Mean-Variance Problems for Finite Horizon Semi-Markov Decision Processes

Mean-Variance Problems for Finite Horizon Semi-Markov Decision Processes This paper deals with a mean-variance problem for finite horizon semi-Markov decision processes. The state and action spaces are Borel spaces, while the reward function may be unbounded. The goal is to seek an optimal policy with minimal finite horizon reward variance over the set of policies with a given mean. Using the theory of $$N$$ N -step contraction, we give a characterization of policies with a given mean and convert the second order moment of the finite horizon reward to a mean of an infinite horizon reward/cost generated by a discrete-time Markov decision processes (MDP) with a two dimension state space and a new one-step reward/cost under suitable conditions. We then establish the optimality equation and the existence of mean-variance optimal policies by employing the existing results of discrete-time MDPs. We also provide a value iteration and a policy improvement algorithms for computing the value function and mean-variance optimal policies, respectively. In addition, a linear program and the dual program are developed for solving the mean-variance problem. Applied Mathematics and Optimization Springer Journals

Mean-Variance Problems for Finite Horizon Semi-Markov Decision Processes

Loading next page...
Springer US
Copyright © 2015 by Springer Science+Business Media New York
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
Publisher site
See Article on Publisher Site


  • Finite-horizon variance penalised Markov decision processes
    Collins, EJ

You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial