mtybilly/Instruct2DS huggingface dataset:
Consistent Estimation for PCA and Sparse Regression with Oblivious Outliers
Authors: Tommaso d'Orsi, Chih-Hung Liu, Rajai Nasser, Gleb Novikov, David Steurer, Stefan Tiegel
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: We develop machinery to design efficiently computable and \emph{consistent} estimators, achieving estimation error approaching zero as the number of observations grows, when facing an oblivious adversary that may corrupt responses in all but an $\alpha$ fraction of the samples.As concrete examples, we investigate two problems: sparse regression and principal component analysis (PCA).For sparse regression, we achieve consistency for optimal sample size $n\gtrsim (k\log d)/\alpha^2$ and optimal error rate $O(\sqrt{(k\log d)/(n\cdot \alpha^2)})$where $n$ is the number of observations, $d$ is the number of dimensions and $k$ is the sparsity of the parameter vector, allowing the fraction of inliers to be inverse-polynomial in the number of samples.Prior to this work, no estimator was known to be consistent when the fraction of inliers $\alpha$ is $o(1/\log \log n)$, even for (non-spherical) Gaussian design matrices.Results holding under weak design assumptions and in the presence of such general noise have only been shown in dense setting (i.e., general linear regression) very recently by d'Orsi et al.~\cite{ICML-linear-regression}.In the context of PCA, we attain optimal error guarantees under broad spikiness assumptions on the parameter matrix (usually used in matrix completion). Previous works could obtain non-trivial guarantees only under the assumptions that the measurement noise corresponding to the inliers is polynomially small in $n$ (e.g., Gaussian with variance $1/n^2$).To devise our estimators, we equip the Huber loss with non-smooth regularizers such as the $\ell_1$ norm or the nuclear norm, and extend d'Orsi et al.'s approach~\cite{ICML-linear-regression} in a novel way to analyze the loss function.Our machinery appears to be easily applicable to a wide range of estimation problems.We complement these algorithmic results with statistical lower bounds showing that the fraction of inliers that our PCA estimator can deal with is optimal up to a constant factor.
Offline Constrained Multi-Objective Reinforcement Learning via Pessimistic Dual Value Iteration
Authors: Runzhe Wu, Yufeng Zhang, Zhuoran Yang, Zhaoran Wang
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: In constrained multi-objective RL, the goal is to learn a policy that achieves the best performance specified by a multi-objective preference function under a constraint. We focus on the offline setting where the RL agent aims to learn the optimal policy from a given dataset. This scenario is common in real-world applications where interactions with the environment are expensive and the constraint violation is dangerous. For such a setting, we transform the original constrained problem into a  primal-dual formulation, which is solved via dual gradient ascent. Moreover, we propose to combine such an approach with pessimism to overcome the uncertainty in offline data, which leads to our Pessimistic Dual Iteration (PEDI). We establish upper bounds on both the suboptimality and constraint violation for the policy learned by PEDI based on an arbitrary dataset, which proves that PEDI is provably sample efficient. We also specialize PEDI to the setting with linear function approximation. To the best of our knowledge, we propose the first provably efficient constrained multi-objective RL algorithm with offline data without any assumption on the coverage of the dataset.
Batch Multi-Fidelity Bayesian Optimization with  Deep Auto-Regressive Networks
Authors: Shibo Li, Robert Kirby, Shandian Zhe
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Bayesian optimization (BO) is a powerful approach for optimizing black-box, expensive-to-evaluate functions. To enable a flexible trade-off between the cost and accuracy, many applications allow the function to be evaluated at different fidelities.  In order to reduce the optimization cost while maximizing the benefit-cost ratio,  in this paper we propose Batch Multi-fidelity Bayesian Optimization with Deep Auto-Regressive Networks (BMBO-DARN). We use a set of Bayesian neural networks to construct a fully auto-regressive model, which is expressive enough to capture strong yet complex relationships across all the fidelities, so as to improve the surrogate learning and optimization performance. Furthermore, to enhance the quality and diversity of queries, we develop a simple yet efficient batch querying method, without any combinatorial search over the fidelities. We propose a batch acquisition function based on Max-value Entropy Search (MES) principle, which penalizes highly correlated queries and encourages diversity. We use posterior samples and moment matching to fulfill efficient computation of the acquisition function, and conduct alternating optimization over every fidelity-input pair, which guarantees an improvement at each step.  We demonstrate the advantage of our approach on four real-world  hyperparameter optimization applications.
Mastering Atari Games with Limited Data
Authors: Weirui Ye, Shaohuai Liu, Thanard Kurutach, Pieter Abbeel, Yang Gao
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Reinforcement learning has achieved great success in many applications. However, sample efficiency remains a key challenge, with prominent methods requiring millions (or even billions) of environment steps to train.  Recently, there has been significant progress in sample efficient image-based RL algorithms; however, consistent human-level performance on the Atari game benchmark remains an elusive goal. We propose a sample efficient model-based visual RL algorithm built on MuZero, which we name EfficientZero. Our method achieves 194.3% mean human performance and 109.0% median performance on the Atari 100k benchmark with only two hours of real-time game experience and outperforms the state SAC in some tasks on the DMControl 100k benchmark. This is the first time an algorithm achieves super-human performance on Atari games with such little data. EfficientZero's performance is also close to DQN's performance at 200 million frames while we consume 500 times less data. EfficientZero's low sample complexity and high performance can bring RL closer to real-world applicability. We implement our algorithm in an easy-to-understand manner and it is available at https://github.com/YeWR/EfficientZero. We hope it will accelerate the research of MCTS-based RL algorithms in the wider community.
Dealing With Misspecification In Fixed-Confidence Linear Top-m Identification
Authors: Clémence Réda, Andrea Tirinzoni, Rémy Degenne
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: We study the problem of the identification of m arms with largest means under a fixed error rate $\delta$ (fixed-confidence Top-m identification), for misspecified linear bandit models. This problem is motivated by practical applications, especially in medicine and recommendation systems, where linear models are popular due to their simplicity and the existence of efficient algorithms, but in which data inevitably deviates from linearity. In this work, we first derive a tractable lower bound on the sample complexity of any $\delta$-correct algorithm for the general Top-m identification problem. We show that knowing the scale of the deviation from linearity is necessary to exploit the structure of the problem. We then describe the first algorithm for this setting, which is both practical and adapts to the amount of misspecification. We derive an upper bound to its sample complexity which confirms this adaptivity and that matches the lower bound when $\delta \rightarrow 0$. Finally, we evaluate our algorithm on both synthetic and real-world data, showing competitive performance with respect to existing baselines.
Why Generalization in RL is Difficult: Epistemic POMDPs and Implicit Partial Observability
Authors: Dibya Ghosh, Jad Rahme, Aviral Kumar, Amy Zhang, Ryan P. Adams, Sergey Levine
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Generalization is a central challenge for the deployment of reinforcement learning (RL) systems in the real world. In this paper, we show that the sequential structure of the RL problem necessitates new approaches to generalization beyond the well-studied techniques used in supervised learning. While supervised learning methods can generalize effectively without explicitly accounting for epistemic uncertainty, we describe why appropriate uncertainty handling can actually be essential in RL. We show that generalization to unseen test conditions from a limited number of training conditions induces a kind of implicit partial observability, effectively turning even fully-observed MDPs into POMDPs. Informed by this observation, we recast the problem of generalization in RL as solving the induced partially observed Markov decision process, which we call the epistemic POMDP. We demonstrate the failure modes of algorithms that do not appropriately handle this partial observability, and suggest a simple ensemble-based technique for approximately solving the partially observed problem. Empirically, we demonstrate that our simple algorithm derived from the epistemic POMDP achieves significant gains in generalization over current methods on the Procgen benchmark suite.
Set Prediction in the Latent Space
Authors: Konpat Preechakul, Chawan Piansaddhayanon, Burin Naowarat, Tirasan Khandhawit, Sira Sriswasdi, Ekapol Chuangsuwanich
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Set prediction tasks require the matching between predicted set and ground truth set in order to propagate the gradient signal. Recent works have performed this matching in the original feature space thus requiring predefined distance functions. We propose a method for learning the distance function by performing the matching in the latent space learned from encoding networks. This method enables the use of teacher forcing which was not possible previously since matching in the feature space must be computed after the entire output sequence is generated. Nonetheless, a naive implementation of latent set prediction might not converge due to permutation instability. To address this problem, we provide sufficient conditions for permutation stability which begets an algorithm to improve the overall model convergence. Experiments on several set prediction tasks, including image captioning and object detection, demonstrate the effectiveness of our method.
Best of Both Worlds: Practical and Theoretically Optimal Submodular Maximization in Parallel
Authors: Yixin Chen, Tonmoy Dey, Alan Kuhnle
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: For the problem of maximizing a monotone, submodular function with respect to a cardinality constraint $k$ on a ground set of size $n$, we provide an algorithm that achieves the state-of-the-art in both its empirical performance and its theoretical properties, in terms of adaptive complexity, query complexity, and approximation ratio; that is, it obtains, with high probability, query complexity of $O(n)$ in expectation, adaptivity of $O(\log(n))$, and approximation ratio of nearly $1-1/e$. The main algorithm is assembled from two components which may be of independent interest. The first component of our algorithm, LINEARSEQ, is useful as a preprocessing algorithm to improve the query complexity of many algorithms. Moreover, a variant of LINEARSEQ is shown to have adaptive complexity of $O( \log (n / k) )$ which is smaller than that of any previous algorithm in the literature. The second component is a parallelizable thresholding procedure THRESHOLDSEQ for adding elements with gain above a constant threshold. Finally, we demonstrate that our main algorithm empirically outperforms, in terms of runtime, adaptive rounds, total queries, and objective values, the previous state-of-the-art algorithm FAST in a comprehensive evaluation with six submodular objective functions.
Fine-grained Generalization Analysis of Inductive Matrix Completion
Authors: Antoine Ledent, Rodrigo Alves, Yunwen Lei, Marius Kloft
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: In this paper, we bridge the gap between the state-of-the-art theoretical results for matrix completion with the nuclear norm and their equivalent in \textit{inductive matrix completion}: (1) In the distribution-free setting, we prove bounds improving the previously best scaling of $O(rd^2)$ to $\widetilde{O}(d^{3/2}\sqrt{r})$, where $d$ is the dimension of the side information and $r$ is the rank. (2) We introduce the (smoothed) \textit{adjusted trace-norm minimization} strategy, an inductive analogue of the weighted trace norm, for which we show guarantees of the order $\widetilde{O}(dr)$ under arbitrary sampling. In the inductive case, a similar rate was previously achieved only under uniform sampling and for exact recovery. Both our results align with the state of the art in the particular case of standard (non-inductive) matrix completion, where they are known to be tight up to log terms. Experiments further confirm that our strategy outperforms standard inductive matrix completion on various synthetic datasets and real problems, justifying its place as an important tool in the arsenal of methods for matrix completion using side information.
Learning Frequency Domain Approximation for Binary Neural Networks
Authors: Yixing Xu, Kai Han, Chang Xu, Yehui Tang, Chunjing XU, Yunhe Wang
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Binary neural networks (BNNs) represent original full-precision weights and activations into 1-bit with sign function. Since the gradient of the conventional sign function is almost zero everywhere which cannot be used for back-propagation, several attempts have been proposed to alleviate the optimization difficulty by using approximate gradient. However, those approximations corrupt the main direction of factual gradient. To this end, we propose to estimate the gradient of sign function in the Fourier frequency domain using the combination of sine functions for training BNNs, namely frequency domain approximation (FDA). The proposed approach does not affect the low-frequency information of the original sign function which occupies most of the overall energy, and high-frequency coefficients will be ignored to avoid the huge computational overhead. In addition, we embed a noise adaptation module into the training phase to compensate the approximation error. The experiments on several benchmark datasets and neural architectures illustrate that the binary network learned using our method achieves the state-of-the-art accuracy. Code will be available at https://gitee.com/mindspore/models/tree/master/research/cv/FDA-BNN.
Reformulating Zero-shot Action Recognition for Multi-label Actions
Authors: Alec Kerrigan, Kevin Duarte, Yogesh Rawat, Mubarak Shah
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: The goal of zero-shot action recognition (ZSAR) is to classify action classes which were not previously seen during training. Traditionally, this is achieved by training a network to map, or regress, visual inputs to a semantic space where a nearest neighbor classifier is used to select the closest target class. We argue that this approach is sub-optimal due to the use of nearest neighbor on static semantic space and is ineffective when faced with multi-label videos - where two semantically distinct co-occurring action categories cannot be predicted with high confidence. To overcome these limitations, we propose a ZSAR framework which does not rely on nearest neighbor classification, but rather consists of a pairwise scoring function. Given a video and a set of action classes, our method predicts a set of confidence scores for each class independently. This allows for the prediction of several semantically distinct classes within one video input. Our evaluations show that our method not only achieves strong performance on three single-label action classification datasets (UCF-101, HMDB, and RareAct), but also outperforms previous ZSAR approaches on a challenging multi-label dataset (AVA) and a real-world surprise activity detection dataset (MEVA).
Optimal Best-Arm Identification Methods for Tail-Risk Measures
Authors: Shubhada Agrawal, Wouter M. Koolen, Sandeep Juneja
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Conditional value-at-risk (CVaR) and value-at-risk (VaR) are popular tail-risk measures in finance and insurance industries as well as in highly reliable, safety-critical uncertain environments where often the underlying probability distributions are heavy-tailed. We use the multi-armed bandit best-arm identification framework and consider the problem of identifying the arm from amongst finitely many that has the smallest CVaR, VaR, or weighted sum of CVaR and mean. The latter captures the risk-return trade-off common in finance. Our main contribution is an optimal $\delta$-correct algorithm that acts on general arms, including heavy-tailed distributions, and matches the lower bound on the expected number of samples needed, asymptotically (as $ \delta$ approaches $0$). The algorithm requires solving a non-convex optimization problem in the space of probability measures, that requires delicate analysis. En-route, we develop new non-asymptotic, anytime-valid, empirical-likelihood-based concentration inequalities for tail-risk measures.
SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Vision
Authors: Irina Higgins, Peter Wirnsberger, Andrew Jaegle, Aleksandar Botev
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: A recently proposed class of models attempts to learn latent dynamics from high-dimensional observations, like images, using priors informed by Hamiltonian mechanics. While these models have important potential applications in areas like robotics or autonomous driving, there is currently no good way to evaluate their performance: existing methods primarily rely on image reconstruction quality, which does not always reflect the quality of the learnt latent dynamics. In this work, we empirically highlight the problems with the existing measures and develop a set of new measures, including a binary indicator of whether the underlying Hamiltonian dynamics have been faithfully captured, which we call Symplecticity Metric or SyMetric. Our measures take advantage of the known properties of Hamiltonian dynamics and are more discriminative of the model's ability to capture the underlying dynamics than reconstruction error. Using SyMetric, we identify a set of architectural choices that significantly improve the performance of a previously proposed model for inferring latent dynamics from pixels, the Hamiltonian Generative Network (HGN). Unlike the original HGN, the new SyMetric is able to discover an interpretable phase space with physically meaningful latents on some datasets. Furthermore, it is stable for significantly longer rollouts on a diverse range of 13 datasets,  producing rollouts of essentially infinite length both forward and backwards in time with no degradation in quality on a subset of the datasets.
Learning with Holographic Reduced Representations
Authors: Ashwinkumar Ganesan, Hang Gao, Sunil Gandhi, Edward Raff, Tim Oates, James Holt, Mark McLean
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Holographic Reduced Representations (HRR) are a method for performing symbolic AI on top of real-valued vectors by associating each vector with an abstract concept, and providing mathematical operations to manipulate vectors as if they were classic symbolic objects. This method has seen little use outside of older symbolic AI work and cognitive science. Our goal is to revisit this approach to understand if it is viable for enabling a hybrid neural-symbolic  approach to learning as a differential component of a deep learning architecture. HRRs today are not effective in a differential solution due to numerical instability, a problem we solve by introducing a projection step that forces the vectors to exist in a well behaved point in space. In doing so we improve the concept retrieval efficacy of HRRs by over $100\times$. Using multi-label classification we demonstrate how to leverage the symbolic HRR properties to develop a output layer and loss function that is able to learn effectively, and allows us to investigate some of the pros and cons of an HRR neuro-symbolic learning approach.
Learning Barrier Certificates: Towards Safe Reinforcement Learning with Zero Training-time Violations
Authors: Yuping Luo, Tengyu Ma
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Training-time safety violations have been a major concern when we deploy reinforcement learning algorithms in the real world.This paper explores the possibility of safe RL algorithms with zero training-time safety violations in the challenging setting where we are only given a safe but trivial-reward initial policy without any prior knowledge of the dynamics and additional offline data.We propose an algorithm, Co-trained Barrier Certificate for Safe RL (CRABS), which iteratively learns barrier certificates, dynamics models, and policies. The barrier certificates are learned via adversarial training and ensure the policy's safety assuming calibrated learned dynamics. We also add a regularization term to encourage larger certified regions to enable better exploration. Empirical simulations show that zero safety violations are already challenging for a suite of simple environments with only 2-4 dimensional state space, especially if high-reward policies have to visit regions near the safety boundary.  Prior methods require hundreds of violations to achieve decent rewards on these tasks,  whereas our proposed algorithms incur zero violations.
On the Second-order Convergence Properties of Random Search Methods
Authors: Aurelien Lucchi, Antonio Orvieto, Adamos Solomou
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: We study the theoretical convergence properties of random-search methods when optimizing non-convex objective functions without having access to derivatives. We prove that standard random-search methods that do not rely on second-order information converge to a second-order stationary point. However, they suffer from an exponential complexity in terms of the input dimension of the problem. In order to address this issue, we propose a novel variant of random search that exploits negative curvature by only relying on function evaluations. We prove that this approach converges to a second-order stationary point at a much faster rate than vanilla methods: namely, the complexity in terms of the number of function evaluations is only linear in the problem dimension. We test our algorithm empirically and find good agreements with our theoretical results.
Noether’s Learning Dynamics: Role of Symmetry Breaking in Neural Networks
Authors: Hidenori Tanaka, Daniel Kunin
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: In nature, symmetry governs regularities, while symmetry breaking brings texture. In artificial neural networks, symmetry has been a central design principle to efficiently capture regularities in the world, but the role of symmetry breaking is not well understood. Here, we develop a theoretical framework to study the "geometry of learning dynamics" in neural networks, and reveal a key mechanism of explicit symmetry breaking behind the efficiency and stability of modern neural networks. To build this understanding, we model the discrete learning dynamics of gradient descent using a continuous-time Lagrangian formulation, in which the learning rule corresponds to the kinetic energy and the loss function corresponds to the potential energy. Then, we identify "kinetic symmetry breaking" (KSB), the condition when the kinetic energy explicitly breaks the symmetry of the potential function. We generalize Noether’s theorem known in physics to take into account KSB and derive the resulting motion of the Noether charge: "Noether's Learning Dynamics" (NLD). Finally, we apply NLD to neural networks with normalization layers and reveal how KSB introduces a mechanism of implicit adaptive optimization, establishing an analogy between learning dynamics induced by normalization layers and RMSProp. Overall, through the lens of Lagrangian mechanics, we have established a theoretical foundation to discover geometric design principles for the learning dynamics of neural networks.
A Theory of the Distortion-Perception Tradeoff in Wasserstein Space
Authors: Dror Freirich, Tomer Michaeli, Ron Meir
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: The lower the distortion of an estimator, the more the distribution of its outputs generally deviates from the distribution of the signals it attempts to estimate. This phenomenon, known as the perception-distortion tradeoff, has captured significant attention in image restoration, where it implies that fidelity to ground truth images comes on the expense of perceptual quality (deviation from statistics of natural images). However, despite the increasing popularity of performing comparisons on the perception-distortion plane, there remains an important open question: what is the minimal distortion that can be achieved under a given perception constraint? In this paper, we derive a closed form expression for this distortion-perception (DP) function for the mean squared-error (MSE) distortion and Wasserstein-2 perception index. We prove that the DP function is always quadratic, regardless of the underlying distribution. This stems from the fact that estimators on the DP curve form a geodesic in Wasserstein space. In the Gaussian setting, we further provide a closed form expression for such estimators. For general distributions, we show how these estimators can be constructed from the estimators at the two extremes of the tradeoff: The global MSE minimizer, and a  minimizer of the MSE under a perfect perceptual quality constraint. The latter can be obtained as a stochastic transformation of the former.
Neural Production Systems
Authors: Anirudh Goyal ALIAS PARTH GOYAL, Aniket Didolkar, Nan Rosemary Ke, Charles Blundell, Philippe Beaudoin, Nicolas Heess, Michael Mozer, Yoshua Bengio
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Visual environments are structured, consisting of distinct  objects or entities. These entities have properties---visible or latent---that determine the manner in which they interact with one another. To partition images into entities, deep-learning researchers have proposed structural inductive biases such as slot-based architectures. To model interactions among entities, equivariant graph neural nets (GNNs) are used, but these are not particularly well suited to the task for two reasons. First, GNNs do not predispose interactions to be sparse, as relationships among independent entities are likely to be.  Second, GNNs do not factorize knowledge about  interactions in an entity-conditional manner. As an alternative, we take inspiration from cognitive science and resurrect a classic approach, production systems, which consist of a set of rule templates that are applied by binding placeholder  variables in the rules to specific entities. Rules are scored on their match to entities, and the best fitting rules are applied to update entity properties. In a series of experiments, we demonstrate that this architecture achieves a flexible, dynamic flow of control and serves to factorize entity-specific and rule-based information. This disentangling of knowledge achieves robust future-state prediction in rich visual environments, outperforming state-of-the-art methods using GNNs, and allows for the extrapolation from simple (few object) environments to more complex environments.
Smoothness Matrices Beat Smoothness Constants: Better  Communication Compression Techniques for Distributed Optimization
Authors: Mher Safaryan, Filip Hanzely, Peter Richtarik
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Large scale distributed optimization has become the default tool for the training of supervised machine learning models with a large number of parameters and training data. Recent advancements in the field provide several mechanisms for speeding up the training, including {\em compressed communication}, {\em variance reduction} and {\em acceleration}. However, none of these methods is capable of exploiting the inherently rich data-dependent smoothness structure of the local losses beyond standard smoothness constants. In this paper, we argue that when training supervised models,  {\em smoothness matrices}---information-rich generalizations of the ubiquitous smoothness constants---can and should be exploited for further dramatic gains, both in theory and practice. In order to further alleviate the communication burden inherent in distributed optimization, we propose a novel communication sparsification strategy that can take full advantage of the smoothness matrices associated with local losses. To showcase the power of this tool, we describe how our sparsification technique can be adapted to three distributed optimization algorithms---DCGD, DIANA and ADIANA---yielding significant savings in terms of communication complexity.  The new methods always outperform the baselines, often dramatically so.
Increasing Liquid State Machine Performance with Edge-of-Chaos Dynamics Organized by Astrocyte-modulated Plasticity
Authors: Vladimir Ivanov, Konstantinos Michmizos
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: The liquid state machine (LSM) combines low training complexity and biological plausibility, which has made it an attractive machine learning framework for edge and neuromorphic computing paradigms. Originally proposed as a model of brain computation, the LSM tunes its internal weights without backpropagation of gradients, which results in lower performance compared to multi-layer neural networks. Recent findings in neuroscience suggest that astrocytes, a long-neglected non-neuronal brain cell, modulate synaptic plasticity and brain dynamics, tuning brain networks to the vicinity of the computationally optimal critical phase transition between order and chaos. Inspired by this disruptive understanding of how brain networks self-tune, we propose the neuron-astrocyte liquid state machine (NALSM) that addresses under-performance through self-organized near-critical dynamics. Similar to its biological counterpart, the astrocyte model integrates neuronal activity and provides global feedback to spike-timing-dependent plasticity (STDP), which self-organizes NALSM dynamics around a critical branching factor that is associated with the edge-of-chaos. We demonstrate that NALSM achieves state-of-the-art accuracy versus comparable LSM methods, without the need for data-specific hand-tuning. With a top accuracy of $97.61\%$ on MNIST, $97.51\%$ on N-MNIST, and $85.84\%$ on Fashion-MNIST, NALSM achieved comparable performance to current fully-connected multi-layer spiking neural networks trained via backpropagation. Our findings suggest that the further development of brain-inspired machine learning methods has the potential to reach the performance of deep learning, with the added benefits of supporting robust and energy-efficient neuromorphic computing on the edge.
Fair Sortition Made Transparent
Authors: Bailey Flanigan, Gregory Kehne, Ariel D Procaccia
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Sortition is an age-old democratic paradigm, widely manifested today through the random selection of citizens' assemblies. Recently-deployed algorithms select assemblies \textit{maximally fairly}, meaning that subject to demographic quotas, they give all potential participants as equal a chance as possible of being chosen.  While these fairness gains can bolster the legitimacy of citizens' assemblies and facilitate their uptake, existing algorithms remain limited by their lack of transparency. To overcome this hurdle, in this work we focus on panel selection by uniform lottery, which is easy to realize in an observable way. By this approach, the final assembly is selected by uniformly sampling some pre-selected set of $m$ possible assemblies.We provide theoretical guarantees on the fairness attainable via this type of uniform lottery, as compared to the existing maximally fair but opaque algorithms, for two different fairness objectives. We complement these results with experiments on real-world instances that demonstrate the viability of the uniform lottery approach as a method of selecting assemblies both fairly and transparently.
A Max-Min Entropy Framework for Reinforcement Learning
Authors: Seungyul Han, Youngchul Sung
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: In this paper, we propose a max-min entropy framework for reinforcement learning (RL) to overcome the limitation of the soft actor-critic (SAC) algorithm implementing the maximum entropy RL in model-free sample-based learning. Whereas the maximum entropy RL guides learning for policies to reach states with high entropy in the future, the proposed max-min entropy framework aims to learn to visit states with low entropy and maximize the entropy of these low-entropy states to promote better exploration. For general Markov decision processes (MDPs), an efficient algorithm is constructed under the proposed max-min entropy framework based on disentanglement of exploration and exploitation. Numerical results show that the proposed algorithm yields drastic performance improvement over the current state-of-the-art RL algorithms.
Reward is enough for convex MDPs
Authors: Tom Zahavy, Brendan O'Donoghue, Guillaume Desjardins, Satinder P. Singh
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Maximising a cumulative reward function that is Markov and stationary, i.e., defined over state-action pairs and independent of time, is sufficient to capture many kinds of goals in a Markov decision process (MDP). However, not all goals can be captured in this manner. In this paper we study convex MDPs in which goals are expressed as convex functions of the stationary distribution and show that they cannot be formulated using stationary reward functions. Convex MDPs generalize the standard reinforcement learning (RL) problem formulation to a larger framework that includes many supervised and unsupervised RL problems, such as apprenticeship learning, constrained MDPs, and so-called pure exploration'. Our approach is to reformulate the convex MDP problem as a min-max game involving policy and cost (negative reward)players', using Fenchel duality. We propose a meta-algorithm for solving this problem and show that it unifies many existing algorithms in the literature.
Fast Doubly-Adaptive MCMC to Estimate the Gibbs Partition Function with Weak Mixing Time Bounds
Authors: Shahrzad Haddadan, Yue Zhuang, Cyrus Cousins, Eli Upfal
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: We present a novel method for reducing the computational complexity of rigorously estimating the partition functions of Gibbs (or Boltzmann) distributions, which arise ubiquitously in probabilistic graphical models. A major obstacle to applying the Gibbs distribution in practice is the need to estimate their partition function (normalizing constant).  The state of the art in addressing this problem is multi-stage algorithms which consist of a cooling schedule and a mean estimator in each step of the schedule.  While the cooling schedule in these algorithms is adaptive, the mean estimate computations use MCMC as a black-box to draw approximately-independent samples. Here we develop a doubly adaptive approach, combining the adaptive cooling schedule with an adaptive MCMC mean estimator, whose number of Markov chain steps adapts dynamically to the underlying chain. Through rigorous theoretical analysis, we prove that our method outperforms the state of the art algorithms in several factors: (1) The computational complexity of our method is smaller; (2) Our method is less sensitive to loose bounds on mixing times, an inherent components in these algorithms; and (3) The improvement obtained by our method is particularly significant in the most challenging regime of high precision estimates. We demonstrate the advantage of our method in experiments run on classic factor graphs, such as voting models and Ising models.
Does enforcing fairness mitigate biases caused by subpopulation shift?
Authors: Subha Maity, Debarghya Mukherjee, Mikhail Yurochkin, Yuekai Sun
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Many instances of algorithmic bias are caused by subpopulation shifts. For example, ML models often perform worse on demographic groups that are underrepresented in the training data. In this paper, we study whether enforcing algorithmic fairness during training improves the performance of the trained model in the \emph{target domain}. On one hand, we conceive scenarios in which enforcing fairness does not improve performance in the target domain. In fact, it may even harm performance. On the other hand, we derive necessary and sufficient conditions under which enforcing algorithmic fairness leads to the Bayes model in the target domain. We also illustrate the practical implications of our theoretical results in simulations and on real data.
Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods
Authors: Desi R Ivanova, Adam Foster, Steven Kleinegesse, Michael U. Gutmann, Thomas Rainforth
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: We introduce implicit Deep Adaptive Design (iDAD), a new method for performing adaptive experiments in real-time with implicit models. iDAD amortizes the cost of Bayesian optimal experimental design (BOED) by learning a design policy network upfront, which can then be deployed quickly at the time of the experiment. The iDAD network can be trained on any model which simulates differentiable samples, unlike previous design policy work that requires a closed form likelihood and conditionally independent experiments. At deployment, iDAD allows design decisions to be made in milliseconds, in contrast to traditional BOED approaches that require heavy computation during the experiment itself. We illustrate the applicability of iDAD on a number of experiments, and show that it provides a fast and effective mechanism for performing adaptive design with implicit models.
Sample-Efficient Learning of Stackelberg Equilibria in General-Sum Games
Authors: Yu Bai, Chi Jin, Huan Wang, Caiming Xiong
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Real world applications such as economics and policy making often involve solving multi-agent games with two unique features: (1) The agents are inherently asymmetric and partitioned into leaders and followers; (2) The agents have different reward functions, thus the game is general-sum. The majority of existing results in this field focuses on either symmetric solution concepts (e.g. Nash equilibrium) or zero-sum games. It remains open how to learn the Stackelberg equilibrium---an asymmetric analog of the Nash equilibrium---in general-sum games efficiently from noisy samples.  This paper initiates the theoretical study of sample-efficient learning of the Stackelberg equilibrium, in the bandit feedback setting where we only observe noisy samples of the reward. We consider three representative two-player general-sum games: bandit games, bandit-reinforcement learning (bandit-RL) games, and linear bandit games. In all these games, we identify a fundamental gap between the exact value of the Stackelberg equilibrium and its estimated version using finitely many noisy samples, which can not be closed information-theoretically regardless of the algorithm. We then establish sharp positive results on sample-efficient learning of Stackelberg equilibrium with value optimal up to the gap identified above, with matching lower bounds in the dependency on the gap, error tolerance, and the size of the action spaces. Overall, our results unveil unique challenges in learning Stackelberg equilibria under noisy bandit feedback, which we hope could shed light on future research on this topic.
Non-approximate Inference for Collective Graphical Models on Path Graphs via Discrete Difference of Convex Algorithm
Authors: Yasunori Akagi, Naoki Marumo, Hideaki Kim, Takeshi Kurashima, Hiroyuki Toda
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: The importance of aggregated count data, which is calculated from the data of multiple individuals, continues to increase. Collective Graphical Model (CGM) is a probabilistic approach to the analysis of aggregated data. One of the most important operations in CGM is maximum a posteriori (MAP) inference of unobserved variables under given observations. Because the MAP inference problem for general CGMs has been shown to be NP-hard, an approach that solves an approximate problem has been proposed. However, this approach has two major drawbacks. First, the quality of the solution deteriorates when the values in the count tables are small, because the approximation becomes inaccurate. Second, since continuous relaxation is applied, the integrality constraints of the output are violated. To resolve these problems, this paper proposes a new method for MAP inference for CGMs on path graphs. Our method is based on the Difference of Convex Algorithm (DCA), which is a general methodology to minimize a function represented as the sum of a convex function and a concave function. In our algorithm, important subroutines in DCA can be efficiently calculated by minimum convex cost flow algorithms. Experiments show that the proposed method outputs higher quality solutions than the conventional approach.
Implicit Task-Driven Probability Discrepancy Measure for Unsupervised Domain Adaptation
Authors: Mao Li, Kaiqi Jiang, Xinhua Zhang
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Probability discrepancy measure is a fundamental construct for numerous machine learning models such as weakly supervised learning and generative modeling.  However, most measures overlook the fact that the distributions are not the end-product of learning, but are the basis of downstream predictor.  Therefore it is important to warp the probability discrepancy measure towards the end tasks, and we hence propose a new bi-level optimization based approach so that the two distributions are compared not uniformly against the entire hypothesis space, but only with respect to the optimal predictor for the downstream end task.  When applied to margin disparity discrepancy and contrastive domain discrepancy, our method significantly improves the performance in unsupervised domain adaptation, and enjoys a much more principled training process.
SBO-RNN: Reformulating Recurrent Neural Networks via Stochastic Bilevel Optimization
Authors: Ziming Zhang, Yun Yue, Guojun Wu, Yanhua Li, Haichong Zhang
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: In this paper we consider the training stability of recurrent neural networks (RNNs) and propose a family of RNNs, namely SBO-RNN, that can be formulated using stochastic bilevel optimization (SBO). With the help of stochastic gradient descent (SGD), we manage to convert the SBO problem into an RNN where the feedforward and backpropagation solve the lower and upper-level optimization for learning hidden states and their hyperparameters, respectively. We prove that under mild conditions there is no vanishing or exploding gradient in training SBO-RNN. Empirically we demonstrate our approach with superior performance on several benchmark datasets, with fewer parameters, less training data, and much faster convergence. Code is available at https://zhang-vislab.github.io.
Navigating to the Best Policy in Markov Decision Processes
Authors: Aymen Al Marjani, Aurélien Garivier, Alexandre Proutiere
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: We investigate the classical active pure exploration problem in Markov Decision Processes, where the agent sequentially selects actions and, from the resulting system trajectory, aims at identifying the best policy as fast as possible. We propose a problem-dependent lower bound on the average number of steps required before a correct answer can be given with probability at least $1-\delta$. We further provide the first algorithm with an instance-specific sample complexity in this setting. This algorithm addresses the general case of communicating MDPs; we also propose a variant with a reduced exploration rate (and hence faster convergence) under an additional ergodicity assumption. This work extends previous results relative to the \emph{generative setting}~\cite{pmlr-v139-marjani21a}, where the agent could at each step query the random outcome of any (state, action) pair. In contrast, we show here how to deal with the \emph{navigation constraints}, induced by the \emph{online setting}. Our analysis relies on an ergodic theorem for non-homogeneous Markov chains which we consider of wide interest in the analysis of Markov Decision Processes.