Iterative jailbreak methods that repeatedly rewrite and input prompts into large language models (LLMs) to induce harmful outputs -- using the model's previous responses to guide each new iteration -- have been found to be a highly effective attack strategy. Despite being an effective attack strategy against LLMs and their safety mechanisms, existing defenses do not proactively disrupt this dynamic trial-and-error cycle. In this study, we propose a novel framework that dynamically updates its defense strategy through online learning in response to each new prompt from iterative jailbreak methods. Leveraging the distinctions between harmful jailbreak-generated prompts and typical harmless prompts, we introduce a reinforcement learning-based approach that optimizes prompts to ensure appropriate responses for harmless tasks while explicitly rejecting harmful prompts. Additionally, to curb overfitting to the narrow band of partial input rewrites explored during an attack, we introduce Past-Direction Gradient Damping (PDGD). Experiments conducted on three LLMs show that our approach significantly outperforms five existing defense methods against five iterative jailbreak methods. Moreover, our results indicate that our prompt optimization strategy simultaneously enhances response quality for harmless tasks.
Adversarial attacks by malicious users that threaten the safety of large language models (LLMs) can be viewed as attempts to infer a target property $T$ that is unknown when an instruction is issued, and becomes knowable only after the model's reply is observed. Examples of target properties $T$ include the binary flag that triggers an LLM's harmful response or rejection, and the degree to which information deleted by unlearning can be restored, both elicited via adversarial instructions. The LLM reveals an \emph{observable signal} $Z$ that potentially leaks hints for attacking through a response containing answer tokens, thinking process tokens, or logits. Yet the scale of information leaked remains anecdotal, leaving auditors without principled guidance and defenders blind to the transparency--risk trade-off. We fill this gap with an information-theoretic framework that computes how much information can be safely disclosed, and enables auditors to gauge how close their methods come to the fundamental limit. Treating the mutual information $I(Z;T)$ between the observation $Z$ and the target property $T$ as the leaked bits per query, we show that achieving error $\varepsilon$ requires at least $\log(1/\varepsilon)/I(Z;T)$ queries, scaling linearly with the inverse leak rate and only logarithmically with the desired accuracy. Thus, even a modest increase in disclosure collapses the attack cost from quadratic to logarithmic in terms of the desired accuracy. Experiments on seven LLMs across system-prompt leakage, jailbreak, and relearning attacks corroborate the theory: exposing answer tokens alone requires about a thousand queries; adding logits cuts this to about a hundred; and revealing the full thinking process trims it to a few dozen. Our results provide the first principled yardstick for balancing transparency and security when deploying LLMs.