As large language models (LLMs) are increasingly being integrated into various real-world applications, the identification of their vulnerabilities to jailbreaking attacks becomes an essential component of ensuring the safety and reliability of LLMs. Previous studies have developed LLM assistants, known as the adversarial prompter, to automatically generate suffixes that manipulate target LLMs into generating harmful and undesirable outputs. However, these approaches often suffer from low performance or generate semantically meaningless prompts, which can be easily identified by perplexity-based defenses. In this paper, we introduce a novel two-stage method, $\texttt{ProAdvPrompter}$, that significantly improves the performance of adversarial prompters. In $\texttt{ProAdvPrompter}$, the first stage (Exploration) utilizes the loss information to guide the adversarial prompter in generating suffixes that are more likely to elicit harmful responses. Then the second stage (Exploitation) iteratively fine-tunes the prompter using high-quality generated adversarial suffixes to further boost performance. Additionally, we incorporate the prompt template to aid in the Exploration stage and propose a filtering mechanism to accelerate the training process in the Exploitation stage. We evaluate $\texttt{ProAdvPrompter}$ against the well-aligned LLMs (i.e., Llama2-Chat-7B and Llama3-chat-8B), achieving attack success rates of 99.68% and 97.12% respectively after 10 trials on the AdvBench dataset, thereby enhancing performance by $\sim 2$ times compared to previous works. Moreover, $\texttt{ProAdvPrompter}$ reduces training time by 20% on Llama3-Instruct-8B, generates more generalized adversarial suffixes, and demonstrates resilience against the perplexity defense. An ablation study further evaluates the effects of key components in $\texttt{ProAdvPrompter}$ (the prompt template and the filtering mechanism).

In decentralized optimization, $m$ agents form a network and only communicate with their neighbors, which gives advantages in data ownership, privacy, and scalability. At the same time, decentralized stochastic gradient descent ($\texttt{SGD}$) methods, as popular decentralized algorithms for training large-scale machine learning models, have shown their superiority over centralized counterparts. Distributed stochastic gradient tracking $\texttt{DSGT}$ has been recognized as the popular and state-of-the-art decentralized $\texttt{SGD}$ method due to its proper theoretical guarantees. However, the theoretical analysis of $\texttt{DSGT}$ shows that its iteration complexity is $\tilde{\mathcal{O}} \left(\frac{\bar{\sigma}^2}{m\mu \varepsilon} + \frac{\sqrt{L}\bar{\sigma}}{\mu(1 - \lambda_2(W))^{1/2} C_W \sqrt{\varepsilon} }\right)$, where the doubly stochastic matrix $W$ represents the network topology and $ C_W $ is a parameter that depends on $W$. Thus, it indicates that the convergence property of $\texttt{DSGT}$ is heavily affected by the topology of the communication network. To overcome the weakness of $\texttt{DSGT}$, we resort to the snap-shot gradient tracking skill and propose two novel algorithms, snap-shot $\texttt{DSGT}$ ($\texttt{SS-DSGT}$) and accelerated snap-shot $\texttt{DSGT}$ ($\texttt{ASS-DSGT}$). We further justify that $\texttt{SS-DSGT}$ exhibits a lower iteration complexity compared to $\texttt{DSGT}$ in the general communication network topology. Additionally, $\texttt{ASS-DSGT}$ matches $\texttt{DSGT}$'s iteration complexity $\mathcal{O}\left( \frac{\bar{\sigma}^2}{m\mu \varepsilon} + \frac{\sqrt{L}\bar{\sigma}}{\mu (1 - \lambda_2(W))^{1/2}\sqrt{\varepsilon}} \right)$ under the same conditions as $\texttt{DSGT}$. Numerical experiments validate $\texttt{SS-DSGT}$'s superior performance performance in the general communication network topology and exhibit better practical performance of $\texttt{ASS-DSGT}$ on the specified $W$ compared to $\texttt{DSGT}$.

Variance reduction techniques are designed to decrease the sampling variance, thereby accelerating convergence rates of first-order (FO) and zeroth-order (ZO) optimization methods. However, in composite optimization problems, ZO methods encounter an additional variance called the coordinate-wise variance, which stems from the random gradient estimation. To reduce this variance, prior works require estimating all partial derivatives, essentially approximating FO information. This approach demands $\mathcal{O}(d)$ function evaluations ($d$ is the dimension size), which incurs substantial computational costs and is prohibitive in high-dimensional scenarios. This paper proposes the Zeroth-order Proximal Double Variance Reduction ($\texttt{ZPDVR}$) method, which utilizes the averaging trick to reduce both sampling and coordinate-wise variances. Compared to prior methods, $\texttt{ZPDVR}$ relies solely on random gradient estimates, calls the stochastic zeroth-order oracle (SZO) in expectation $\mathcal{O}(1)$ times per iteration, and achieves the optimal $\mathcal{O}(d(n + \kappa)\log (\frac{1}{\epsilon}))$ SZO query complexity in the strongly convex and smooth setting, where $\kappa$ represents the condition number and $\epsilon$ is the desired accuracy. Empirical results validate $\texttt{ZPDVR}$’s linear convergence and demonstrate its superior performance over other related methods.

As virtualization becomes more and more popular, how to guarantee survivability of a virtual infrastructure (VI) over a wide-area optical network is increasingly important. In this paper, we approach the problem of survivable VI mapping (SVIM) from a few unique perspectives. One of the most distinguishing perspectives is that a large-scale regional failure could destroy one or more facility nodes to which some VI nodes are mapped. Accordingly, redundant facility nodes at different geographical locations and redundant optical connections have to be provisioned such that the VI can still be mapped after the failure. Another distinguishing perspective is that with failure-dependent protection, the SVIM problem can be decomposed into several instances of the basic non-survivable VI mapping (NSVIM) problem, whose solution permits effective sharing of the redundant resources among all failures. In this paper, we first formulate the minimum-cost SVIM problem using mixed integer linear programming (MILP). We then propose an efficient heuristic solution to NSVIM, based on which two novel heuristic SVIM algorithms called Separate Optimization with Unconstrained Mapping (SOUM) and Incremental Optimization with Constrained Mapping (IOCM). Simulations are performed to study and compare the performance of the MILP and heuristics.