Mechanism Design

Optimization over trained machine learning models has applications including: verification, minimizing neural acquisition functions, and integrating a trained surrogate into a larger decision-making problem. This paper formulates and solves optimization problems constrained by trained graph neural networks (GNNs). To circumvent the symmetry issue caused by graph isomorphism, we propose two types of symmetry-breaking constraints: one indexing a node 0 and one indexing the remaining nodes by lexicographically ordering their neighbor sets. To guarantee that adding these constraints will not remove all symmetric solutions, we construct a graph indexing algorithm and prove that the resulting graph indexing satisfies the proposed symmetry-breaking constraints. For the classical GNN architectures considered in this paper, optimizing over a GNN with a fixed graph is equivalent to optimizing over a dense neural network. Thus, we study the case where the input graph is not fixed, implying that each edge is a decision variable, and develop two mixed-integer optimization formulations. To test our symmetry-breaking strategies and optimization formulations, we consider an application in molecular design.

Online A/B tests have become increasingly popular and important for social platforms. However, accurately estimating the global average treatment effect (GATE) has proven to be challenging due to network interference, which violates the Stable Unit Treatment Value Assumption (SUTVA) and poses great challenge to experimental design. Existing network experimental design research was mostly based on the unbiased Horvitz-Thompson (HT) estimator with substantial data trimming to ensure unbiasedness at the price of high resultant estimation variance. In this paper, we strive to balance the bias and variance in designing randomized network experiments. Under a potential outcome model with 1-hop interference, we derive the bias and variance of the standard HT estimator and reveal their relation to the network topological structure and the covariance of the treatment assignment vector. We then propose to formulate the experimental design problem as to optimize the covariance matrix of the treatment assignment vector to achieve the bias and variance balance by minimizing the mean squared error (MSE) of the estimator. An efficient projected gradient descent algorithm is presented to the implement of the desired randomization scheme. Finally, we carry out extensive simulation studies to demonstrate the advantages of our proposed method over other existing methods in many settings, with different levels of model misspecification.

The ResNet architecture has been widely adopted in deep learning due to its significant boost to performance through the use of simple skip connections, yet the underlying mechanisms leading to its success remain largely unknown. In this paper, we conduct a thorough empirical study of the ResNet architecture in classification tasks by linearizing its constituent residual blocks using Residual Jacobians and measuring their singular value decompositions. Our measurements ([code](https://colab.research.google.com/drive/1yKjEg2yF616tnZFAfuN0aQ-E9v3JmyjN?usp=sharing)) reveal a process called Residual Alignment (RA) characterized by four properties: - **(RA1):** intermediate representations of a given input are *equispaced* on a *line*, embedded in high dimensional space, as observed by Gai and Zhang [2021]; - **(RA2):** top left and right singular vectors of Residual Jacobians align with each other and across different depths; - **(RA3):** Residual Jacobians are at most rank $C$ for fully-connected ResNets, where $C$ is the number of classes; and - **(RA4):** top singular values of Residual Jacobians scale inversely with depth. RA consistently occurs in models that generalize well, in both fully-connected and convolutional architectures, across various depths and widths, for varying numbers of classes, on all tested benchmark datasets, but ceases to occur once the skip connections are removed. It also provably occurs in a novel mathematical model we propose. This phenomenon reveals a strong alignment between residual branches of a ResNet (RA2+4), imparting a highly rigid geometric structure to the intermediate representations as they progress *linearly* through the network (RA1) up to the final layer, where they undergo Neural Collapse.

We introduce a new approach for computing optimal equilibria via learning in games. It applies to extensive-form settings with any number of players, including mechanism design, information design, and solution concepts such as correlated, communication, and certification equilibria. We observe that optimal equilibria are minimax equilibrium strategies of a player in an extensive-form zero-sum game. This reformulation allows to apply techniques for learning in zero-sum games, yielding the first learning dynamics that converge to optimal equilibria, not only in empirical averages, but also in iterates. We demonstrate the practical scalability and flexibility of our approach by attaining state-of-the-art performance in benchmark tabular games, and by computing an optimal mechanism for a sequential auction design problem using deep reinforcement learning.

We study collaborative normal mean estimation, where $m$ strategic agents collect i.i.d samples from a normal distribution $\mathcal{N}(\mu, \sigma^2)$ at a cost. They all wish to estimate the mean $\mu$. By sharing data with each other, agents can obtain better estimates while keeping the cost of data collection small. To facilitate this collaboration, we wish to design mechanisms that encourage agents to collect a sufficient amount of data and share it truthfully, so that they are all better off than working alone. In naive mechanisms, such as simply pooling and sharing all the data, an individual agent might find it beneficial to under-collect and/or fabricate data, which can lead to poor social outcomes. We design a novel mechanism that overcomes these challenges via two key techniques: first, when sharing the others' data with an agent, the mechanism corrupts this dataset proportional to how much the data reported by the agent differs from the others; second, we design minimax optimal estimators for the corrupted dataset. Our mechanism, which is Nash incentive compatible and individually rational, achieves a social penalty (sum of all agents' estimation errors and data collection costs) that is at most a factor 2 of the global minimum. When applied to high dimensional (non-Gaussian) distributions with bounded variance, this mechanism retains these three properties, but with slightly weaker results. Finally, in two special cases where we restrict the strategy space of the agents, we design mechanisms that essentially achieve the global minimum.

The past decade has witnessed the flourishing of a new profession as media content creators, who rely on revenue streams from online content recommendation platforms. The reward mechanism employed by these platforms creates a competitive environment among creators which affects their production choices and, consequently, content distribution and system welfare. It is thus crucial to design the platform's reward mechanism in order to steer the creators' competition towards a desirable welfare outcome in the long run. This work makes two major contributions in this regard: first, we uncover a fundamental limit about a class of widely adopted mechanisms, coined \emph{Merit-based Monotone Mechanisms}, by showing that they inevitably lead to a constant fraction loss of the optimal welfare. To circumvent this limitation, we introduce \emph{Backward Rewarding Mechanisms} (BRMs) and show that the competition game resultant from BRMs possesses a potential game structure. BRMs thus naturally induce strategic creators' collective behaviors towards optimizing the potential function, which can be designed to match any given welfare metric. In addition, the class of BRM can be parameterized so that it allows the platform to directly optimize welfare within the feasible mechanism space even when the welfare metric is not explicitly defined.

Data valuation, a principled way to rank the importance of each training datum, has become increasingly important. However, existing value-based approaches (e.g., Shapley) are known to suffer from the stochasticity inherent in utility functions that render consistent and reliable ranking difficult. Recently, Wang and Jia (2023) proposed the noise-structure-agnostic framework to advocate the Banzhaf value for its robustness against such stochasticity as it achieves the largest safe margin among many alternatives. Surprisingly, our empirical study shows that the Banzhaf value is not always the most robust when compared with a broader family: weighted Banzhaf values. To analyze this scenario, we introduce the concept of Kronecker noise to parameterize stochasticity, through which we prove that the uniquely robust semi-value, which can be analytically derived from the underlying Kronecker noise, lies in the family of weighted Banzhaf values while minimizing the worst-case entropy. In addition, we adopt the maximum sample reuse principle to design an estimator to efficiently approximate weighted Banzhaf values, and show that it enjoys the best time complexity in terms of achieving an $(\epsilon, \delta)$-approximation. Our theory is verified under both synthetic and authentic noises. For the latter, we fit a Kronecker noise to the inherent stochasticity, which is then plugged in to generate the predicted most robust semi-value. Our study suggests that weighted Banzhaf values are promising when facing undue noises in data valuation.

Vision-based emergent communication (EC) aims to learn to communicate through sketches and demystify the evolution of human communication. Ironically, previous works neglect multi-round interaction, which is indispensable in human communication. To fill this gap, we first introduce a novel Interactive Sketch Question Answering (ISQA) task, where two collaborative players are interacting through sketches to answer a question about an image. To accomplish this task, we design a new and efficient interactive EC system, which can achieve an effective balance among three evaluation factors, including the question answering accuracy, drawing complexity and human interpretability. Our experimental results demonstrate that multi-round interactive mechanism facilitates tar- geted and efficient communication between intelligent agents. The code will be released.

The _data market design_ problem is a problem in economic theory to find a set of signaling schemes (statistical experiments) to maximize expected revenue to the information seller, where each experiment reveals some of the information known to a seller and has a corresponding price. Each buyer has their own decision to make in a world environment, and their subjective expected value for the information associated with a particular experiment comes from the improvement in this decision and depends on their prior and value for different outcomes. In a setting with multiple buyers, a buyer's expected value for an experiment may also depend on the information sold to others. We introduce the application of deep learning for the design of revenue-optimal data markets, looking to expand the frontiers of what can be understood and achieved. Relative to earlier work on deep learning for auction design, we must learn signaling schemes rather than allocation rules and handle _obedience constraints_ — these arising from modeling the downstream actions of buyers — in addition to incentive constraints on bids. Our experiments demonstrate that this new deep learning framework can almost precisely replicate all known solutions from theory, expand to more complex settings, and be used to establish the optimality of new designs for data markets and make conjectures in regard to the structure of optimal designs.

The limited availability of annotations in small molecule datasets presents a challenge to machine learning models. To address this, one common strategy is to collaborate with additional auxiliary datasets. However, having more data does not always guarantee improvements. Negative transfer can occur when the knowledge in the target dataset differs or contradicts that of the auxiliary molecule datasets. In light of this, identifying the auxiliary molecule datasets that can benefit the target dataset when jointly trained remains a critical and unresolved problem. Through an empirical analysis, we observe that combining graph structure similarity and task similarity can serve as a more reliable indicator for identifying high-affinity auxiliary datasets. Motivated by this insight, we propose MolGroup, which separates the dataset affinity into task and structure affinity to predict the potential benefits of each auxiliary molecule dataset. MolGroup achieves this by utilizing a routing mechanism optimized through a bi-level optimization framework. Empowered by the meta gradient, the routing mechanism is optimized toward maximizing the target dataset's performance and quantifies the affinity as the gating score. As a result, MolGroup is capable of predicting the optimal combination of auxiliary datasets for each target dataset. Our extensive experiments demonstrate the efficiency and effectiveness of MolGroup, showing an average improvement of 4.41%/3.47% for GIN/Graphormer trained with the group of molecule datasets selected by MolGroup on 11 target molecule datasets.

We study the problem of designing mechanisms when agents' valuation functions are drawn from unknown and correlated prior distributions. In particular, we are given a prior distribution $D$, and we are interested in designing a (truthful) mechanism that has good performance for all "true distributions" that are close to $D$ in Total Variation (TV) distance. We show that DSIC and BIC mechanisms in this setting are strongly robust with respect to TV distance, for any bounded objective function $\mathcal{O}$, extending a recent result of Brustle et al. ([BCD20], EC 2020). At the heart of our result is a fundamental duality property of total variation distance. As direct applications of our result, we (i) demonstrate how to find approximately revenue-optimal and approximately BIC mechanisms for weakly dependent prior distributions; (ii) show how to find correlation-robust mechanisms when only ``noisy'' versions of marginals are accessible, extending recent results of Bei et. al. ([BGLT19], SODA 2019); (iii) prove that prophet-inequality type guarantees are preserved for correlated priors, recovering a variant of a result of D{\"u}tting and Kesselheim ([DK19], EC 2019) as a special case; (iv) give a new necessary condition for a correlated distribution to witness an infinite separation in revenue between simple and optimal mechanisms, complementing recent results of Psomas et al. ([PSCW22], NeurIPS 2022); (v) give a new condition for simple mechanisms to approximate revenue-optimal mechanisms for the case of a single agent whose type is drawn from a correlated distribution that can be captured by a Markov Random Field, complementing recent results of Cai and Oikonomou ([CO21], EC 2021).

Continual learning (CL) has remained a persistent challenge for deep neural networks due to catastrophic forgetting (CF) of previously learned tasks. Several techniques such as weight regularization, experience rehearsal, and parameter isolation have been proposed to alleviate CF. Despite their relative success, these research directions have predominantly remained orthogonal and suffer from several shortcomings, while missing out on the advantages of competing strategies. On the contrary, the brain continually learns, accommodates, and transfers knowledge across tasks by simultaneously leveraging several neurophysiological processes, including neurogenesis, active forgetting, neuromodulation, metaplasticity, experience rehearsal, and context-dependent gating, rarely resulting in CF. Inspired by how the brain exploits multiple mechanisms concurrently, we propose TriRE, a novel CL paradigm that encompasses retaining the most prominent neurons for each task, revising and solidifying the extracted knowledge of current and past tasks, and actively promoting less active neurons for subsequent tasks through rewinding and relearning. Across CL settings, TriRE significantly reduces task interference and surpasses different CL approaches considered in isolation.

Contract design involves a principal who establishes contractual agreements about payments for outcomes that arise from the actions of an agent. In this paper, we initiate the study of deep learning for the automated design of optimal contracts. We introduce a novel representation: the Discontinuous ReLU (DeLU) network, which models the principal's utility as a discontinuous piecewise affine function of the design of a contract where each piece corresponds to the agent taking a particular action. DeLU networks implicitly learn closed-form expressions for the incentive compatibility constraints of the agent and the utility maximization objective of the principal, and support parallel inference on each piece through linear programming or interior-point methods that solve for optimal contracts. We provide empirical results that demonstrate success in approximating the principal's utility function with a small number of training samples and scaling to find approximately optimal contracts on problems with a large number of actions and outcomes.

We revisit the classical problem of designing Budget-Feasible Mechanisms (BFMs) for submodular valuation functions, which has been extensively studied since the seminal paper of Singer [FOCS’10] due to its wide applications in crowdsourcing and social marketing. We propose TripleEagle, a novel algorithmic framework for designing BFMs, based on which we present several simple yet effective BFMs that achieve better approximation ratios than the state-of-the-art work for both monotone and non-monotone submodular valuation functions. Moreover, our BFMs are the first in the literature to achieve linear complexities while ensuring obvious strategyproofness, making them more practical than the previous BFMs. We conduct extensive experiments to evaluate the empirical performance of our BFMs, and the experimental results strongly demonstrate the efficiency and effectiveness of our approach.

With the advent of deep learning, progressively larger neural networks have been designed to solve complex tasks. We take advantage of these capacity-rich models to lower the cost of inference by exploiting computation in superposition. To reduce the computational burden per input, we propose Multiple-Input-Multiple-Output Neural Networks (MIMONets) capable of handling many inputs at once. MIMONets augment various deep neural network architectures with variable binding mechanisms to represent an arbitrary number of inputs in a compositional data structure via fixed-width distributed representations. Accordingly, MIMONets adapt nonlinear neural transformations to process the data structure holistically, leading to a speedup nearly proportional to the number of superposed input items in the data structure. After processing in superposition, an unbinding mechanism recovers each transformed input of interest. MIMONets also provide a dynamic trade-off between accuracy and throughput by an instantaneous on-demand switching between a set of accuracy-throughput operating points, yet within a single set of fixed parameters. We apply the concept of MIMONets to both CNN and Transformer architectures resulting in MIMOConv and MIMOFormer, respectively. Empirical evaluations show that MIMOConv achieves $\approx 2$–$4\times$ speedup at an accuracy delta within [+0.68, -3.18]% compared to WideResNet CNNs on CIFAR10 and CIFAR100. Similarly, MIMOFormer can handle $2$–$4$ inputs at once while maintaining a high average accuracy within a [-1.07, -3.43]% delta on the long range arena benchmark. Finally, we provide mathematical bounds on the interference between superposition channels in MIMOFormer. Our code is available at https://github.com/IBM/multiple-input-multiple-output-nets.

Particle-based variational inference methods (ParVIs) such as Stein variational gradient descent (SVGD) update the particles based on the kernelized Wasserstein gradient flow for the Kullback-Leibler (KL) divergence. However, the design of kernels is often non-trivial and can be restrictive for the flexibility of the method. Recent works show that functional gradient flow approximations with quadratic form regularization terms can improve performance. In this paper, we propose a ParVI framework, called generalized Wasserstein gradient descent (GWG), based on a generalized Wasserstein gradient flow of the KL divergence, which can be viewed as a functional gradient method with a broader class of regularizers induced by convex functions. We show that GWG exhibits strong convergence guarantees. We also provide an adaptive version that automatically chooses Wasserstein metric to accelerate convergence. In experiments, we demonstrate the effectiveness and efficiency of the proposed framework on both simulated and real data problems.

In the past years, YOLO-series models have emerged as the leading approaches in the area of real-time object detection. Many studies pushed up the baseline to a higher level by modifying the architecture, augmenting data and designing new losses. However, we find previous models still suffer from information fusion problem, although Feature Pyramid Network (FPN) and Path Aggregation Network (PANet) have alleviated this. Therefore, this study provides an advanced Gatherand-Distribute mechanism (GD) mechanism, which is realized with convolution and self-attention operations. This new designed model named as Gold-YOLO, which boosts the multi-scale feature fusion capabilities and achieves an ideal balance between latency and accuracy across all model scales. Additionally, we implement MAE-style pretraining in the YOLO-series for the first time, allowing YOLOseries models could be to benefit from unsupervised pretraining. Gold-YOLO-N attains an outstanding 39.9% AP on the COCO val2017 datasets and 1030 FPS on a T4 GPU, which outperforms the previous SOTA model YOLOv6-3.0-N with similar FPS by +2.4%. The PyTorch code is available at https://github.com/huawei-noah/Efficient-Computing/tree/master/Detection/Gold-YOLO, and the MindSpore code is available at https://gitee.com/mindspore/models/tree/master/research/cv/Gold_YOLO.

In this work, we decouple the iterative bi-level offline RL (value estimation and policy extraction) from the offline training phase, forming a non-iterative bi-level paradigm and avoiding the iterative error propagation over two levels. Specifically, this non-iterative paradigm allows us to conduct inner-level optimization (value estimation) in training, while performing outer-level optimization (policy extraction) in testing. Naturally, such a paradigm raises three core questions that are not fully answered by prior non-iterative offline RL counterparts like reward-conditioned policy: (q1) What information should we transfer from the inner-level to the outer-level? (q2) What should we pay attention to when exploiting the transferred information for safe/confident outer-level optimization? (q3) What are the benefits of concurrently conducting outer-level optimization during testing? Motivated by model-based optimization (MBO), we propose DROP (design from policies), which fully answers the above questions. Specifically, in the inner-level, DROP decomposes offline data into multiple subsets, and learns an MBO score model (a1). To keep safe exploitation to the score model in the outer-level, we explicitly learn a behavior embedding and introduce a conservative regularization (a2). During testing, we show that DROP permits deployment adaptation, enabling an adaptive inference across states (a3). Empirically, we evaluate DROP on various tasks, showing that DROP gains comparable or better performance compared to prior methods.

The efficient exploration of chemical space to design molecules with intended properties enables the accelerated discovery of drugs, materials, and catalysts, and is one of the most important outstanding challenges in chemistry. Encouraged by the recent surge in computer power and artificial intelligence development, many algorithms have been developed to tackle this problem. However, despite the emergence of many new approaches in recent years, comparatively little progress has been made in developing realistic benchmarks that reflect the complexity of molecular design for real-world applications. In this work, we develop a set of practical benchmark tasks relying on physical simulation of molecular systems mimicking real-life molecular design problems for materials, drugs, and chemical reactions. Additionally, we demonstrate the utility and ease of use of our new benchmark set by demonstrating how to compare the performance of several well-established families of algorithms. Overall, we believe that our benchmark suite will help move the field towards more realistic molecular design benchmarks, and move the development of inverse molecular design algorithms closer to the practice of designing molecules that solve existing problems in both academia and industry alike.

Therapeutic antibodies are an essential and rapidly flourishing drug modality. The binding specificity between antibodies and antigens is decided by complementarity-determining regions (CDRs) at the tips of these Y-shaped proteins. In this paper, we propose a \textbf{h}ierarchical \textbf{t}raining \textbf{p}aradigm (HTP) for the antibody sequence-structure co-design. HTP consists of four levels of training stages, each corresponding to a specific protein modality within a particular protein domain. Through carefully crafted tasks in different stages, HTP seamlessly and effectively integrates geometric graph neural networks (GNNs) with large-scale protein language models to excavate evolutionary information from not only geometric structures but also vast antibody and non-antibody sequence databases, which determines ligand binding pose and strength. Empirical experiments show HTP sets the new state-of-the-art performance in the co-design problem as well as the fix-backbone design. Our research offers a hopeful path to unleash the potential of deep generative architectures and seeks to illuminate the way forward for the antibody sequence and structure co-design challenge.