risk-neutral to worst-case. We propose efficient
non-parametric algorithms based on linear programming and semi-parametric
algorithms based on maximum likelihood for inferring a human's underlying risk
measure and cost function for a rich class of static and dynamic
decision-making settings. The resulting approach is demonstrated on a simulated
driving game with ten human participants. Our method is able to infer and mimic
a wide range of qualitatively different driving styles from highly risk-averse
to risk-neutral in a data-efficient manner. Moreover, comparisons of the
Risk-Sensitive (RS) IRL approach with a risk-neutral model show that the RS-IRL
framework more accurately captures observed participant behavior both
qualitatively and quantitatively, especially in scenarios where catastrophic
outcomes such as collisions can occur.Comment: Submitted to International Journal of Robotics Research; Revision 1:
(i) Clarified minor technical points; (ii) Revised proof for Theorem 3 to
hold under weaker assumptions; (iii) Added additional figures and expanded
discussions to improve readabilit
The exponential cost optimality for finite horizon semi-Markov decision processes
summary:This paper considers an exponential cost optimality problem for finite horizon semi-Markov decision processes (SMDPs). The objective is to calculate an optimal policy with minimal exponential costs over the full set of policies in a finite horizon. First, under the standard regular and compact-continuity conditions, we establish the optimality equation, prove that the value function is the unique solution of the optimality equation and the existence of an optimal policy by using the minimum nonnegative solution approach. Second, we establish a new value iteration algorithm to calculate both the value function and the -optimal policy. Finally, we give a computable machine maintenance system to illustrate the convergence of the algorithm
Markov Decision Processes with Applications in Wireless Sensor Networks: A Survey
Wireless sensor networks (WSNs) consist of autonomous and resource-limited
devices. The devices cooperate to monitor one or more physical phenomena within
an area of interest. WSNs operate as stochastic systems because of randomness
in the monitored environments. For long service time and low maintenance cost,
WSNs require adaptive and robust methods to address data exchange, topology
formulation, resource and power optimization, sensing coverage and object
detection, and security challenges. In these problems, sensor nodes are to make
optimized decisions from a set of accessible strategies to achieve design
goals. This survey reviews numerous applications of the Markov decision process
(MDP) framework, a powerful decision-making tool to develop adaptive algorithms
and protocols for WSNs. Furthermore, various solution methods are discussed and
compared to serve as a guide for using MDPs in WSNs
Algorithms for CVaR Optimization in MDPs
In many sequential decision-making problems we may want to manage risk by
minimizing some measure of variability in costs in addition to minimizing a
standard criterion. Conditional value-at-risk (CVaR) is a relatively new risk
measure that addresses some of the shortcomings of the well-known
variance-related risk measures, and because of its computational efficiencies
has gained popularity in finance and operations research. In this paper, we
consider the mean-CVaR optimization problem in MDPs. We first derive a formula
for computing the gradient of this risk-sensitive objective function. We then
devise policy gradient and actor-critic algorithms that each uses a specific
method to estimate this gradient and updates the policy parameters in the
descent direction. We establish the convergence of our algorithms to locally
risk-sensitive optimal policies. Finally, we demonstrate the usefulness of our
algorithms in an optimal stopping problem.Comment: Submitted to NIPS 1
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