Optimal Cost Almost-Sure Reachability in POMDPs


  • Krishnendu Chatterjee IST Austria
  • Martin Chmelik IST Austria
  • Raghav Gupta IIT Bombay
  • Ayush Kanodia IIT Bombay




POMDPs, Reachability objectives, Total cost, Approximation algorithms


We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objective we study asks to minimize the expected total cost till the target set is reached, while ensuring that the target set is reached almost-surely (with probability 1). We show that for integer costs approximating the optimal cost is undecidable. For positive costs, our results are as follows: (i) we establish matching lower and upper bounds for the optimal cost and the bound is double exponential; (ii) we show that the problem of approximating the optimal cost is decidable and present approximation algorithms developing on the existing algorithms for POMDPs with finite-horizon objectives. While the worst-case running time of our algorithm is double exponential, we present efficient stopping criteria for the algorithm and show experimentally that it performs well in many examples of interest.




How to Cite

Chatterjee, K., Chmelik, M., Gupta, R., & Kanodia, A. (2015). Optimal Cost Almost-Sure Reachability in POMDPs. Proceedings of the AAAI Conference on Artificial Intelligence, 29(1). https://doi.org/10.1609/aaai.v29i1.9683



AAAI Technical Track: Reasoning under Uncertainty