# The Smoothed Complexity of Policy Iteration for Markov Decision Processes

arXiv: https://arxiv.org/abs/2212.00083 · HTML: https://mlsanity.com/paper/2212.00083/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2022.

## Built on by (most cited first, 2 of 2)

- [TCS-BENCH: Benchmarking State-of-the-Art Generative AI Theoretical Computer Science Research Ability](https://mlsanity.com/paper/2608.09538/) (2026)
- [Lower Bound on Howard Policy Iteration for Deterministic Markov Decision Processes](https://mlsanity.com/paper/2506.12254/) (2025)

## Abstract (arXiv)

We show subexponential lower bounds (i.e., 2Omega (nc)) on the smoothed complexity of the classical Howard's Policy Iteration algorithm for Markov Decision Processes. The bounds hold for the total reward and the average reward criteria. The constructions are robust in the sense that the subexponential bound holds not only on the average for independent random perturbations of the MDP parameters (transition probabilities and rewards), but for all arbitrary perturbations within an inverse polynomial range. We show also an exponential lower bound on the worst-case complexity for the simple reachability objective.