An Efficient Solution to s-Rectangular Robust Markov Decision Processes

• URL: http://arxiv.org/abs/2301.13642v1
• Date: Tue, 31 Jan 2023 13:54:23 GMT
• Title: An Efficient Solution to s-Rectangular Robust Markov Decision Processes
• Authors: Navdeep Kumar, Kfir Levy, Kaixin Wang, Shie Mannor
• Abstract summary: We present an efficient robust value iteration for texttts-rectangular robust Markov Decision Processes (MDPs) We do so by deriving the optimal robust Bellman operator in concrete forms using our $L_p$ water filling lemma. We unveil the exact form of the optimal policies, which turn out to be novel threshold policies with the probability of playing an action proportional to its advantage.
• Score: 49.05403412954533
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present an efficient robust value iteration for \texttt{s}-rectangular robust Markov Decision Processes (MDPs) with a time complexity comparable to standard (non-robust) MDPs which is significantly faster than any existing method. We do so by deriving the optimal robust Bellman operator in concrete forms using our $L_p$ water filling lemma. We unveil the exact form of the optimal policies, which turn out to be novel threshold policies with the probability of playing an action proportional to its advantage.

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