# Distributionally Robust Optimization for Sequential Decision Making

arXiv: https://arxiv.org/abs/1801.04745 · HTML: https://mlsanity.com/paper/1801.04745/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2018.

## Built on by (most cited first, 12 of 12)

- [Distributionally Robust Learning](https://mlsanity.com/paper/2108.08993/) (2021)
- [Policy Gradient in Robust MDPs with Global Convergence Guarantee](https://mlsanity.com/paper/2212.10439/) (2022)
- [Trustworthy Reinforcement Learning Against Intrinsic Vulnerabilities: Robustness, Safety, and Generalizability](https://mlsanity.com/paper/2209.08025/) (2022)
- [On the Optimality of Batch Policy Optimization Algorithms](https://mlsanity.com/paper/2104.02293/) (2021)
- [Near-Optimal Policy Identification in Robust Constrained Markov Decision Processes via Epigraph Form](https://mlsanity.com/paper/2408.16286/) (2024)
- [Markov Decision Processes under Model Uncertainty](https://mlsanity.com/paper/2206.06109/) (2022)
- [Decision-Dependent Distributionally Robust Markov Decision Process Method in Dynamic Epidemic Control](https://mlsanity.com/paper/2306.14051/) (2023)
- [Sequential Decision-Making under Uncertainty: A Robust MDPs review](https://mlsanity.com/paper/2404.00940/) (2024)
- [Robust Phi-Divergence MDPs](https://mlsanity.com/paper/2205.14202/) (2022)
- [Robust probabilistic inference via a constrained transport metric](https://mlsanity.com/paper/2303.10085/) (2023)
- [On the Convergence of Modified Policy Iteration in Risk Sensitive Exponential Cost Markov Decision Processes](https://mlsanity.com/paper/2302.03811/) (2023)
- [Solving Robust MDPs through No-Regret Dynamics](https://mlsanity.com/paper/2305.19035/) (2023)

## Abstract (arXiv)

The distributionally robust Markov Decision Process (MDP) approach asks for a distributionally robust policy that achieves the maximal expected total reward under the most adversarial distribution of uncertain parameters. In this paper, we study distributionally robust MDPs where ambiguity sets for the uncertain parameters are of a format that can easily incorporate in its description the uncertainty's generalized moment as well as statistical distance information. In this way, we generalize existing works on distributionally robust MDP with generalized-moment-based and statistical-distance-based ambiguity sets to incorporate information from the former class such as moments and dispersions to the latter class that critically depends on empirical observations of the uncertain parameters. We show that, under this format of ambiguity sets, the resulting distributionally robust MDP remains tractable under mild technical conditions. To be more specific, a distributionally robust policy can be constructed by solving a sequence of one-stage convex optimization subproblems.