United States

We study the expressibility and learnability of solution functions of convex optimization and their multi-layer architectural extension. The main results are: (1) the class of solution functions of linear programming (LP) and quadratic programming (QP) is a universal approximant for the $C^k$ smooth model class or some restricted Sobolev space, and we characterize the rate-distortion, (2) the approximation power is investigated through a viewpoint of regression error, where information about the target function is provided in terms of data observations, (3) compositionality in the form of deep architecture with optimization as a layer is shown to reconstruct some basic functions used in numerical analysis without error, which implies that (4) a substantial reduction in rate-distortion can be achieved with a universal network architecture, and (5) we discuss the statistical bounds of empirical covering numbers for LP/QP, as well as a generic optimization problem (possibly nonconvex) by exploiting tame geometry. Our results provide the **first rigorous analysis of the approximation and learning-theoretic properties of solution functions** with implications for algorithmic design and performance guarantees.

AAAI 2023

On Solution Functions of Optimization: Universal Approximation and Covering Number Bounds

approximation property

covering number

solution functions

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-23 is the Thirty-Seventh AAAI Conference on Artificial Intelligence. The theme of this conference is to create collaborative bridges within and beyond AI. Like previous AAAI conferences, AAAI-23 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and two new activities: a Bridge Program and a Lab Program. Many of these activities are tailored to the theme of bridges and all are selected according to the highest standards, with additional programs for students and young researchers. 
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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.

poster

Multi-view deep classification expects to obtain better classification performance than using a single view. However, due to the uncertainty and inconsistency of data sources, adding data views does not necessarily lead to the performance improvements in multi-view classification. How to avoid worsening classification performance when adding views is crucial for multi-view deep learning but rarely studied. To tackle this limitation, in this paper, we reformulate the multi-view classification problem from the perspective of safe learning and thereby propose a Safe Multi-view Deep Classification (SMDC) method, which can guarantee that the classification performance does not deteriorate when fusing multiple views. In the SMDC method, we dynamically integrate multiple views and estimate the inherent uncertainties among multiple views with different root causes based on evidence theory. Through minimizing the uncertainties, SMDC promotes the evidences from data views for correct classification, and in the meantime excludes the incorrect evidences to produce the safe multi-view classification results. Furthermore, we theoretically prove that in the safe multi-view classification, adding data views will certainly not increase the empirical risk of classification. The experiments on various kinds of multi-view datasets validate that the proposed SMDC method can achieve precise and safe classification results.

Safe Multi-View Deep Classification

In this paper, we present a ranking-based underwater image quality assessment (UIQA) method, abbreviated as URanker. The URanker is built on the efficient conv-attentional image Transformer. In terms of underwater images, we specially devise (1) the histogram prior that embeds the color distribution of an underwater image as histogram token to attend global degradation and (2) the dynamic cross-scale correspondence to model local degradation. The final prediction depends on the class tokens from different scales, which comprehensively considers multi-scale dependencies. With the margin ranking loss, our URanker can accurately rank the order of underwater images of the same scene enhanced by different underwater image enhancement (UIE) algorithms according to their visual quality. To achieve that, we also contribute a dataset, URankerSet, containing sufficient results enhanced by different UIE algorithms and the corresponding perceptual rankings, to train our URanker. Apart from the good performance of URanker, we found that a simple U-shape UIE network can obtain promising performance when it is coupled with our pre-trained URanker as additional supervision. In addition, we also propose a normalization tail that can significantly improve the performance of UIE networks. Extensive experiments demonstrate the state-of-the-art performance of our method. The key designs of our method are discussed. Our code and dataset are available at https://li-chongyi.github.io/URanker_files/.

Underwater Ranker: Learn Which Is Better and How to Be Better

The synthesis of programmatic strategies requires one to search in large non-differentiable spaces of computer programs. Current search algorithms use self-play approaches to guide this search. The issue with these approaches is that the guiding function often provides a weak search signal. This is because self-play functions only measure how well a program performs against other programs. Thus, while small changes to a losing program might not transform it into a winning one, such changes might represent steps in the direction of a winning program. In this paper we introduce a hierarchical search algorithm that searches concurrently in the space of programs and in a space of state features. Each iteration of the search in the space of features defines a set of target features that the search in the program space attempts to achieve (i.e., features one observes while following the strategy encoded in a program). We hypothesize the combination of a self-play function and a feature-based one provides a stronger search signal for synthesis. While both functions are used to guide the search in the program space, the self-play function is used to guide the search in the feature space, to allow for the selection of target features that are more likely to lead to winning programs. We evaluated our hierarchical approach in MicroRTS, a real-time strategy game. Our results show that the hierarchical search synthesizes stronger strategies than methods that search only in the program space. Also, the strategies our method synthesizes obtained the highest winning rate in a simulated tournament with several baseline agents, including the best agents from the two latest MicroRTS competitions.

Show Me the Way! Hierarchical Search for Synthesizing Programmatic Strategies

Non-intrusive load monitoring (NILM) aims to decompose aggregated electrical usage signal into appliance-specific power consumption and it amounts to a classical example of blind source separation tasks. Leveraging recent progress on deep learning techniques, we design a new neural NILM model Multi-State Dual CNN (MSDC). Different from previous models, MSDC explicitly extracts information about the appliance's multiple states and state transitions, which in turn regulates the prediction of signals for appliances. More specifically, we employ a dual-CNN architecture: one CNN for outputting state distributions and the other for predicting the power of each state. A new technique is invented that utilizes conditional random fields (CRF) to capture state transitions. Experiments on two real-world datasets REDD and UK-DALE demonstrate that our model significantly outperform state-of-the-art models  while having good generalization capacity, achieving 6%-10% MAE gain and 33%-51% SAE gain to unseen appliances.

MSDC: Exploiting Multi-State Power Consumption in Non-intrusive load monitoring based on A Dual-CNN Model

Designing a planning domain is a difficult task in AI planning. Assisting tools are thus required if we want planning to be used more broadly. In this paper, we are interested in automatically correcting a flawed domain. In particular, we are concerned with the scenario where a domain contradicts a plan that is known to be valid. Our goal is to repair the domain so as to turn the plan into a solution. Specifically, we consider both grounded and lifted representations support for negative preconditions and show how to explore the space of repairs to find the optimal one efficiently. As an evidence of the efficiency of our approach, the experiment results show that all flawed domains except one in the benchmark set can be repaired optimally by our approach within one second.

Towards Automated Modeling Assistance: An Efficient Approach for Repairing Flawed Planning Domains

Very recently, the first mathematical runtime analyses for the NSGA-II, the most common multi-objective evolutionary algorithm, have been conducted (Zheng, Liu, Doerr (AAAI 2022)). Continuing this research direction, we prove that the NSGA-II optimizes the OneJumpZeroJump benchmark asymptotically faster when crossover is employed. This is the first time such an advantage of crossover is proven for the NSGA-II. Our arguments can be transferred to single-objective optimization. They then prove that crossover can speed-up the $(\mu+1)$ genetic algorithm in a different way and more pronounced than known before. Our experiments confirm the added value of crossover and show that the observed speed-ups  are even larger than what our proofs can guarantee. 

Runtime Analysis for the NSGA-II: Provable Speed-Ups From Crossover

Recent Text-to-Speech (TTS) systems trained on reading or acted corpora have achieved near human-level naturalness. The diversity of human speech, however, often goes beyond the coverage of these corpora. We believe the ability to handle such diversity is crucial for AI systems to achieve human-level communication. Our work explores the use of more abundant real-world data for building speech synthesizers. We train TTS systems using real-world speech from YouTube and podcasts. We observe the mismatch between training and inference alignments in mel-spectrogram based autoregressive models, leading to unintelligible synthesis, and demonstrate that learned discrete codes within multiple code groups effectively resolves this issue. We introduce our MQTTS system whose architecture is designed for multiple code generation and monotonic alignment, along with the use of a clean silence prompt to improve synthesis quality. We conduct ablation analyses to identify the efficacy of our methods. We show that MQTTS outperforms existing TTS systems in several objective and subjective measures.

A Vector Quantized Approach for Text to Speech Synthesis on Real-World Spontaneous Speech

As we all know, multi-view data is more expressive than single-view data and multi-label annotation enjoys richer supervision information than single-label, which makes multi-view multi-label learning widely applicable for various pattern recognition tasks. In this complex representation learning problem, three main challenges can be characterized as follows: i) How to learn consistent representations of samples across all views? ii) How to exploit and utilize category correlations of multi-label to guide inference? iii) How to avoid the negative impact resulting from the incompleteness of views or labels? To cope with these problems, we propose a general multi-view multi-label learning framework named label-guided masked view- and category-aware transformers in this paper. First, we design two transformer-style based modules for cross-view features aggregation and multi-label classification, respectively. The former aggregates information from different views in the process of extracting view-specific features, and the latter learns subcategory embedding to improve classification performance. Second, considering the imbalance of expressive power among views, an adaptively weighted view fusion module is proposed to obtain view-consistent embedding features. Third, we impose a label manifold constraint in sample-level representation learning to maximize the utilization of supervised information. Last but not least, all the modules are designed under the premise of incomplete views and labels, which makes our method adaptable to arbitrary multi-view and multi-label data. Extensive experiments on five datasets confirm that our method has clear advantages over other state-of-the-art methods.

Incomplete Multi-View Multi-Label Learning via Label-Guided Masked View- and Category-Aware Transformers

Transformer-based text-to-image synthesis generates images from abstractive textual conditions and achieves prompt results. Since transformer-based models predict visual tokens step by step in testing, where the early error is hard to be corrected and would be propagated. To alleviate this issue, the common practice is drawing multi-paths from the transformer-based models and re-ranking the multi-images decoded from multi-paths to find the best one and filter out others. Therefore, the computing procedure of excluding images may be inefficient. To improve the effectiveness and efficiency of decoding, we exploit a reject decoding algorithm with tiny multi-modal models to enlarge the searching space and exclude the useless paths as early as possible. Specifically, we build tiny multi-modal models to evaluate the similarities between the partial paths and the caption at multi scales. Then, we propose a reject decoding algorithm to exclude some lowest quality partial paths at the inner steps. Thus, under the same computing load as the original decoding, we could search across more multi-paths to improve the decoding efficiency and synthesizing quality. The experiments conducted on the MS-COCO dataset and large-scale datasets show that the proposed reject decoding algorithm can exclude the useless paths and enlarge the searching paths to improve the synthesizing quality by consuming less time.

Reject Decoding via Language-Vision Models for Text-to-Image Synthesis

We propose a novel algorithm for generalized linear contextual bandits (GLBs) with an $\tilde{O}(\sqrt{\kappa^{-1} \phi^{-1} T})$ regret over $T$ rounds where $\phi$ is the minimum eigenvalue of the covariance of contexts and $\kappa$ is a lower bound of the variance of rewards. 
In several identified cases of $\phi^{-1}=O(d)$, where $d$ is the dimension of contexts, our result is the first regret bound for generalized linear  bandits (GLBs) achieving the order $\sqrt{d}$ without discarding the observed rewards.
Previous approaches achieve the regret bound of order $\sqrt{d}$ by discarding the observed rewards, whereas our algorithm achieves the bound incorporating contexts from all arms in our double doubly-robust (DDR) estimator.
The DDR estimator is a subclass of doubly-robust estimator but with a tighter error bound.
We also provide an $O(\kappa^{-1} \phi^{-1} \log (NT) \log T)$ regret bound for $N$ arms under a probabilistic margin condition.
This is the first regret bound under the margin condition for linear models or GLMs when contexts are different for all arms but coefficients are common.
We conduct empirical studies using synthetic data and real examples, demonstrating the effectiveness of our algorithm.

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On Solution Functions of Optimization: Universal Approximation and Covering Number Bounds

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