# Optimistic Reinforcement Learning with Quantile Objectives

arXiv: https://arxiv.org/abs/2511.09652 · HTML: https://mlsanity.com/paper/2511.09652/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- First posted on arXiv 12 Nov 2025.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Built on by (most cited first, 1 of 1)

- [Deep Reinforcement Learning with Buffered Quantile Objectives](https://mlsanity.com/paper/2609.21327/) (2026)

## Abstract (arXiv)

Reinforcement Learning (RL) has achieved tremendous success in recent years. However, the classical foundations of RL do not account for the risk sensitivity of the objective function, which is critical in various fields, including healthcare and finance. A popular approach to incorporate risk sensitivity is to optimize a specific quantile of the cumulative reward distribution. In this paper, we develop UCB-QRL, an optimistic learning algorithm for the τ-quantile objective in finite-horizon Markov decision processes (MDPs). UCB-QRL is an iterative algorithm in which, at each iteration, we first estimate the underlying transition probability and then optimize the quantile value function over a confidence ball around this estimate. We show that UCB-QRL yields a high-probability regret bound mathcal Oleft((2/kappa)H+1H√SATHlog(2SATH/δ)right) in the episodic setting with S states, A actions, T episodes, and H horizons. Here, kappa>0 is a problem-dependent constant that captures the sensitivity of the underlying MDP's quantile value.