pwc-archive/papers-with-abstracts huggingface dataset:
P-split formulations: A class of intermediate formulations between big-M and convex hull for disjunctive constraints
Authors: Jan Kronqvist, Ruth Misener, Calvin Tsay
Date: 2022-02-10 00:00:00
Tasks: Clustering

We develop a class of mixed-integer formulations for disjunctive constraints intermediate to the big-M and convex hull formulations in terms of relaxation strength. The main idea is to capture the best of both the big-M and convex hull formulations: a computationally light formulation with a tight relaxation. The "P-split" formulations are based on a lifted transformation that splits convex additively separable constraints into P partitions and forms the convex hull of the linearized and partitioned disjunction. The "P-split" formulations are derived for disjunctive constraints with convex constraints within each disjunct, and we generalize the results for the case with nonconvex constraints within the disjuncts. We analyze the continuous relaxation of the P-split formulations and show that, under certain assumptions, the formulations form a hierarchy starting from a big-M equivalent and converging to the convex hull. We computationally compare the P-split formulations against big-M and convex hull formulations on 344 test instances. The test problems include K-means clustering, semi-supervised clustering, P_ball problems, and optimization over trained ReLU neural networks. The computational results show promising potential of the P-split formulations. For many of the test problems, P-split formulations are solved with a similar number of explored nodes as the convex hull formulation, while reducing the solution time by an order of magnitude and outperforming big-M both in time and number of explored nodes.
Suboptimal Performance of the Bayes Optimal Algorithm in Frequentist Best Arm Identification
Authors: Junpei Komiyama
Date: 2022-02-10 00:00:00

We consider the fixed-budget best arm identification problem with rewards following normal distributions. In this problem, the forecaster is given $K$ arms (or treatments) and $T$ time steps. The forecaster attempts to find the arm with the largest mean, via an adaptive experiment conducted using an algorithm. The algorithm's performance is evaluated by simple regret, reflecting the quality of the estimated best arm. While frequentist simple regret can decrease exponentially with respect to $T$, Bayesian simple regret decreases polynomially. This paper demonstrates that the Bayes optimal algorithm, which minimizes the Bayesian simple regret, does not yield an exponential decrease in simple regret under certain parameter settings. This contrasts with the numerous findings that suggest the asymptotic equivalence of Bayesian and frequentist approaches in fixed sampling regimes. Although the Bayes optimal algorithm is formulated as a recursive equation that is virtually impossible to compute exactly, we lay the groundwork for future research by introducing a novel concept termed the expected Bellman improvement.
Remote Contextual Bandits
Authors: Francesco Pase, Deniz Gunduz, Michele Zorzi
Date: 2022-02-10 00:00:00
Tasks: Marketing, Multi-Armed Bandits, Thompson Sampling

We consider a remote contextual multi-armed bandit (CMAB) problem, in which the decision-maker observes the context and the reward, but must communicate the actions to be taken by the agents over a rate-limited communication channel. This can model, for example, a personalized ad placement application, where the content owner observes the individual visitors to its website, and hence has the context information, but must convey the ads that must be shown to each visitor to a separate entity that manages the marketing content. In this remote CMAB (R-CMAB) problem, the constraint on the communication rate between the decision-maker and the agents imposes a trade-off between the number of bits sent per agent and the acquired average reward. We are particularly interested in characterizing the rate required to achieve sub-linear regret. Consequently, this can be considered as a policy compression problem, where the distortion metric is induced by the learning objectives. We first study the fundamental information theoretic limits of this problem by letting the number of agents go to infinity, and study the regret achieved when Thompson sampling strategy is adopted. In particular, we identify two distinct rate regions resulting in linear and sub-linear regret behavior, respectively. Then, we provide upper bounds on the achievable regret when the decision-maker can reliably transmit the policy without distortion.
Game of Privacy: Towards Better Federated Platform Collaboration under Privacy Restriction
Authors: Chuhan Wu, Fangzhao Wu, Tao Qi, Yanlin Wang, Yuqing Yang, Yongfeng Huang, Xing Xie
Date: 2022-02-10 00:00:00
Tasks: Federated Learning, Vertical Federated Learning

Vertical federated learning (VFL) aims to train models from cross-silo data with different feature spaces stored on different platforms. Existing VFL methods usually assume all data on each platform can be used for model training. However, due to the intrinsic privacy risks of federated learning, the total amount of involved data may be constrained. In addition, existing VFL studies usually assume only one platform has task labels and can benefit from the collaboration, making it difficult to attract other platforms to join in the collaborative learning. In this paper, we study the platform collaboration problem in VFL under privacy constraint. We propose to incent different platforms through a reciprocal collaboration, where all platforms can exploit multi-platform information in the VFL framework to benefit their own tasks. With limited privacy budgets, each platform needs to wisely allocate its data quotas for collaboration with other platforms. Thereby, they naturally form a multi-party game. There are two core problems in this game, i.e., how to appraise other platforms' data value to compute game rewards and how to optimize policies to solve the game. To evaluate the contributions of other platforms' data, each platform offers a small amount of "deposit" data to participate in the VFL. We propose a performance estimation method to predict the expected model performance when involving different amount combinations of inter-platform data. To solve the game, we propose a platform negotiation method that simulates the bargaining among platforms and locally optimizes their policies via gradient descent. Extensive experiments on two real-world datasets show that our approach can effectively facilitate the collaborative exploitation of multi-platform data in VFL under privacy restrictions.
Quantization in Layer's Input is Matter
Authors: Daning Cheng, WenGuang Chen
Date: 2022-02-10 00:00:00
Tasks: Quantization

In this paper, we will show that the quantization in layer's input is more important than parameters' quantization for loss function. And the algorithm which is based on the layer's input quantization error is better than hessian-based mixed precision layout algorithm.
Group-Agent Reinforcement Learning
Authors: Kaiyue Wu, Xiao-jun Zeng
Date: 2022-02-10 00:00:00
Tasks: Multi-agent Reinforcement Learning, reinforcement-learning, Reinforcement Learning, Reinforcement Learning (RL)

It can largely benefit the reinforcement learning (RL) process of each agent if multiple geographically distributed agents perform their separate RL tasks cooperatively. Different from multi-agent reinforcement learning (MARL) where multiple agents are in a common environment and should learn to cooperate or compete with each other, in this case each agent has its separate environment and only communicates with others to share knowledge without any cooperative or competitive behaviour as a learning outcome. In fact, this scenario exists widely in real life whose concept can be utilised in many applications, but is not well understood yet and not well formulated. As the first effort, we propose group-agent system for RL as a formulation of this scenario and the third type of RL system with respect to single-agent and multi-agent systems. We then propose a distributed RL framework called DDAL (Decentralised Distributed Asynchronous Learning) designed for group-agent reinforcement learning (GARL). We show through experiments that DDAL achieved desirable performance with very stable training and has good scalability.
Low-Rank Approximation with $1/ε^{1/3}$ Matrix-Vector Products
Authors: Ainesh Bakshi, Kenneth L. Clarkson, David P. Woodruff
Date: 2022-02-10 00:00:00

We study iterative methods based on Krylov subspaces for low-rank approximation under any Schatten-$p$ norm. Here, given access to a matrix $A$ through matrix-vector products, an accuracy parameter $\epsilon$, and a target rank $k$, the goal is to find a rank-$k$ matrix $Z$ with orthonormal columns such that $\| A(I -ZZ^\top)\|_{S_p} \leq (1+\epsilon)\min_{U^\top U = I_k} \|A(I - U U^\top)\|_{S_p}$, where $\|M\|_{S_p}$ denotes the $\ell_p$ norm of the the singular values of $M$. For the special cases of $p=2$ (Frobenius norm) and $p = \infty$ (Spectral norm), Musco and Musco (NeurIPS 2015) obtained an algorithm based on Krylov methods that uses $\tilde{O}(k/\sqrt{\epsilon})$ matrix-vector products, improving on the na\"ive $\tilde{O}(k/\epsilon)$ dependence obtainable by the power method, where $\tilde{O}$ suppresses poly$(\log(dk/\epsilon))$ factors. Our main result is an algorithm that uses only $\tilde{O}(kp^{1/6}/\epsilon^{1/3})$ matrix-vector products, and works for all $p \geq 1$. For $p = 2$ our bound improves the previous $\tilde{O}(k/\epsilon^{1/2})$ bound to $\tilde{O}(k/\epsilon^{1/3})$. Since the Schatten-$p$ and Schatten-$\infty$ norms are the same up to a $(1+ \epsilon)$-factor when $p \geq (\log d)/\epsilon$, our bound recovers the result of Musco and Musco for $p = \infty$. Further, we prove a matrix-vector query lower bound of $\Omega(1/\epsilon^{1/3})$ for any fixed constant $p \geq 1$, showing that surprisingly $\tilde{\Theta}(1/\epsilon^{1/3})$ is the optimal complexity for constant~$k$. To obtain our results, we introduce several new techniques, including optimizing over multiple Krylov subspaces simultaneously, and pinching inequalities for partitioned operators. Our lower bound for $p \in [1,2]$ uses the Araki-Lieb-Thirring trace inequality, whereas for $p>2$, we appeal to a norm-compression inequality for aligned partitioned operators.
Reinforcement Learning in the Wild: Scalable RL Dispatching Algorithm Deployed in Ridehailing Marketplace
Authors: Soheil Sadeghi Eshkevari, Xiaocheng Tang, Zhiwei Qin, Jinhan Mei, Cheng Zhang, Qianying Meng, Jia Xu
Date: 2022-02-10 00:00:00
Tasks: Causal Inference, reinforcement-learning, Reinforcement Learning (RL)

In this study, a real-time dispatching algorithm based on reinforcement learning is proposed and for the first time, is deployed in large scale. Current dispatching methods in ridehailing platforms are dominantly based on myopic or rule-based non-myopic approaches. Reinforcement learning enables dispatching policies that are informed of historical data and able to employ the learned information to optimize returns of expected future trajectories. Previous studies in this field yielded promising results, yet have left room for further improvements in terms of performance gain, self-dependency, transferability, and scalable deployment mechanisms. The present study proposes a standalone RL-based dispatching solution that is equipped with multiple mechanisms to ensure robust and efficient on-policy learning and inference while being adaptable for full-scale deployment. A new form of value updating based on temporal difference is proposed that is more adapted to the inherent uncertainty of the problem. For the driver-order assignment, a customized utility function is proposed that when tuned based on the statistics of the market, results in remarkable performance improvement and interpretability. In addition, for reducing the risk of cancellation after drivers' assignment, an adaptive graph pruning strategy based on the multi-arm bandit problem is introduced. The method is evaluated using offline simulation with real data and yields notable performance improvement. In addition, the algorithm is deployed online in multiple cities under DiDi's operation for A/B testing and is launched in one of the major international markets as the primary mode of dispatch. The deployed algorithm shows over 1.3% improvement in total driver income from A/B testing. In addition, by causal inference analysis, as much as 5.3% improvement in major performance metrics is detected after full-scale deployment.
Probabilistic learning inference of boundary value problem with uncertainties based on Kullback-Leibler divergence under implicit constraints
Authors: Christian Soize
Date: 2022-02-10 00:00:00

In a first part, we present a mathematical analysis of a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a stochastic boundary value problem from a prior probability model. The given targets are statistical moments for which the underlying realizations are not available. Under these conditions, the Kullback-Leibler divergence minimum principle is used for estimating the posterior probability measure. A statistical surrogate model of the implicit mapping, which represents the constraints, is introduced. The MCMC generator and the necessary numerical elements are given to facilitate the implementation of the methodology in a parallel computing framework. In a second part, an application is presented to illustrate the proposed theory and is also, as such, a contribution to the three-dimensional stochastic homogenization of heterogeneous linear elastic media in the case of a non-separation of the microscale and macroscale. For the construction of the posterior probability measure by using the probabilistic learning inference, in addition to the constraints defined by given statistical moments of the random effective elasticity tensor, the second-order moment of the random normalized residue of the stochastic partial differential equation has been added as a constraint. This constraint guarantees that the algorithm seeks to bring the statistical moments closer to their targets while preserving a small residue.
Adaptively Exploiting d-Separators with Causal Bandits
Authors: Blair Bilodeau, Linbo Wang, Daniel M. Roy
Date: 2022-02-10 00:00:00

Multi-armed bandit problems provide a framework to identify the optimal intervention over a sequence of repeated experiments. Without additional assumptions, minimax optimal performance (measured by cumulative regret) is well-understood. With access to additional observed variables that d-separate the intervention from the outcome (i.e., they are a d-separator), recent "causal bandit" algorithms provably incur less regret. However, in practice it is desirable to be agnostic to whether observed variables are a d-separator. Ideally, an algorithm should be adaptive; that is, perform nearly as well as an algorithm with oracle knowledge of the presence or absence of a d-separator. In this work, we formalize and study this notion of adaptivity, and provide a novel algorithm that simultaneously achieves (a) optimal regret when a d-separator is observed, improving on classical minimax algorithms, and (b) significantly smaller regret than recent causal bandit algorithms when the observed variables are not a d-separator. Crucially, our algorithm does not require any oracle knowledge of whether a d-separator is observed. We also generalize this adaptivity to other conditions, such as the front-door criterion.
AD-NEGF: An End-to-End Differentiable Quantum Transport Simulator for Sensitivity Analysis and Inverse Problems
Authors: Yingzhanghao Zhou, Xiang Chen, Peng Zhang, Jun Wang, Lei Wang, Hong Guo
Date: 2022-02-10 00:00:00
Tasks: Sensitivity

Since proposed in the 70s, the Non-Equilibrium Green Function (NEGF) method has been recognized as a standard approach to quantum transport simulations. Although it achieves superiority in simulation accuracy, the tremendous computational cost makes it unbearable for high-throughput simulation tasks such as sensitivity analysis, inverse design, etc. In this work, we propose AD-NEGF, to our best knowledge the first end-to-end differentiable NEGF model for quantum transport simulations. We implement the entire numerical process in PyTorch, and design customized backward pass with implicit layer techniques, which provides gradient information at an affordable cost while guaranteeing the correctness of the forward simulation. The proposed model is validated with applications in calculating differential physical quantities, empirical parameter fitting, and doping optimization, which demonstrates its capacity to accelerate the material design process by conducting gradient-based parameter optimization.
Near-Optimal Statistical Query Lower Bounds for Agnostically Learning Intersections of Halfspaces with Gaussian Marginals
Authors: Daniel Hsu, Clayton Sanford, Rocco Servedio, Emmanouil-Vasileios Vlatakis-Gkaragkounis
Date: 2022-02-10 00:00:00

We consider the well-studied problem of learning intersections of halfspaces under the Gaussian distribution in the challenging \emph{agnostic learning} model. Recent work of Diakonikolas et al. (2021) shows that any Statistical Query (SQ) algorithm for agnostically learning the class of intersections of $k$ halfspaces over $\mathbb{R}^n$ to constant excess error either must make queries of tolerance at most $n^{-\tilde{\Omega}(\sqrt{\log k})}$ or must make $2^{n^{\Omega(1)}}$ queries. We strengthen this result by improving the tolerance requirement to $n^{-\tilde{\Omega}(\log k)}$. This lower bound is essentially best possible since an SQ algorithm of Klivans et al. (2008) agnostically learns this class to any constant excess error using $n^{O(\log k)}$ queries of tolerance $n^{-O(\log k)}$. We prove two variants of our lower bound, each of which combines ingredients from Diakonikolas et al. (2021) with (an extension of) a different earlier approach for agnostic SQ lower bounds for the Boolean setting due to Dachman-Soled et al. (2014). Our approach also yields lower bounds for agnostically SQ learning the class of "convex subspace juntas" (studied by Vempala, 2010) and the class of sets with bounded Gaussian surface area; all of these lower bounds are nearly optimal since they essentially match known upper bounds from Klivans et al. (2008).
Backpropagation Clipping for Deep Learning with Differential Privacy
Authors: Timothy Stevens, Ivoline C. Ngong, David Darais, Calvin Hirsch, David Slater, Joseph P. Near
Date: 2022-02-10 00:00:00
Tasks: Deep Learning, Privacy Preserving, Privacy Preserving Deep Learning, Sensitivity

We present backpropagation clipping, a novel variant of differentially private stochastic gradient descent (DP-SGD) for privacy-preserving deep learning. Our approach clips each trainable layer's inputs (during the forward pass) and its upstream gradients (during the backward pass) to ensure bounded global sensitivity for the layer's gradient; this combination replaces the gradient clipping step in existing DP-SGD variants. Our approach is simple to implement in existing deep learning frameworks. The results of our empirical evaluation demonstrate that backpropagation clipping provides higher accuracy at lower values for the privacy parameter $\epsilon$ compared to previous work. We achieve 98.7% accuracy for MNIST with $\epsilon = 0.07$ and 74% accuracy for CIFAR-10 with $\epsilon = 3.64$.
Cross-speaker style transfer for text-to-speech using data augmentation
Authors: Manuel Sam Ribeiro, Julian Roth, Giulia Comini, Goeric Huybrechts, Adam Gabrys, Jaime Lorenzo-Trueba
Date: 2022-02-10 00:00:00
Tasks: Data Augmentation, Style Transfer, text-to-speech, Text to Speech, Voice Conversion

We address the problem of cross-speaker style transfer for text-to-speech (TTS) using data augmentation via voice conversion. We assume to have a corpus of neutral non-expressive data from a target speaker and supporting conversational expressive data from different speakers. Our goal is to build a TTS system that is expressive, while retaining the target speaker's identity. The proposed approach relies on voice conversion to first generate high-quality data from the set of supporting expressive speakers. The voice converted data is then pooled with natural data from the target speaker and used to train a single-speaker multi-style TTS system. We provide evidence that this approach is efficient, flexible, and scalable. The method is evaluated using one or more supporting speakers, as well as a variable amount of supporting data. We further provide evidence that this approach allows some controllability of speaking style, when using multiple supporting speakers. We conclude by scaling our proposed technology to a set of 14 speakers across 7 languages. Results indicate that our technology consistently improves synthetic samples in terms of style similarity, while retaining the target speaker's identity.
Transfer-Learning Across Datasets with Different Input Dimensions: An Algorithm and Analysis for the Linear Regression Case
Authors: Luis Pedro Silvestrin, Harry van Zanten, Mark Hoogendoorn, Ger Koole
Date: 2022-02-10 00:00:00
Tasks: Transfer Learning

With the development of new sensors and monitoring devices, more sources of data become available to be used as inputs for machine learning models. These can on the one hand help to improve the accuracy of a model. On the other hand, combining these new inputs with historical data remains a challenge that has not yet been studied in enough detail. In this work, we propose a transfer learning algorithm that combines new and historical data with different input dimensions. This approach is easy to implement, efficient, with computational complexity equivalent to the ordinary least-squares method, and requires no hyperparameter tuning, making it straightforward to apply when the new data is limited. Different from other approaches, we provide a rigorous theoretical study of its robustness, showing that it cannot be outperformed by a baseline that utilizes only the new data. Our approach achieves state-of-the-art performance on 9 real-life datasets, outperforming the linear DSFT, another linear transfer learning algorithm, and performing comparably to non-linear DSFT.
Controlling the Complexity and Lipschitz Constant improves polynomial nets
Authors: Zhenyu Zhu, Fabian Latorre, Grigorios G Chrysos, Volkan Cevher
Date: 2022-02-10 00:00:00
Proceeding: ICLR 2022 4

While the class of Polynomial Nets demonstrates comparable performance to neural networks (NN), it currently has neither theoretical generalization characterization nor robustness guarantees. To this end, we derive new complexity bounds for the set of Coupled CP-Decomposition (CCP) and Nested Coupled CP-decomposition (NCP) models of Polynomial Nets in terms of the $\ell_\infty$-operator-norm and the $\ell_2$-operator norm. In addition, we derive bounds on the Lipschitz constant for both models to establish a theoretical certificate for their robustness. The theoretical results enable us to propose a principled regularization scheme that we also evaluate experimentally in six datasets and show that it improves the accuracy as well as the robustness of the models to adversarial perturbations. We showcase how this regularization can be combined with adversarial training, resulting in further improvements.