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The uniqueness of an optimal solution to a combinatorial optimization problem attracts many fields of researchers&#39; attention because it has a wide range of applications, it is related to important classes in computational complexity, and the existence of only one solution is often critical for algorithm designs in theory. However, as the authors know, there is no major benchmark set consisting of only instances with unique solutions, and no algorithm generating instances with unique solutions is known; a systematic approach to getting a problem instance guaranteed having a unique solution would be helpful. A possible approach is as follows: Given a problem instance, we specify a small part of a solution in advance so that only one optimal solution meets the specification. This paper formulates such a ``pre-assignment&#39;&#39; approach for the
vertex cover problem as a typical combinatorial optimization
problem and discusses its computational complexity.
First, we show that the problem is $\Sigma^P_2$-complete in general, while 
the problem becomes NP-complete when an input graph is bipartite. 
We then present an $O(2.1996^n)$-time algorithm for general graphs and an $O(1.9181^n)$-time algorithm for bipartite graphs, where $n$ is the number of vertices. The latter is based on an FPT algorithm with $O^*(3.6791^{\tau})$ time for vertex cover number $\tau$. Furthermore, we show that the problem for trees can be solved in $O(1.4143^n)$ time.

AAAI 2024

Theoretical Aspects of Generating Instances with Unique Solutions: Pre-assignment Models for Unique Vertex Cover | VIDEO

exact algorithms

vertex cover

computational complexity

uniqueness

The uniqueness of an optimal solution to a combinatorial optimization problem attracts many fields of researchers' attention because it has a wide range of applications, it is related to important classes in computational complexity, and the existence of only one solution is often critical for algorithm designs in theory. However, as the authors know, there is no major benchmark set consisting of only instances with unique solutions, and no algorithm generating instances with unique solutions is known; a systematic approach to getting a problem instance guaranteed having a unique solution would be helpful. A possible approach is as follows: Given a problem instance, we specify a small part of a solution in advance so that only one optimal solution meets the specification. This paper formulates such a ``pre-assignment'' approach for the
vertex cover problem as a typical combinatorial optimization
problem and discusses its computational complexity.
First, we show that the problem is $\Sigma^P_2$-complete in general, while 
the problem becomes NP-complete when an input graph is bipartite. 
We then present an $O(2.1996^n)$-time algorithm for general graphs and an $O(1.9181^n)$-time algorithm for bipartite graphs, where $n$ is the number of vertices. The latter is based on an FPT algorithm with $O^*(3.6791^{\tau})$ time for vertex cover number $\tau$. Furthermore, we show that the problem for trees can be solved in $O(1.4143^n)$ time.

technical paper

We are pleased to announce the Thirty-Eighth AAAI Conference on Artificial Intelligence (AAAI-24), which will be held in Vancouver, British Columbia at the Vancouver Convention Centre – West Building from 20-27 February, 2024.

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-24 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and a range of other activities to be announced.

We expect for AAAI-24 to be an in-person conference – one author of all accepted papers will be expected to present work in person unless there are exceptional circumstances that prevent this.<br><br><br><br>

In order to access the AAAI-24 event page you need to register [here](https://aaai.org/aaai-conference/registration/)

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. 

The widespread adoption of Graph Neural Networks (GNNs) has led to an increasing focus on their reliability. To address the issue of underconfidence in GNNs, various calibration methods have been developed to gain notable reductions in calibration error. However, we observe that existing approaches generally fail to enhance consistently, and in some cases even deteriorate, GNNs' ability to discriminate between correct and incorrect predictions. In this study, we advocate the significance of discriminative ability and the inclusion of relevant evaluation metrics. Our rationale is twofold: 1) Overlooking discriminative ability can inadvertently compromise the overall quality of the model; 2) Leveraging discriminative ability can significantly inform and improve calibration outcomes. Therefore, we thoroughly explore the reasons why existing calibration methods have ineffectiveness and even degradation regarding the discriminative ability of GNNs. Building upon these insights, we conduct GNN calibration experiments across multiple datasets using a straightforward example model, denoted as DC(GNN). Its excellent performance confirms the potential of integrating discriminative ability as a key consideration in the calibration of GNNs, thereby establishing a pathway toward more effective and reliable network calibration.

Improving GNN Calibration with Discriminative Ability: Insights and Strategies

Efficient communication learning among agents has been shown crucial for cooperative multi-agent reinforcement learning (MARL), as it can promote the action coordination of agents and ultimately improve performance. Graph neural network (GNN) provide a general paradigm for communication learning, which consider agents and communication channels as nodes and edges in a graph, with the action selection corresponding to node labeling. Under such paradigm, an agent aggregates information from neighbor agents, which can reduce uncertainty in local decision-making and induce implicit action coordination. However, this communication paradigm is vulnerable to adversarial attacks and noise, and how to learn robust and efficient communication under perturbations has largely not been studied. To this end, this paper introduces a novel Multi-Agent communication mechanism via Graph Information bottleneck (MAGI), which can optimally balance the robustness and expressiveness of the message representation learned by agents. This communication mechanism is aim at learning the minimal sufficient message representation for an agent by maximizing the mutual information (MI) between the message representation and the selected action, and simultaneously constraining the MI between the message representation and the agent feature. Empirical results demonstrate that MAGI is more robust and efficient than state-of-the-art GNN-based MARL methods.

Learning Efficient and Robust Multi-Agent Communication via Graph Information Bottleneck | VIDEO

This work explores the zero-shot adaptation capability of semantic skills, semantically interpretable experts' behavior patterns, in cross-domain settings, where a user input in interleaved multi-modal snippets can prompt a new long-horizon task for different domains. In these cross-domain settings, we present a semantic skill translator framework SemTra which utilizes a set of multi-modal models to extract skills from the snippets, and leverages the reasoning capabilities of a pretrained language model to adapt these extracted skills to the target domain. The framework employs a two-level hierarchy for adaptation: task adaptation and skill adaptation. During task adaptation, seq-to-seq translation by the language model transforms the extracted skills into a semantic skill sequence, which is tailored to fit the cross-domain contexts. Skill adaptation focuses on optimizing each semantic skill for the target domain context, through parametric instantiations that are facilitated by language prompting and contrastive learning-based context inferences. This hierarchical adaptation empowers the framework to not only infer a complex task specification in one-shot from the interleaved multi-modal snippets, but also adapt it to new domains with zero-shot learning abilities. We evaluate our framework with Meta-World, Franka Kitchen, RLBench, and CARLA environments. The results clarify the framework's superiority in performing long-horizon tasks and adapting to different domains, showing its broad applicability in practical use cases, such as cognitive robots interpreting abstract instructions and autonomous vehicles operating under varied configurations.

SemTra: A Semantic Skill Translator for Cross-Domain Zero-Shot Policy Adaptation

Generative models can serve as surrogates for some real data sources by creating synthetic training datasets, but in doing so they may transfer biases to downstream tasks. We focus on protecting quality and diversity when generating synthetic training datasets. We propose quality-diversity generative sampling (QDGS), a framework for sampling data uniformly across a user-defined measure space, despite the data coming from a biased generator. QDGS is a model-agnostic framework that uses prompt guidance to optimize a quality objective across measures of diversity for synthetically generated data, without fine-tuning the generative model. Using balanced synthetic datasets generated by QDGS, we first debias classifiers trained on color-biased shape datasets as a proof-of-concept. By applying QDGS to facial data synthesis, we prompt for desired semantic concepts, such as skin tone and age, to create an intersectional dataset with a combined blend of visual features. Leveraging this balanced data for training classifiers improves fairness while maintaining accuracy on facial recognition benchmarks. Code available at: github.com/Cylumn/qd-generative-sampling

Quality-Diversity Generative Sampling for Learning with Synthetic Data | VIDEO

Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for various downstream tasks, e.g., image classification, time series classification, image generation, etc. Its key part is how to model the time-derivative of the hidden state, denoted dh(t)/dt. People have habitually used conventional neural network architectures, e.g., fully-connected layers followed by non-linear activations. In this paper, however, we present a neural operator-based method to define the time-derivative term. Neural operators were initially proposed to model the differential operator of partial differential equations (PDEs). Since the time-derivative of NODEs can be understood as a special type of the differential operator, our proposed method, called branched Fourier neural operator (BFNO), makes sense. In our experiments with general downstream tasks, our method significantly outperforms existing methods.

Operator-Learning-Inspired Modeling of Neural Ordinary Differential Equations

Structured  Complex  Task  Decomposition  (SCTD)  is  the problem of breaking down a complex real-world task (such as planning a wedding) into a directed acyclic graph over individual steps that contribute to achieving the task, with edges specifying temporal dependencies between steps. SCTD is an important component of assistive planning tools, and a challenge  for  commonsense  reasoning  systems.  We  probe  how accurately SCTD can be done with the knowledge extracted from  pre-trained  Large  Language  Models  (LLMs).  We  introduce a new high-quality human-annotated dataset for this problem and novel metrics to fairly assess  performance of LLMs against several baselines. Our experiments reveal that LLMs  are able to decompose complex tasks into individual steps effectively, with a relative improvement of 15% to 280% over the best baseline. We also propose a number of approaches to further improve their performance, with a relative improvement of 7% to 37%. However, we find that LLMs still struggle to predict pairwise temporal dependencies, which reveals a gap in their understanding of complex tasks.

TaskLAMA: Probing the Complex Task Understanding of Language Models | VIDEO

Classical planning considers a given task and searches for a plan to solve it. Some tasks are harder to solve than others. We can measure the 'hardness' of a task with the novelty width and the correlation complexity. In this work, we compare these measures.
Additionally, we introduce the river measure, a new measure that is based on potential heuristics and therefore similar to the correlation complexity but also comparable to the novelty width.
We show that the river measure is upper bounded by the correlation complexity and by the novelty width +1. 
Furthermore, we show that we can convert a planning task with a polynomial blowup of the task size to ensure that a heuristic of dimension 2 exists that gives rise to backtrack-free search.

Novelty vs. Potential Heuristics: A Comparison of Hardness Measures for Satisficing Planning

In this paper, we consider an infinite horizon average reward Markov Decision Process (MDP). Distinguishing itself from existing works within this context, our approach harnesses the power of the general policy gradient-based algorithm, liberating it from the constraints of assuming a linear MDP structure. We propose a vanilla policy gradient-based algorithm and show its global convergence property. We then prove that the proposed algorithm has O(T^3/4) regret. Remarkably, this paper marks a pioneering effort by presenting the first exploration into regret bound computation for the general parameterized policy gradient algorithm in the context of average reward scenarios.

Regret Analysis of Policy Gradient Algorithm for Infinite Horizon Average Reward Markov Decision Processes

Successful machine learning involves a complete pipeline of data, model, and downstream applications. Instead of treating them separately, there has been a prominent increase of attention within the constrained optimization (CO) and machine learning (ML) communities towards combining prediction and optimization models. The so-called end-to-end (E2E) learning captures the task-based objective for which they will be used for decision making. Although a large variety of E2E algorithms have been presented, it has not been fully investigated how to systematically address uncertainties involved in such models. Most of the existing work considers the uncertainties of ML in the input space and improves robustness through adversarial training. We extend this idea to E2E learning and prove that there is a robustness certification procedure by solving augmented integer programming. Furthermore, we show that neglecting the uncertainty of COs during training causes a new trigger for generalization errors. To include all these components, we propose a unified framework that covers the uncertainties emerging in both the input feature space of the ML models and the COs. The framework is described as a robust optimization problem and is practically solved via end-to-end adversarial training (E2E-AT). Finally, the performance of E2E-AT is evaluated by a real-world end-to-end power system operation problem, including load forecasting and sequential scheduling tasks.

E2E-AT: A Unified Framework for Tackling Uncertainty in Task-Aware End-to-End Learning | VIDEO

Recent studies reveal the connection between GNNs and the diffusion process, which motivates many diffusion based GNNs to be proposed. However, since these two mechanisms are closely related, one fundamental question naturally arises: Is there a general diffusion framework that can formally unify these GNNs? The answer to this question can not only deepen our understanding of the learning process of GNNs, but also may open a new door to design a broad new class of GNNs. In this paper, we propose a general diffusion equation framework with the fidelity term, which formally establishes the relationship between the diffusion process with more GNNs. Meanwhile, with this framework, we identify one characteristic of graph diffusion networks, i.e., the current neural diffusion process only corresponds to the first-order diffusion equation. However, by an experimental investigation, we show that the labels of high-order neighbors actually appear monophily property, which induces the similarity based on labels among high-order neighbors without requiring the similarity among first-order neighbors. This discovery motives to design a new high-order neighbor-aware diffusion equation, and derive a new type of graph diffusion network (HiD-Net) based on the framework. With the high-order diffusion equation, HiD-Net is more robust against attacks and works on both homophily and heterophily graphs. We not only theoretically analyze the relation between HiD-Net with high-order random walk, but also provide a theoretical convergence guarantee. Extensive experimental results well demonstrate the effectiveness of HiD-Net over state-of-the-art graph diffusion networks.

Theoretical Aspects of Generating Instances with Unique Solutions: Pre-assignment Models for Unique Vertex Cover | VIDEO

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Improving GNN Calibration with Discriminative Ability: Insights and Strategies

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Theoretical Aspects of Generating Instances with Unique Solutions: Pre-assignment Models for Unique Vertex Cover | VIDEO

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Next from AAAI 2024

Improving GNN Calibration with Discriminative Ability: Insights and Strategies

Stay up to date with the latest Underline news!

PRESENTATIONS

CONFERENCES

COMPANY

RESOURCES

Downloads