Abstract

Robust reinforcement learning (RRL) aims to tackle unexpected environmental changes by optimizing policies against the worst case. However, RRL remains impractical due to the cost of the Max-Min optimization, where it suffers from the exhaustive query complexity for finding the worst-case (dubbed 'Min') within the environmental uncertainty set U , ie, O (|U|). By viewing this via a lens of quantum perspective, we raise a pivotal question: If we can query from the environment with quantum superpositions, is it possible to accelerate the Max-Min optimization of RRL? Our answer is 'Yes'. Our method, called quantum robust inner minimization (QRIM), encodes the uncertainty set with quantum superposition and amplifies low-return cases, thus enabling RL for solving the robust (ie, worst-case) Bellman equation. Importantly, QRIM achieves a quadratic speed-up in query complexity without altering the outer RL pipeline, ie, O (|U|). Validated through classical simulations to real quantum hardware execution, QRIM learns more robust policies with quadratically reduced queries than classical RL.

Artificial intelligence systems deployed in the real world must continue to make reliable decisions even when conditions differ from those encountered during training. Robust reinforcement learning (RRL) addresses this challenge by preparing AI agents for the worst-case scenarios they may face. However, identifying those worst-case conditions requires searching a large uncertainty space, making training increasingly expensive as the number of possible environmental variations grows.

To this bottleneck, Professor Sung Whan Yoon of the Graduate School of Artificial Intelligence at UNIST, in collaboration with Professor Joongheon Kim of Korea University, developed Quantum Robust Inner Minimization (QRIM), a method that replaces only the inner optimization responsible for identifying worst-case environments, while leaving the overall reinforcement learning pipeline unchanged.

QRIM exploits quantum superposition to evaluate many possible environmental conditions simultaneously rather than examining each one individually. By amplifying the worst-case scenarios through a quantum search routine, the method reduces the number of required environment queries from N to √N—a quadratic improvement in query complexity—without modifying the surrounding reinforcement learning procedure. 

Across a series of experiments, QRIM learned more robust policies while requiring only 20–30% of the computation used by conventional methods. The researchers validated the algorithm through both classical simulations and experiments on IBM's 127-qubit quantum processor, demonstrating that the quadratic speed-up remained effective even in the presence of hardware noise.

“QRIM redesigns the most computationally demanding component of RRL—the search for worst-case environments—using a quantum algorithm,” said first author Hyun Kyu Lee. "Because only the inner optimization is replaced, existing reinforcement learning algorithms can be readily incorporate the quantum module, making the approach broadly applicable across robust reinforcement learning."

“This study demonstrates how quantum computing can complement artificial intelligence by addressing a well-defined computational bottleneck,” said Professor Yoon. "As quantum hardware continues to advance, approaches like QRIM could help make RRL practical for applications that require reliable decision-making under uncertainty, including robotics and autonomous driving."

The findings have been accepted for presentation at the International Conference on Machine Learning (ICML) 2026, one of the world's leading conferences on machine learning. Among the quantum AI papers accepted to ICML 2026, QRIM is the only study led by a Korean research institution. The research was supported by the National Research Foundation of Korea (NRF) and the Institute for Information & Communications Technology Planning & Evaluation (IITP) through programs funded by the Ministry of Science and ICT (MSIT).

Journal Reference

Hyun Kyu Lee, Joongheon Kim, and Sung Whan Yoon, “Quantum Robust Inner Minimization for Reinforcement Learning with Quadratic Speed-Up in Query Complexity,”    ICML,  (2026)    .