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The increasingly large size of modern pretrained language models not only makes them inherit more human-like biases from the training corpora, but also makes it computationally expensive to mitigate such biases. In this paper, we investigate recent parameter-efficient methods in combination with counterfactual data augmentation (CDA) for bias mitigation. We conduct extensive experiments with prefix tuning, prompt tuning, and adapter tuning on different language models and bias types to evaluate their debiasing performance and abilities to preserve the internal knowledge of a pre-trained model. We find that the parameter-efficient methods (i) are effective in mitigating gender bias, where adapter tuning is consistently the most effective one and prompt tuning is more suitable for GPT-2 than BERT, (ii) are less effective when it comes to racial and religious bias, which may be attributed to the limitations of CDA, and (iii) can perform similarly to or sometimes better than full fine-tuning with improved time and memory efficiency, as well as maintain the internal knowledge in BERT and GPT-2, evaluated via fact retrieval and downstream fine-tuning.

A parametric class of trust-region algorithms for unconstrained nonconvex optimization is considered where the value of the objective function is never computed. The class contains a deterministic version of the first-order Adagrad method typically used for minimization of noisy function, but also allows the use of (possibly approximate) second-order information when available. The rate of convergence of methods in the class is analyzed and is shown to be identical to that known for first-order optimization methods using both function and gradients values, recovering existing results for purely-first order variants and improving the explicit dependence on problem dimension. This rate is shown to be essentially sharp. A new class of methods is also presented, for which a slightly worse and essentially sharp complexity result holds. Limited numerical experiments show that the new methods' performance may be comparable to that of standard steepest descent, despite using significantly less information, and that this performance is relatively insensitive to noise.

In many machine learning applications, labeling datasets can be an arduous and time-consuming task. Although research has shown that semi-supervised learning techniques can achieve high accuracy with very few labels within the field of computer vision, little attention has been given to how images within a dataset should be selected for labeling. In this paper, we propose a novel approach based on well-established self-supervised learning, clustering, and manifold learning techniques that address this challenge of selecting an informative image subset to label in the first instance, which is known as the cold-start or unsupervised selective labelling problem. We test our approach using several publicly available datasets, namely CIFAR10, Imagenette, DeepWeeds, and EuroSAT, and observe improved performance with both supervised and semi-supervised learning strategies when our label selection strategy is used, in comparison to random sampling. We also obtain superior performance for the datasets considered with a much simpler approach compared to other methods in the literature.

This paper introduces a numerical approach to solve singularly perturbed convection diffusion boundary value problems for second-order ordinary differential equations that feature a small positive parameter {\epsilon} multiplying the highest derivative. We specifically examine Dirichlet boundary conditions. To solve this differential equation, we propose an upwind finite difference method and incorporate the Shishkin mesh scheme to capture the solution near boundary layers. Our solver is both direct and of high accuracy, with computation time that scales linearly with the number of grid points. MATLAB code of the numerical recipe is made publicly available. We present numerical results to validate the theoretical results and assess the accuracy of our method. The tables and graphs included in this paper demonstrate the numerical outcomes, which indicate that our proposed method offers a highly accurate approximation of the exact solution.

The discrete $\alpha$-neighbor $p$-center problem (d-$\alpha$-$p$CP) is an emerging variant of the classical $p$-center problem which recently got attention in literature. In this problem, we are given a discrete set of points and we need to locate $p$ facilities on these points in such a way that the maximum distance between each point where no facility is located and its $\alpha$-closest facility is minimized. The only existing algorithms in literature for solving the d-$\alpha$-$p$CP are approximation algorithms and two recently proposed heuristics. In this work, we present two integer programming formulations for the d-$\alpha$-$p$CP, together with lifting of inequalities, valid inequalities, inequalities that do not change the optimal objective function value and variable fixing procedures. We provide theoretical results on the strength of the formulations and convergence results for the lower bounds obtained after applying the lifting procedures or the variable fixing procedures in an iterative fashion. Based on our formulations and theoretical results, we develop branch-and-cut (B&C) algorithms, which are further enhanced with a starting heuristic and a primal heuristic. We evaluate the effectiveness of our B&C algorithms using instances from literature. Our algorithms are able to solve 116 out of 194 instances from literature to proven optimality, with a runtime of under a minute for most of them. By doing so, we also provide improved solution values for 116 instances.

Compared to on-policy counterparts, off-policy model-free deep reinforcement learning can improve data efficiency by repeatedly using the previously gathered data. However, off-policy learning becomes challenging when the discrepancy between the underlying distributions of the agent's policy and collected data increases. Although the well-studied importance sampling and off-policy policy gradient techniques were proposed to compensate for this discrepancy, they usually require a collection of long trajectories and induce additional problems such as vanishing/exploding gradients or discarding many useful experiences, which eventually increases the computational complexity. Moreover, their generalization to either continuous action domains or policies approximated by deterministic deep neural networks is strictly limited. To overcome these limitations, we introduce a novel policy similarity measure to mitigate the effects of such discrepancy in continuous control. Our method offers an adequate single-step off-policy correction that is applicable to deterministic policy networks. Theoretical and empirical studies demonstrate that it can achieve a "safe" off-policy learning and substantially improve the state-of-the-art by attaining higher returns in fewer steps than the competing methods through an effective schedule of the learning rate in Q-learning and policy optimization.

The geometric median, an instrumental component of the secure machine learning toolbox, is known to be effective when robustly aggregating models (or gradients), gathered from potentially malicious (or strategic) users. What is less known is the extent to which the geometric median incentivizes dishonest behaviors. This paper addresses this fundamental question by quantifying its strategyproofness. While we observe that the geometric median is not even approximately strategyproof, we prove that it is asymptotically $\alpha$-strategyproof: when the number of users is large enough, a user that misbehaves can gain at most a multiplicative factor $\alpha$, which we compute as a function of the distribution followed by the users. We then generalize our results to the case where users actually care more about specific dimensions, determining how this impacts $\alpha$. We also show how the skewed geometric medians can be used to improve strategyproofness.

Algorithmic fairness has attracted increasing attention in the machine learning community. Various definitions are proposed in the literature, but the differences and connections among them are not clearly addressed. In this paper, we review and reflect on various fairness notions previously proposed in machine learning literature, and make an attempt to draw connections to arguments in moral and political philosophy, especially theories of justice. We also consider fairness inquiries from a dynamic perspective, and further consider the long-term impact that is induced by current prediction and decision. In light of the differences in the characterized fairness, we present a flowchart that encompasses implicit assumptions and expected outcomes of different types of fairness inquiries on the data generating process, on the predicted outcome, and on the induced impact, respectively. This paper demonstrates the importance of matching the mission (which kind of fairness one would like to enforce) and the means (which spectrum of fairness analysis is of interest, what is the appropriate analyzing scheme) to fulfill the intended purpose.

At the end of the 19th century the logician C.S. Peirce coined the term "fallibilism" for the "... the doctrine that our knowledge is never absolute but always swims, as it were, in a continuum of uncertainty and of indeterminacy". In terms of scientific practice, this means we are obliged to reexamine the assumptions, the evidence, and the arguments for conclusions that subsequent experience has cast into doubt. In this paper we examine an assumption that underpinned the development of the Internet architecture, namely that a loosely synchronous point-to-point datagram delivery service could adequately meet the needs of all network applications, including those which deliver content and services to a mass audience at global scale. We examine how the inability of the Networking community to provide a public and affordable mechanism to support such asynchronous point-to-multipoint applications led to the development of private overlay infrastructure, namely CDNs and Cloud networks, whose architecture stands at odds with the Open Data Networking goals of the early Internet advocates. We argue that the contradiction between those initial goals and the monopolistic commercial imperatives of hypergiant overlay infrastructure operators is an important reason for the apparent contradiction posed by the negative impact of their most profitable applications (e.g., social media) and strategies (e.g., targeted advertisement). We propose that, following the prescription of Peirce, we can only resolve this contradiction by reconsidering some of our deeply held assumptions.

In this paper, we propose new techniques for solving geometric optimization problems involving interpoint distances of a point set in the plane. Given a set $P$ of $n$ points in the plane and an integer $1 \leq k \leq \binom{n}{2}$, the distance selection problem is to find the $k$-th smallest interpoint distance among all pairs of points of $P$. The previously best deterministic algorithm solves the problem in $O(n^{4/3} \log^2 n)$ time [Katz and Sharir, SIAM J. Comput. 1997 and SoCG 1993]. In this paper, we improve their algorithm to $O(n^{4/3} \log n)$ time. Using similar techniques, we also give improved algorithms on both the two-sided and the one-sided discrete Fr\'{e}chet distance with shortcuts problem for two point sets in the plane. For the two-sided problem (resp., one-sided problem), we improve the previous work [Avraham, Filtser, Kaplan, Katz, and Sharir, ACM Trans. Algorithms 2015 and SoCG 2014] by a factor of roughly $\log^2(m+n)$ (resp., $(m+n)^{\epsilon}$), where $m$ and $n$ are the sizes of the two input point sets, respectively. Other problems whose solutions can be improved by our techniques include the reverse shortest path problems for unit-disk graphs. Our techniques are quite general and we believe they will find many other applications in future.