United States

We study fair resource allocation when the resources contain a mixture of divisible and indivisible goods, focusing on the well-studied fairness notion of maximin share fairness (MMS). With only indivisible goods, a full MMS allocation may not exist, but a constant multiplicative approximate allocation always does. We analyze how the MMS approximation guarantee would be affected when the resources to be allocated also contain divisible goods. In particular, we show that the worst-case MMS approximation guarantee with mixed goods is no worse than that with only indivisible goods. However, there exist problem instances to which adding some divisible resources would strictly decrease the MMS approximation ratios of the instances. On the algorithmic front, we propose a constructive algorithm that will always produce an \alpha-MMS allocation for any number of agents, where \alpha takes values between 1/2 and 1 and is a monotonically increasing function determined by how agents value the divisible goods relative to their MMS values.

AAAI 2021

Maximin Fairness with Mixed Divisible and Indivisible Goods

technical paper

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

This paper tackles the problem of Lipschitz regularization of Convolutional Neural Networks. Lipschitz regularity is now established as a key property of modern deep learning with implications in training stability, generalization, robustness against adversarial examples, etc. However, computing the exact value of the Lipschitz constant of a neural network is known to be NP-hard. Recent attempts from the literature introduce upper bounds to approximate this constant that are either efficient but loose or accurate but computationally expensive. In this work, by leveraging the theory of Toeplitz matrices, we introduce a new upper bound for convolutional layers that is both tight and easy to compute. Based on this result we devise an algorithm to train Lipschitz regularized Convolutional Neural Networks.

On Lipschitz Regularization of Convolutional Layers Using Toeplitz Matrix Theory

Eye-catching headlines function as the first device to trigger more clicks, bringing reciprocal effect between producers and viewers. Producers can obtain more traffic and profits, and readers can have access to outstanding articles. When generating attractive headlines, it is important to not only capture the attractive content but also follow an eye-catching writtenstyle. In this paper, we propose a Disentanglement-based Attractive Headline Generator (DAHG) that generates headline which captures the attractive content following the attractive style. Concretely, we first devise a disentanglement module to divide the style and content of an attractive prototype headline into latent spaces, with two auxiliary constraints to ensure the two spaces are indeed disentangled. The latent content information is then used to further polish the document representation and help capture the salient part. Finally, the generator takes the polished document as input to generate headline under the guidance of the attractive style.  Extensive experiments on the public Kuaibao dataset show that DAHG achieves state-of-the-art performance.  Human evaluation also demonstrates that DAHG triggers 22% more clicks than existing models.

The Style-Content Duality of Attractiveness: Learning to Write Eye-Catching Headlines via Disentanglement

Ad creatives are one of the prominent mediums for online e-commerce advertisements. Ad creatives with enjoyable visual appearance may increase the click-through rate (CTR) of products. Ad creatives are typically handcrafted by advertisers and then delivered to the advertising platforms for advertisement. In recent years, advertising platforms are capable of instantly compositing ad creatives with arbitrarily designated elements of each ingredient, so advertisers are only required to provide basic materials. While facilitating the advertisers, a great number of potential ad creatives can be composited, making it difficult to accurately estimate CTR for them given limited real-time feedback. To this end, we propose an Adaptive and Efficient ad creative Selection (AES) framework based on a tree structure. The tree structure on compositing ingredients enables dynamic programming for efficient ad creative selection on the basis of CTR. Due to limited feedback, the CTR estimator is usually of high variance. Exploration techniques based on Thompson sampling are widely used for reducing variances of the CTR estimator, alleviating feedback sparsity. Based on the tree structure, Thompson sampling is adapted with dynamic programming, leading to efficient exploration for potential ad creatives with the largest CTR. We finally evaluate the proposed algorithm on the synthetic dataset and the real-world dataset. The results show that our approach can outperform competing baselines in terms of convergence rate and overall CTR.

Efficient Optimal Selection for Composited Advertising Creatives with Tree Structure

Exploration-exploitation is a powerful and practical tool in multi-agent learning (MAL), however, its effects are far from understood. To make progress in this direction, we study a smooth analogue of Q-learning. We start by showing that our learning model has strong theoretical justification as an optimal model for studying exploration-exploitation. Specifically, we prove that smooth Q-learning has bounded regret in arbitrary games for a cost model that explicitly captures the balance between game and exploration costs and that it always converges to the set of quantal-response equilibria (QRE), the standard solution concept for games under bounded rationality, in weighted potential games with heterogeneous learning agents. In our main task, we then turn to measure the effect of exploration in collective system performance. We characterize the geometry of the QRE surface in low-dimensional MAL systems and link our findings with catastrophe (bifurcation) theory. In particular, as the exploration hyperparameter evolves over-time, the system undergoes phase transitions where the number and stability of equilibria can change radically given an infinitesimal change to the exploration parameter. Based on this, we provide a formal theoretical treatment of how tuning the exploration parameter can provably lead to equilibrium selection with both positive as well as negative (and potentially unbounded) effects to system performance.

Exploration-Exploitation in Multi-Agent Learning: Catastrophe Theory Meets Game Theory

In a collective decision-making process, having the possibility to provide non-expert agents with a justification for why a target outcome is a good compromise given their individual preferences, is an appealing idea. Such questions have recently been addressed in the computational social choice community at large---whether it was to explain the outcomes of a specific rule in voting theory or to seek transparency and accountability in multi-criteria decision making. Ultimately, the development of real-life applications based on these notions depends on their practical feasibility and on the scalability of the approach taken. In this paper, we provide computational complexity results that address the problem of finding and verifying justifications for collective decisions.

In particular, we focus on the recent development of a general notion of justification for outcomes in voting theory. Such a justification consists of a step-by-step explanation, grounded in a normative basis, showing how the selection of the target outcome follows from the normative principles considered. We consider a language in which normative principles can be encoded---either as an explicit list of instances of the principles (by means of quantifier-free sentences), or in a succinct fashion (using quantifiers). We then analyse the computational complexity of identifying and checking justifications. For the case where the normative principles are given in the form of a list of instances, verifying the correctness of a justification is DP-complete and deciding on the existence of such a justification is complete for Sigma 2 P. For the case where the normative principles are given succinctly, deciding whether a justification is correct is in NEXP wedge coNEXP, and NEXP-hard, and deciding whether a justification exists is in EXP with access to an NP oracle  and is NEXP-hard.

On the Complexity of Finding Justifications for Collective Decisions

We address the problem of performing Principal Component Analysis over a family of probability measures on the real line, using the Wasserstein geometry. We present a novel representation of the 2-Wasserstein space, based on a well known isometric bijection and a B-spline expansion. Thanks to this representation, we are able to reinterpret previous work and derive more efficient optimization routines for existing approaches. As shown in our simulations, the solution of these optimization problems can be costly in practice and thus pose a limit to their usage. We propose a novel definition of Principal Component Analysis in the Wasserstein space that, when used in combination with the B-spline representation, yields a straightforward optimization problem that is extremely fast to compute. Through extensive simulation studies, we show how our PCA performs similarly to the ones already proposed in the literature while retaining a much smaller computational cost. We apply our method to a real dataset of mortality rates due to Covid-19 in the US, concluding that our analyses are consistent with the current scientific consensus on the disease.

Fast PCA in 1-D Wasserstein Spaces via B-splines Representation and Metric Projection

Generalized Zero-Shot Learning (GZSL) targets recognizing new categories by learning transferable image representations. Existing methods find that, by aligning image representations with corresponding semantic labels, the semantic-aligned representations can be transferred to unseen categories. However, supervised by only seen category labels, the learned semantic knowledge is highly task-specific, which makes image representations biased towards seen categories. In this paper, we propose a novel Dual-Contrastive Embedding Network (DCEN) that simultaneously learns task-specific and task-independent knowledge via semantic alignment and instance discrimination. First, DCEN leverages task labels to cluster representations of the same semantic category by cross-modal contrastive learning and exploring semantic-visual complementarity. Besides task-specific knowledge, DCEN then introduces task-independent knowledge by attracting representations of different views of the same image and repelling representations of different images. Compared to high-level seen category supervision, this instance discrimination supervision encourages DCEN to capture low-level visual knowledge, which is less biased toward seen categories and alleviates the representation bias. Consequently, the task-specific and task-independent knowledge jointly make for transferable representations of DCEN, which obtains averaged 4.1% improvement on four public benchmarks.

Task-Independent Knowledge Makes for Transferable Representations for Generalized Zero-Shot Learning

In stochastic contextual bandit (SCB) problems, an agent selects an action based on certain observed context to maximize the cumulative reward over iterations. Recently there have been a few studies using a deep neural network (DNN) to predict the expected reward for an action, and the DNN is trained by a stochastic gradient based method. However, convergence analysis has been greatly ignored to examine whether and where these methods converge. In this work, we formulate the SCB that uses a DNN reward function as a non-convex stochastic optimization problem, and design a stage-wised stochastic gradient descent algorithm to optimize the problem and determine the action policy. We prove that with high probability, the action sequence chosen by our algorithm converges to a greedy action policy respecting a local optimal reward function. Extensive experiments have been performed to demonstrate the effectiveness and efficiency of the proposed algorithm on multiple real-world datasets.

An Efficient Algorithm for Deep Stochastic Contextual Bandits

In social choice there often arises a conflict between the majority principle (the search for a candidate that is as good as possible for as many voters as possible), and the protection of minority rights (choosing a candidate that is not overly bad for particular individuals or groups). In a context where the latter is our main concern, veto-based rules -- giving individuals or groups the ability to strike off certain candidates from the list -- are a natural and effective way of ensuring that no minority is left with an outcome they find untenable. However, such rules often fail to be anonymous, or impose specific restrictions on the number of voters and candidates. These issues can be addressed by considering the proportional veto core -- the solution to a cooperative game where every coalition is given the power to veto a number of candidates proportional to its size. However, the naive algorithm for the veto core is exponential, and the only known rules for selecting from the veto core, with an arbitrary number of voters, violate either anonymity or neutrality. In this paper we present a polynomial time algorithm for computing the veto core and present a neutral and anonymous algorithm for selecting a candidate from it. We also show that a pessimist can manipulate the veto core in polynomial time.

Computing the Proportional Veto Core

This paper investigates the indistinguishable points (difficult to predict label) in semantic segmentation for large-scale 3D point clouds. The indistinguishable points consist of those located in complex boundary, points with similar local textures but different categories, and points in isolate small hard areas, which largely harm the performance of 3D semantic segmentation. To address this challenge, we propose a novel Indistinguishable Area Focalization Network (IAF-Net), which select indistinguishable points adaptively by utilizing the hierarchical semantic features and enhance fine-grained features for points especially those indistinguishable points. We also introduce multi-stage loss to improve the feature representation in a progressive way. Moreover, in order to analyze the segmentation performances of indistinguishable areas, we propose a new evaluation metric called Indistinguishable Points Based Metric (IPBM). Our IAF-Net achieves the state-of-the-art performance on several popular 3D point datasets e.g. S3DIS and ScanNet, and clearly outperform other methods on IPBM. Our code will be available at  https://github.com/MingyeXu/IAF-Net.

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On Lipschitz Regularization of Convolutional Layers Using Toeplitz Matrix Theory

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