A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and structure-from-motion, the problem of synchronizing rotations also finds applications in visual simultaneous localization and mapping, where it is used as an initialization for iterative solvers, and camera network calibration. Nevertheless, this optimization problem is both non-convex and high-dimensional. In this paper, we address it from a maximum likelihood estimation standpoint and make a twofold contribution. Firstly, we set forth a novel primal-dual method, motivated by the widely accepted spectral initialization. Further, we characterize stationary points of rotation averaging in cycle graphs topologies and contextualize this result within spectral graph theory. We benchmark the proposed method in multiple settings and certify our solution via duality theory, achieving a significant gain in precision and performance.

Dynamic Vehicle Routing Problem (DVRP), is an extension of the classic Vehicle Routing Problem (VRP), which is a fundamental problem in logistics and transportation. Typically, DVRPs involve two stakeholders: service providers that deliver services to customers and customers who raise requests from different locations. Many real-world applications can be formulated as DVRP such as ridesharing and non-compliance capture. Apart from original objectives like optimising total utility or efficiency, DVRP should also consider fairness for all parties. Unfairness can induce service providers and customers to give up on the systems, leading to negative financial and social impacts. However, most existing DVRP-related applications focus on improving fairness from a single side, and there have been few works considering two-sided fairness and utility optimisation concurrently. To this end, we propose a novel framework, a Two-sided Fairness-aware Genetic Algorithm (named 2FairGA), which expands the genetic algorithm from the original objective solely focusing on utility to multi-objectives that incorporate two-sided fairness. Subsequently, the impact of injecting two fairness definitions into the utility-focused model and the correlation between any pair of the three objectives are explored. Extensive experiments demonstrate the superiority of our proposed framework compared to the state-of-the-art.

We present a new algorithm based on posterior sampling for learning in Constrained Markov Decision Processes (CMDP) in the infinite-horizon undiscounted setting. The algorithm achieves near-optimal regret bounds while being advantageous empirically compared to the existing algorithms. Our main theoretical result is a Bayesian regret bound for each cost component of $\tilde{O} (DS\sqrt{AT})$ for any communicating CMDP with $S$ states, $A$ actions, and diameter $D$. This regret bound matches the lower bound in order of time horizon $T$ and is the best-known regret bound for communicating CMDPs achieved by a computationally tractable algorithm. Empirical results show that our posterior sampling algorithm outperforms the existing algorithms for constrained reinforcement learning.

Bagging is a popular ensemble technique to improve the accuracy of machine learning models. It hinges on the well-established rationale that, by repeatedly retraining on resampled data, the aggregated model exhibits lower variance and hence higher stability, especially for discontinuous base learners. In this paper, we provide a new perspective on bagging: By suitably aggregating the base learners at the parametrization instead of the output level, bagging improves generalization performances exponentially, a strength that is significantly more powerful than variance reduction. More precisely, we show that for general stochastic optimization problems that suffer from slowly (i.e., polynomially) decaying generalization errors, bagging can effectively reduce these errors to an exponential decay. Moreover, this power of bagging is agnostic to the solution schemes, including common empirical risk minimization, distributionally robust optimization, and various regularizations. We demonstrate how bagging can substantially improve generalization performances in a range of examples involving heavy-tailed data that suffer from intrinsically slow rates.

Multi-objective optimization can be found in many real-world applications where some conflicting objectives can not be optimized by a single solution. Existing optimization methods often focus on finding a set of Pareto solutions with different optimal trade-offs among the objectives. However, the required number of solutions to well approximate the whole Pareto optimal set could be exponentially large with respect to the number of objectives, which makes these methods unsuitable for handling many optimization objectives. In this work, instead of finding a dense set of Pareto solutions, we propose a novel Tchebycheff set scalarization method to find a few representative solutions (e.g., 5) to cover a large number of objectives (e.g., $>100$) in a collaborative and complementary manner. In this way, each objective can be well addressed by at least one solution in the small solution set. In addition, we further develop a smooth Tchebycheff set scalarization approach for efficient optimization with good theoretical guarantees. Experimental studies on different problems with many optimization objectives demonstrate the effectiveness of our proposed method.

A long-standing goal of data management systems has been to build systems which can compute quantitative insights over large corpora of unstructured data in a cost-effective manner. Until recently, it was difficult and expensive to extract facts from company documents, data from scientific papers, or metrics from image and video corpora. Today's models can accomplish these tasks with high accuracy. However, a programmer who wants to answer a substantive AI-powered query must orchestrate large numbers of models, prompts, and data operations. For even a single query, the programmer has to make a vast number of decisions such as the choice of model, the right inference method, the most cost-effective inference hardware, the ideal prompt design, and so on. The optimal set of decisions can change as the query changes and as the rapidly-evolving technical landscape shifts. In this paper we present Palimpzest, a system that enables anyone to process AI-powered analytical queries simply by defining them in a declarative language. The system uses its cost optimization framework to implement the query plan with the best trade-offs between runtime, financial cost, and output data quality. We describe the workload of AI-powered analytics tasks, the optimization methods that Palimpzest uses, and the prototype system itself. We evaluate Palimpzest on tasks in Legal Discovery, Real Estate Search, and Medical Schema Matching. We show that even our simple prototype offers a range of appealing plans, including one that is 3.3x faster and 2.9x cheaper than the baseline method, while also offering better data quality. With parallelism enabled, Palimpzest can produce plans with up to a 90.3x speedup at 9.1x lower cost relative to a single-threaded GPT-4 baseline, while obtaining an F1-score within 83.5% of the baseline. These require no additional work by the user.

Recent advances in large language models (LLMs) have made them indispensable, raising significant concerns over managing their safety. Automated red teaming offers a promising alternative to the labor-intensive and error-prone manual probing for vulnerabilities, providing more consistent and scalable safety evaluations. However, existing approaches often compromise diversity by focusing on maximizing attack success rate. Additionally, methods that decrease the cosine similarity from historical embeddings with semantic diversity rewards lead to novelty stagnation as history grows. To address these issues, we introduce DiveR-CT, which relaxes conventional constraints on the objective and semantic reward, granting greater freedom for the policy to enhance diversity. Our experiments demonstrate DiveR-CT's marked superiority over baselines by 1) generating data that perform better in various diversity metrics across different attack success rate levels, 2) better-enhancing resiliency in blue team models through safety tuning based on collected data, 3) allowing dynamic control of objective weights for reliable and controllable attack success rates, and 4) reducing susceptibility to reward overoptimization. Project details and code can be found at https://andrewzh112.github.io/#diverct.

In cross-domain few-shot classification, nearest Cross-domain few-shot classification (Dvornik et al., 2020; centroid classifier (NCC) aims to learn representations Li et al., 2021a; Liu et al., 2021a; Triantafillou et al., 2020), to construct a metric space where few-shot also known as CFC, is a learning paradigm which aims at classification can be performed by measuring the learning to perform classification on tasks sampled from similarities between samples and the prototype of previously unseen data or domains with only a few labeled each class. An intuition behind NCC is that each data available. Compared with conventional few-shot classification sample is pulled closer to the class centroid it belongs (Finn et al., 2017; Ravi & Larochelle, 2017; Snell to while pushed away from those of other et al., 2017; Vinyals et al., 2016) which learns to adapt to classes. However, in this paper, we find that there new tasks sampled from unseen data with the same distribution exist high similarities between NCC-learned representations as seen data, cross-domain few-shot classification of two samples from different classes. is a much more challenging learning task since there exist In order to address this problem, we propose a discrepancies between the distributions of source and target bi-level optimization framework, maximizing optimized domains (Chi et al., 2021; Kuzborskij & Orabona, 2013).

The principle of data minimization aims to reduce the amount of data collected, processed or retained to minimize the potential for misuse, unauthorized access, or data breaches. Rooted in privacy-by-design principles, data minimization has been endorsed by various global data protection regulations. However, its practical implementation remains a challenge due to the lack of a rigorous formulation. This paper addresses this gap and introduces an optimization framework for data minimization based on its legal definitions. It then adapts several optimization algorithms to perform data minimization and conducts a comprehensive evaluation in terms of their compliance with minimization objectives as well as their impact on user privacy. Our analysis underscores the mismatch between the privacy expectations of data minimization and the actual privacy benefits, emphasizing the need for approaches that account for multiple facets of real-world privacy risks.

While stochastic bilevel optimization methods have been extensively studied for addressing large-scale nested optimization problems in machine learning, it remains an open question whether the optimal complexity bounds for solving bilevel optimization are the same as those in single-level optimization. Our main result resolves this question: SPABA, an adaptation of the PAGE method for nonconvex optimization in (Li et al., 2021) to the bilevel setting, can achieve optimal sample complexity in both the finite-sum and expectation settings. We show the optimality of SPABA by proving that there is no gap in complexity analysis between stochastic bilevel and single-level optimization when implementing PAGE. Notably, as indicated by the results of (Dagr\'eou et al., 2022), there might exist a gap in complexity analysis when implementing other stochastic gradient estimators, like SGD and SAGA. In addition to SPABA, we propose several other single-loop stochastic bilevel algorithms, that either match or improve the state-of-the-art sample complexity results, leveraging our convergence rate and complexity analysis. Numerical experiments demonstrate the superior practical performance of the proposed methods.