This paper considers the problem of annotating datapoints using an expert with only a few annotation rounds in a label-scarce setting. We propose soliciting reliable feedback on difficulty in annotating a datapoint from the expert in addition to ground truth label. Existing literature in active learning or coreset selection turns out to be less relevant to our setting since they presume the existence of a reliable trained model, which is absent in the label-scarce regime. However, the literature on coreset selection emphasizes the presence of difficult data points in the training set to perform supervised learning in downstream tasks (Mindermann et al., 2022). Therefore, for a given fixed annotation budget of $\mathsf{T}$ rounds, we model the sequential decision-making problem of which (difficult) datapoints to choose for annotation in a sparse linear bandits framework with the constraint that no arm can be pulled more than once (blocking constraint). With mild assumptions on the datapoints, our (computationally efficient) Explore-Then-Commit algorithm BSLB achieves a regret guarantee of $\widetilde{\mathsf{O}}(k^{\frac{1}{3}} \mathsf{T}^{\frac{2}{3}} +k^{-\frac{1}{2}} \beta_k + k^{-\frac{1}{12}} \beta_k^{\frac{1}{2}}\mathsf{T}^{\frac{5}{6}})$ where the unknown parameter vector has tail magnitude $\beta_k$ at sparsity level $k$. To this end, we show offline statistical guarantees of Lasso estimator with mild Restricted Eigenvalue (RE) condition that is also robust to sparsity. Finally, we propose a meta-algorithm C-BSLB that does not need knowledge of the optimal sparsity parameters at a no-regret cost. We demonstrate the efficacy of our BSLB algorithm for annotation in the label-scarce setting for an image classification task on the PASCAL-VOC dataset, where we use real-world annotation difficulty scores.

Balancing helpfulness and safety (harmlessness) is a critical challenge in aligning large language models (LLMs). Current approaches often decouple these two objectives, training separate preference models for helpfulness and safety, while framing safety as a constraint within a constrained Markov Decision Process (CMDP) framework. However, these methods can lead to ``safety interference'', where average-based safety constraints compromise the safety of some prompts in favor of others. To address this issue, we propose \textbf{Rectified Policy Optimization (RePO)}, which replaces the average safety constraint with stricter (per prompt) safety constraints. At the core of RePO is a policy update mechanism driven by rectified policy gradients, which penalizes the strict safety violation of every prompt, thereby enhancing safety across nearly all prompts. Our experiments on Alpaca-7B demonstrate that RePO improves the safety alignment and reduces the safety interference compared to baseline methods. Code is available at https://github.com/pxyWaterMoon/RePO.

In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces adversary-correction constraints to ensure correct classification of adversarial data and minimizes changes to the model parameters. We propose an efficient cutting-plane-based algorithm to iteratively solve the large-scale nonconvex optimization problem by approximating the feasible region through polyhedral cuts and balancing between robustness and accuracy. Computational experiments on standard datasets such as MNIST and CIFAR10 demonstrate that the proposed approach significantly improves robustness, even with a very small set of adversarial data, while maintaining minimal impact on accuracy.

In this article, we consider the problem of unconstrained time-varying convex optimization, where the cost function changes with time. We provide an in-depth technical analysis of the problem and argue why freezing the cost at each time step and taking finite steps toward the minimizer is not the best tracking solution for this problem. We propose a set of algorithms that by taking into account the temporal variation of the cost aim to reduce the tracking error of the time-varying minimizer of the problem. The main contribution of our work is that our proposed algorithms only require the first-order derivatives of the cost function with respect to the decision variable. This approach significantly reduces computational cost compared to the existing algorithms, which use the inverse of the Hessian of the cost. Specifically, the proposed algorithms reduce the computational cost from $O(n^3)$ to $O(n)$ per timestep, where $n$ is the size of the decision variable. Avoiding the inverse of the Hessian also makes our algorithms applicable to non-convex optimization problems. We refer to these algorithms as $O(n)$-algorithms. These $O(n)$-algorithms are designed to solve the problem for different scenarios based on the available temporal information about the cost. We illustrate our results through various examples, including the solution of a model predictive control problem framed as a convex optimization problem with a streaming time-varying cost function.

Numerous Optimization Algorithms have a time-varying update rule thanks to, for instance, a changing step size, momentum parameter or, Hessian approximation. In this paper, we apply unrolled or automatic differentiation to a time-varying iterative process and provide convergence (rate) guarantees for the resulting derivative iterates. We adapt these convergence results and apply them to proximal gradient descent with variable step size and FISTA when solving partly smooth problems. We confirm our findings numerically by solving $\ell_1$ and $\ell_2$-regularized linear and logisitc regression respectively. Our theoretical and numerical results show that the convergence rate of the algorithm is reflected in its derivative iterates.

This paper introduces the inverse modeling constrained multi-objective evolutionary algorithm based on decomposition (IM-C-MOEA/D) for addressing constrained real-world optimization problems. Our research builds upon the advancements made in evolutionary computing-based inverse modeling, and it strategically bridges the gaps in applying inverse models based on decomposition to problem domains with constraints. The proposed approach is experimentally evaluated on diverse real-world problems (RWMOP1-35), showing superior performance to state-of-the-art constrained multi-objective evolutionary algorithms (CMOEAs). The experimental results highlight the robustness of the algorithm and its applicability in real-world constrained optimization scenarios.

Abstract: This paper presents a new method for learning dissipative Hamiltonian dynamics from a limited and noisy dataset. The method uses the Helmholtz decomposition to learn a vector field as the sum of a symplectic and a dissipative vector field. The two vector fields are learned using two reproducing kernel Hilbert spaces, defined by a symplectic and a curl-free kernel, where the kernels are specialized to enforce odd symmetry. Random Fourier features are used to approximate the kernels to reduce the dimension of the optimization problem. The performance of the method is validated in simulations for two dissipative Hamiltonian systems, and it is shown that the method improves predictive accuracy significantly compared to a method where a Gaussian separable kernel is used.

Survival analysis is an important research topic with applications in healthcare, business, and manufacturing. One essential tool in this area is the Cox proportional hazards (CPH) model, which is widely used for its interpretability, flexibility, and predictive performance. However, for modern data science challenges such as high dimensionality (both $n$ and $p$) and high feature correlations, current algorithms to train the CPH model have drawbacks, preventing us from using the CPH model at its full potential. The root cause is that the current algorithms, based on the Newton method, have trouble converging due to vanishing second order derivatives when outside the local region of the minimizer. To circumvent this problem, we propose new optimization methods by constructing and minimizing surrogate functions that exploit hidden mathematical structures of the CPH model. Our new methods are easy to implement and ensure monotonic loss decrease and global convergence. Empirically, we verify the computational efficiency of our methods. As a direct application, we show how our optimization methods can be used to solve the cardinality-constrained CPH problem, producing very sparse high-quality models that were not previously practical to construct. We list several extensions that our breakthrough enables, including optimization opportunities, theoretical questions on CPH's mathematical structure, as well as other CPH-related applications.

As powerful Large Language Models (LLMs) are now widely used for numerous practical applications, their safety is of critical importance. While alignment techniques have significantly improved overall safety, LLMs remain vulnerable to carefully crafted adversarial inputs. Consequently, adversarial attack methods are extensively used to study and understand these vulnerabilities. However, current attack methods face significant limitations. Those relying on optimizing discrete tokens suffer from limited efficiency, while continuous optimization techniques fail to generate valid tokens from the model's vocabulary, rendering them impractical for real-world applications. In this paper, we propose a novel technique for adversarial attacks that overcomes these limitations by leveraging regularized gradients with continuous optimization methods. Our approach is two orders of magnitude faster than the state-of-the-art greedy coordinate gradient-based method, significantly improving the attack success rate on aligned language models. Moreover, it generates valid tokens, addressing a fundamental limitation of existing continuous optimization methods. We demonstrate the effectiveness of our attack on five state-of-the-art LLMs using four datasets.

We introduce the Principled Reasoning and Acting (PRAct) framework, a novel method for learning and enforcing action principles from trajectory data. Central to our approach is the use of text gradients from a reflection and optimization engine to derive these action principles. To adapt action principles to specific task requirements, we propose a new optimization framework, Reflective Principle Optimization (RPO). After execution, RPO employs a reflector to critique current action principles and an optimizer to update them accordingly. We develop the RPO framework under two scenarios: Reward-RPO, which uses environmental rewards for reflection, and Self-RPO, which conducts self-reflection without external rewards. Additionally, two RPO methods, RPO-Traj and RPO-Batch, is introduced to adapt to different settings. Experimental results across four environments demonstrate that the PRAct agent, leveraging the RPO framework, effectively learns and applies action principles to enhance performance.