Long-Term Sequential Decision Making under Risk

• URL: http://arxiv.org/abs/2607.19914v1
• Date: Wed, 22 Jul 2026 08:44:25 GMT
• Title: Long-Term Sequential Decision Making under Risk
• Abstract summary: We study finite-horizon MDP planning under emphroot-based (resolute) risk objectives that apply a rank-dependent functional to the distribution of total returns.<n>We propose textbfERQDP, an enumeration-free and sampling-free method that solves a rank--quantile surrogate via exact DP.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study finite-horizon MDP planning under \emph{root-based} (resolute) risk objectives that apply a rank-dependent functional to the distribution of total returns. Such objectives are non-linear in the return distribution and generally break Bellman optimality, so direct optimization by scenario-tree enumeration is intractable. We propose \textbf{ERQDP}, an enumeration-free and sampling-free method that solves a rank--quantile surrogate via exact DP (Dynamic Programming), evaluates candidate policies exactly by DP over return Probability Mass Functions (PMFs) on a discretized return grid (with an explicit rounding bound), and refines the surrogate in an anytime loop that reports an explicit upper--lower gap (certificate) for the target objective up to discretization budgets. Across tested benchmarks, ERQDP returns certified solutions or explicit residual gaps, enables fast risk-parameter sweeps with substantial runtime gains, and supports both risk-averse and risk-seeking behaviors.

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