# Risk-Averse Online POMDP Planning via CVaR of the Immediate Cost with Performance Guarantees

arXiv: https://arxiv.org/abs/2609.35874 · HTML: https://mlsanity.com/paper/2609.35874/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 9 of 9)

- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [Algorithms for CVaR Optimization in MDPs](https://mlsanity.com/paper/1406.3339/) (2014)
- [Online algorithms for POMDPs with continuous state, action, and observation spaces](https://mlsanity.com/paper/1709.06196/) (2017)
- [How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Robotics](https://mlsanity.com/paper/1710.11040/) (2017)
- [Provably Efficient Risk-Sensitive Reinforcement Learning: Iterated CVaR and Worst Path](https://mlsanity.com/paper/2206.02678/) (2022)
- [Optimality Guarantees for Particle Belief Approximation of POMDPs](https://mlsanity.com/paper/2210.05015/) (2022)
- [Risk-Averse Planning Under Uncertainty](https://mlsanity.com/paper/1909.12499/) (2019)
- [Online Risk-Averse Planning in POMDPs Using Iterated CVaR Value Function](https://mlsanity.com/paper/2601.20554/) (2026)
- [Accelerated Online Risk-Averse Policy Evaluation in POMDPs with Theoretical Guarantees and Novel CVaR Bounds](https://mlsanity.com/paper/2602.23073/) (2026)

## Abstract (arXiv)

Online POMDP planners optimize the expected cumulative cost, which can mask dangerous states when the belief places significant mass on high-cost states. Existing risk-averse methods apply static or dynamic Conditional Value at Risk (CVaR) to the value function, capturing trajectory-level risk, but share two gaps: (i) by retaining the immediate cost as an expectation of a state-dependent cost over the belief, the risk within the belief is left unaddressed; and (ii) by modifying the value function, they require new tailored algorithms rather than reusing existing expectation-based planners. We instead apply CVaR to the immediate cost over the belief at each step, directly targeting per-step uncertainty about the current state. The standard expected cumulative return is retained as the objective, so the resulting problem has a standard MDP structure: any expectation-based POMDP planner can be made risk-sensitive by changing only the cost computation. We inherit finite-time guarantees for policy evaluation and sparse sampling---with estimation error independent of the risk level---and, as our central theoretical result, prove a finite-time bound on the gap between the particle belief MDP surrogate and the original POMDP, which together yield an end-to-end guarantee from the true POMDP value to the algorithmic estimate. In the risk-neutral limit, the formulation recovers standard expectation-based planning.