$M^3$: A Multi-LLM System for Multi-Turn Jailbreaking as a Markov Decision Process

Modern Large Language Models (LLMs) remain vulnerable to carefully orchestrated multi-turn interactions that progressively bypass safety mechanisms. However, many existing red-teaming approaches rely on heuristics or impose strong assumptions that limit their applicability in fully black box settings. We address this gap by introducing $M^3$, an automated red-teaming framework that formalizes multi-turn jailbreaking as a finite-horizon Markov Decision Process (MDP). In $M^3$, an attacker LLM interacts with a target LLM while operating over a compact internal state produced by a state LLM. Across two benchmarks and six target models, $M^3$ consistently outperforms state‑of‑the‑art multi‑turn red‑teaming methods in Attack Success Rates (ASR), achieving improvements of up to 53\% in ASR@5. Even with lightweight attacker, $M^3$ attains gains up to 26\% in ASR@1 and 34\% in ASR@5, compared to baselines that use higher capacity attackers. Beyond improved effectiveness, $M^3$ exhibits steeper risk escalation over conversational turns and achieves more consistent performance across risk categories (up to 4.82 improvement in Gini index) without relying on predefined risk taxonomy, providing a scalable and principled framework for multi‑turn red‑teaming and safety evaluation.