In bilevel optimization problems, a leader and a follower make their decisions in a hierarchy, and both decisions influence each other. Usually one assumes that both players have full knowledge also of the other player's data. In a more realistic model, uncertainty can be quantified, e.g., using the robust optimization approach: We assume that the leader does not know the follower's objective precisely, but only up to some uncertainty set, and her aim is to optimize the worst case of the corresponding scenarios. Now the question arises how the complexity of bilevel optimization changes under the additional complications of this uncertainty. We make a further step towards answering this question by examining an easy bilevel problem. In the Bilevel Selection Problem (BSP), the leader and the follower each select some items, while a common number of items to select in total is given, and each player minimizes the total costs of the selected items, according to different sets of item costs. We show that the BSP can be solved in polynomial time and then investigate its robust version. If the item sets controlled by the players are disjoint, it can still be solved in polynomial time for several types of uncertainty sets. Otherwise, we show that the Robust BSP is NP-hard and present a 2-approximation algorithm and exact exponential-time approaches. Furthermore, we investigate variants of the BSP where one or both of the two players take a continuous decision. One variant leads to an example of a bilevel optimization problem whose optimum value may not be attained. For the Robust Continuous BSP, where all variables are continuous, we also develop a new approach for the setting of discrete uncorrelated uncertainty, which gives a polynomial-time algorithm for the Robust Continuous BSP and a pseudopolynomial-time algorithm for the Robust Bilevel Continuous Knapsack Problem.
We propose a noble, comprehensive and robust agile requirements change management (ARCM) model that addresses the limitations of existing models and is tailored for agile software development in the global software development paradigm. To achieve this goal, we conducted an exhaustive literature review and an empirical study with RCM industry experts. Our study evaluated the effectiveness of the proposed RCM model in a real-world setting and identifies any limitations or areas for improvement. The results of our study provide valuable insights into how the proposed RCM model can be applied in agile global software development environments to improve software development practices and optimize project success rates.
We introduce the convex bundle method to solve convex, non-smooth optimization problems on Riemannian manifolds. Each step of our method is based on a model that involves the convex hull of previously collected subgradients, parallely transported into the current serious iterate. This approach generalizes the dual form of classical bundle subproblems in Euclidean space. We prove that, under mild conditions, the convex bundle method converges to a minimizer. Several numerical examples implemented using the Julia package Manopt.jl illustrate the performance of the proposed method and compare it to the subgradient method, the cyclic proximal point, as well as the proximal bundle algorithm from Hoseini Monjezi, Nobakhtian, Pouryayevali, 2021.
We present a method for upper and lower bounding the right and the left tail probabilities of continuous random variables (RVs). For the right tail probability of RV $X$ with probability density function $f_X(x)$, this method requires first setting a continuous, positive, and strictly decreasing function $g_X(x)$ such that $-f_X(x)/g'_X(x)$ is a decreasing and increasing function, $\forall x>x_0$, which results in upper and lower bounds, respectively, given in the form $-f_X(x) g_X(x)/g'_X(x)$, $\forall x>x_0$, where $x_0$ is some point. Similarly, for the upper and lower bounds on the left tail probability of $X$, this method requires first setting a continuous, positive, and strictly increasing function $g_X(x)$ such that $f_X(x)/g'_X(x)$ is an increasing and decreasing function, $\forall x<x_0$, which results in upper and lower bounds, respectively, given in the form $f_X(x) g_X(x)/g'_X(x)$, $\forall x<x_0$. We provide some examples of good candidates for the function $g_X(x)$. We also establish connections between the new bounds and Markov's inequality and Chernoff's bound. In addition, we provide an iterative method for obtaining ever tighter lower and upper bounds, under certain conditions. Finally, we provide numerical examples, where we show the tightness of these bounds, for some chosen $g_X(x)$.
Large language models (LLMs) are pivotal in advancing natural language processing (NLP) tasks, yet their efficacy is hampered by inaccuracies and outdated knowledge. Model editing emerges as a promising solution to address these challenges. However, existing editing methods struggle to track and incorporate changes in knowledge associated with edits, which limits the generalization ability of postedit LLMs in processing edited knowledge. To tackle these problems, we propose a novel model editing method that leverages knowledge graphs for enhancing LLM editing, namely GLAME. Specifically, we first utilize a knowledge graph augmentation module to uncover associated knowledge that has changed due to editing, obtaining its internal representations within LLMs. This approach allows knowledge alterations within LLMs to be reflected through an external graph structure. Subsequently, we design a graph-based knowledge edit module to integrate structured knowledge into the model editing. This ensures that the updated parameters reflect not only the modifications of the edited knowledge but also the changes in other associated knowledge resulting from the editing process. Comprehensive experiments conducted on GPT-J and GPT-2 XL demonstrate that GLAME significantly improves the generalization capabilities of post-edit LLMs in employing edited knowledge.
We reveal and address the frequently overlooked yet important issue of disguised procedural unfairness, namely, the potentially inadvertent alterations on the behavior of neutral (i.e., not problematic) aspects of data generating process, and/or the lack of procedural assurance of the greatest benefit of the least advantaged individuals. Inspired by John Rawls's advocacy for pure procedural justice, we view automated decision-making as a microcosm of social institutions, and consider how the data generating process itself can satisfy the requirements of procedural fairness. We propose a framework that decouples the objectionable data generating components from the neutral ones by utilizing reference points and the associated value instantiation rule. Our findings highlight the necessity of preventing disguised procedural unfairness, drawing attention not only to the objectionable data generating components that we aim to mitigate, but also more importantly, to the neutral components that we intend to keep unaffected.
Counterfactual reasoning is pivotal in human cognition and especially important for providing explanations and making decisions. While Judea Pearl's influential approach is theoretically elegant, its generation of a counterfactual scenario often requires interventions that are too detached from the real scenarios to be feasible. In response, we propose a framework of natural counterfactuals and a method for generating counterfactuals that are natural with respect to the actual world's data distribution. Our methodology refines counterfactual reasoning, allowing changes in causally preceding variables to minimize deviations from realistic scenarios. To generate natural counterfactuals, we introduce an innovative optimization framework that permits but controls the extent of backtracking with a naturalness criterion. Empirical experiments indicate the effectiveness of our method.
Disentangled Representation Learning (DRL) aims to learn a model capable of identifying and disentangling the underlying factors hidden in the observable data in representation form. The process of separating underlying factors of variation into variables with semantic meaning benefits in learning explainable representations of data, which imitates the meaningful understanding process of humans when observing an object or relation. As a general learning strategy, DRL has demonstrated its power in improving the model explainability, controlability, robustness, as well as generalization capacity in a wide range of scenarios such as computer vision, natural language processing, data mining etc. In this article, we comprehensively review DRL from various aspects including motivations, definitions, methodologies, evaluations, applications and model designs. We discuss works on DRL based on two well-recognized definitions, i.e., Intuitive Definition and Group Theory Definition. We further categorize the methodologies for DRL into four groups, i.e., Traditional Statistical Approaches, Variational Auto-encoder Based Approaches, Generative Adversarial Networks Based Approaches, Hierarchical Approaches and Other Approaches. We also analyze principles to design different DRL models that may benefit different tasks in practical applications. Finally, we point out challenges in DRL as well as potential research directions deserving future investigations. We believe this work may provide insights for promoting the DRL research in the community.
Graph Convolutional Networks (GCNs) and their variants have experienced significant attention and have become the de facto methods for learning graph representations. GCNs derive inspiration primarily from recent deep learning approaches, and as a result, may inherit unnecessary complexity and redundant computation. In this paper, we reduce this excess complexity through successively removing nonlinearities and collapsing weight matrices between consecutive layers. We theoretically analyze the resulting linear model and show that it corresponds to a fixed low-pass filter followed by a linear classifier. Notably, our experimental evaluation demonstrates that these simplifications do not negatively impact accuracy in many downstream applications. Moreover, the resulting model scales to larger datasets, is naturally interpretable, and yields up to two orders of magnitude speedup over FastGCN.
We introduce an approach for deep reinforcement learning (RL) that improves upon the efficiency, generalization capacity, and interpretability of conventional approaches through structured perception and relational reasoning. It uses self-attention to iteratively reason about the relations between entities in a scene and to guide a model-free policy. Our results show that in a novel navigation and planning task called Box-World, our agent finds interpretable solutions that improve upon baselines in terms of sample complexity, ability to generalize to more complex scenes than experienced during training, and overall performance. In the StarCraft II Learning Environment, our agent achieves state-of-the-art performance on six mini-games -- surpassing human grandmaster performance on four. By considering architectural inductive biases, our work opens new directions for overcoming important, but stubborn, challenges in deep RL.
The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.