mtybilly/Instruct2DS huggingface dataset:
Quant-BnB: A Scalable Branch-and-Bound Method for Optimal Decision Trees with Continuous Features
Authors: Rahul Mazumder, Xiang Meng, Haoyue Wang
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Decision trees are one of the most useful and popular methods in the machine learning toolbox. In this paper, we consider the problem of learning optimal decision trees, a combinatorial optimization problem that is challenging to solve at scale. A common approach in the literature is to use greedy heuristics, which may not be optimal. Recently there has been significant interest in learning optimal decision trees using various approaches (e.g., based on integer programming, dynamic programming)—to achieve computational scalability, most of these approaches focus on classification tasks with binary features. In this paper, we present a new discrete optimization method based on branch-and-bound (BnB) to obtain optimal decision trees. Different from existing customized approaches, we consider both regression and classification tasks with continuous features. The basic idea underlying our approach is to split the search space based on the quantiles of the feature distribution—leading to upper and lower bounds for the underlying optimization problem along the BnB iterations. Our proposed algorithm Quant-BnB shows significant speedups compared to existing approaches for shallow optimal trees on various real datasets.
Optimizing Tensor Network Contraction Using Reinforcement Learning
Authors: Eli Meirom, Haggai Maron, Shie Mannor, Gal Chechik
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Quantum Computing (QC) stands to revolutionize computing, but is currently still limited. To develop and test quantum algorithms today, quantum circuits are often simulated on classical computers. Simulating a complex quantum circuit requires computing the contraction of a large network of tensors. The order (path) of contraction can have a drastic effect on the computing cost, but finding an efficient order is a challenging combinatorial optimization problem. We propose a Reinforcement Learning (RL) approach combined with Graph Neural Networks (GNN) to address the contraction ordering problem. The problem is extremely challenging due to the huge search space, the heavy-tailed reward distribution, and the challenging credit assignment. We show how a carefully implemented RL-agent that uses a GNN as the basic policy construct can address these challenges and obtain significant improvements over state-of-the-art techniques in three varieties of circuits, including the largest scale networks used in contemporary QC.
Causal Transformer for Estimating Counterfactual Outcomes
Authors: Valentyn Melnychuk, Dennis Frauen, Stefan Feuerriegel
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Estimating counterfactual outcomes over time from observational data is relevant for many applications (e.g., personalized medicine). Yet, state-of-the-art methods build upon simple long short-term memory (LSTM) networks, thus rendering inferences for complex, long-range dependencies challenging. In this paper, we develop a novel Causal Transformer for estimating counterfactual outcomes over time. Our model is specifically designed to capture complex, long-range dependencies among time-varying confounders. For this, we combine three transformer subnetworks with separate inputs for time-varying covariates, previous treatments, and previous outcomes into a joint network with in-between cross-attentions. We further develop a custom, end-to-end training procedure for our Causal Transformer. Specifically, we propose a novel counterfactual domain confusion loss to address confounding bias: it aims to learn adversarial balanced representations, so that they are predictive of the next outcome but non-predictive of the current treatment assignment. We evaluate our Causal Transformer based on synthetic and real-world datasets, where it achieves superior performance over current baselines. To the best of our knowledge, this is the first work proposing transformer-based architecture for estimating counterfactual outcomes from longitudinal data.
Steerable 3D Spherical Neurons
Authors: Pavlo Melnyk, Michael Felsberg, Mårten Wadenbäck
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Emerging from low-level vision theory, steerable filters found their counterpart in prior work on steerable convolutional neural networks equivariant to rigid transformations. In our work, we propose a steerable feed-forward learning-based approach that consists of neurons with spherical decision surfaces and operates on point clouds. Such spherical neurons are obtained by conformal embedding of Euclidean space and have recently been revisited in the context of learning representations of point sets. Focusing on 3D geometry, we exploit the isometry property of spherical neurons and derive a 3D steerability constraint. After training spherical neurons to classify point clouds in a canonical orientation, we use a tetrahedron basis to quadruplicate the neurons and construct rotation-equivariant spherical filter banks. We then apply the derived constraint to interpolate the filter bank outputs and, thus, obtain a rotation-invariant network. Finally, we use a synthetic point set and real-world 3D skeleton data to verify our theoretical findings. The code is available at https://github.com/pavlo-melnyk/steerable-3d-neurons.
Transformers are Meta-Reinforcement Learners
Authors: Luckeciano C Melo
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: The transformer architecture and variants presented a remarkable success across many machine learning tasks in recent years. This success is intrinsically related to the capability of handling long sequences and the presence of context-dependent weights from the attention mechanism. We argue that these capabilities suit the central role of a Meta-Reinforcement Learning algorithm. Indeed, a meta-RL agent needs to infer the task from a sequence of trajectories. Furthermore, it requires a fast adaptation strategy to adapt its policy for a new task - which can be achieved using the self-attention mechanism. In this work, we present TrMRL (Transformers for Meta-Reinforcement Learning), a meta-RL agent that mimics the memory reinstatement mechanism using the transformer architecture. It associates the recent past of working memories to build an episodic memory recursively through the transformer layers. We show that the self-attention computes a consensus representation that minimizes the Bayes Risk at each layer and provides meaningful features to compute the best actions. We conducted experiments in high-dimensional continuous control environments for locomotion and dexterous manipulation. Results show that TrMRL presents comparable or superior asymptotic performance, sample efficiency, and out-of-distribution generalization compared to the baselines in these environments.
ButterflyFlow: Building Invertible Layers with Butterfly Matrices
Authors: Chenlin Meng, Linqi Zhou, Kristy Choi, Tri Dao, Stefano Ermon
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Normalizing flows model complex probability distributions using maps obtained by composing invertible layers. Special linear layers such as masked and 1×1 convolutions play a key role in existing architectures because they increase expressive power while having tractable Jacobians and inverses. We propose a new family of invertible linear layers based on butterfly layers, which are known to theoretically capture complex linear structures including permutations and periodicity, yet can be inverted efficiently. This representational power is a key advantage of our approach, as such structures are common in many real-world datasets. Based on our invertible butterfly layers, we construct a new class of normalizing flow mod- els called ButterflyFlow. Empirically, we demonstrate that ButterflyFlows not only achieve strong density estimation results on natural images such as MNIST, CIFAR-10, and ImageNet-32×32, but also obtain significantly better log-likelihoods on structured datasets such as galaxy images and MIMIC-III patient cohorts—all while being more efficient in terms of memory and computation than relevant baselines.
In defense of dual-encoders for neural ranking
Authors: Aditya Menon, Sadeep Jayasumana, Ankit Singh Rawat, Seungyeon Kim, Sashank Reddi, Sanjiv Kumar
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Transformer-based models such as BERT have proven successful in information retrieval problem, which seek to identify relevant documents for a given query. There are two broad flavours of such models: cross-attention (CA) models, which learn a joint embedding for the query and document, and dual-encoder (DE) models, which learn separate embeddings for the query and document. Empirically, CA models are often found to be more accurate, which has motivated a series of works seeking to bridge this gap. However, a more fundamental question remains less explored: does this performance gap reflect an inherent limitation in the capacity of DE models, or a limitation in the training of such models? And does such an understanding suggest a principled means of improving DE models? In this paper, we study these questions, with three contributions. First, we establish theoretically that with a sufficiently large embedding dimension, DE models have the capacity to model a broad class of score distributions. Second, we show empirically that on real-world problems, DE models may overfit to spurious correlations in the training set, and thus under-perform on test samples. To mitigate this behaviour, we propose a suitable distillation strategy, and confirm its practical efficacy on the MSMARCO-Passage and Natural Questions benchmarks.
Equivariant Quantum Graph Circuits
Authors: Peter Mernyei, Konstantinos Meichanetzidis, Ismail Ilkan Ceylan
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: We investigate quantum circuits for graph representation learning, and propose equivariant quantum graph circuits (EQGCs), as a class of parameterized quantum circuits with strong relational inductive bias for learning over graph-structured data. Conceptually, EQGCs serve as a unifying framework for quantum graph representation learning, allowing us to define several interesting subclasses which subsume existing proposals. In terms of the representation power, we prove that the studied subclasses of EQGCs are universal approximators for functions over the bounded graph domain. This theoretical perspective on quantum graph machine learning methods opens many directions for further work, and could lead to models with capabilities beyond those of classical approaches. We empirically verify the expressive power of EQGCs through a dedicated experiment on synthetic data, and additionally observe that the performance of EQGCs scales well with the depth of the model and does not suffer from barren plateu issues.
Stochastic Rising Bandits
Authors: Alberto Maria Metelli, Francesco Trovò, Matteo Pirola, Marcello Restelli
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: This paper is in the field of stochastic Multi-Armed Bandits (MABs), i.e., those sequential selection techniques able to learn online using only the feedback given by the chosen option (a.k.a. arm). We study a particular case of the rested and restless bandits in which the arms’ expected payoff is monotonically non-decreasing. This characteristic allows designing specifically crafted algorithms that exploit the regularity of the payoffs to provide tight regret bounds. We design an algorithm for the rested case (R-ed-UCB) and one for the restless case (R-less-UCB), providing a regret bound depending on the properties of the instance and, under certain circumstances, of $\widetilde\mathcalO(T^\frac23)$. We empirically compare our algorithms with state-of-the-art methods for non-stationary MABs over several synthetically generated tasks and an online model selection problem for a real-world dataset. Finally, using synthetic and real-world data, we illustrate the effectiveness of the proposed approaches compared with state-of-the-art algorithms for the non-stationary bandits.
Minimizing Control for Credit Assignment with Strong Feedback
Authors: Alexander Meulemans, Matilde Tristany Farinha, Maria R. Cervera, João Sacramento, Benjamin F. Grewe
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: The success of deep learning ignited interest in whether the brain learns hierarchical representations using gradient-based learning. However, current biologically plausible methods for gradient-based credit assignment in deep neural networks need infinitesimally small feedback signals, which is problematic in biologically realistic noisy environments and at odds with experimental evidence in neuroscience showing that top-down feedback can significantly influence neural activity. Building upon deep feedback control (DFC), a recently proposed credit assignment method, we combine strong feedback influences on neural activity with gradient-based learning and show that this naturally leads to a novel view on neural network optimization. Instead of gradually changing the network weights towards configurations with low output loss, weight updates gradually minimize the amount of feedback required from a controller that drives the network to the supervised output label. Moreover, we show that the use of strong feedback in DFC allows learning forward and feedback connections simultaneously, using learning rules fully local in space and time. We complement our theoretical results with experiments on standard computer-vision benchmarks, showing competitive performance to backpropagation as well as robustness to noise. Overall, our work presents a fundamentally novel view of learning as control minimization, while sidestepping biologically unrealistic assumptions.
A Dynamical System Perspective for Lipschitz Neural Networks
Authors: Laurent Meunier, Blaise J Delattre, Alexandre Araujo, Alexandre Allauzen
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: The Lipschitz constant of neural networks has been established as a key quantity to enforce the robustness to adversarial examples. In this paper, we tackle the problem of building $1$-Lipschitz Neural Networks. By studying Residual Networks from a continuous time dynamical system perspective, we provide a generic method to build $1$-Lipschitz Neural Networks and show that some previous approaches are special cases of this framework. Then, we extend this reasoning and show that ResNet flows derived from convex potentials define $1$-Lipschitz transformations, that lead us to define the <em>Convex Potential Layer</em> (CPL). A comprehensive set of experiments on several datasets demonstrates the scalability of our architecture and the benefits as an $\ell_2$-provable defense against adversarial examples. Our code is available at r̆lhttps://github.com/MILES-PSL/Convex-Potential-Layer
Distribution Regression with Sliced Wasserstein Kernels
Authors: Dimitri Meunier, Massimiliano Pontil, Carlo Ciliberto
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: The problem of learning functions over spaces of probabilities - or distribution regression - is gaining significant interest in the machine learning community. The main challenge in these settings is to identify a suitable representation capturing all relevant properties of a distribution. The well-established approach in this sense is to use kernel mean embeddings, which lift kernel-induced similarity on the input domain at the probability level. This strategy effectively tackles the two-stage sampling nature of the problem, enabling one to derive estimators with strong statistical guarantees, such as universal consistency and excess risk bounds. However, kernel mean embeddings implicitly hinge on the maximum mean discrepancy (MMD), a metric on probabilities, which is not the most suited to capture geometrical relations between distributions. In contrast, optimal transport (OT) metrics, are potentially more appealing. In this work, we propose an OT-based estimator for distribution regression. We build on the Sliced Wasserstein distance to obtain an OT-based representation. We study the theoretical properties of a kernel ridge regression estimator based on such representation, for which we prove universal consistency and excess risk bounds. Preliminary experiments complement our theoretical findings by showing the effectiveness of the proposed approach and compare it with MMD-based estimators.
Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism
Authors: Siqi Miao, Mia Liu, Pan Li
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Interpretable graph learning is in need as many scientific applications depend on learning models to collect insights from graph-structured data. Previous works mostly focused on using post-hoc approaches to interpret pre-trained models (graph neural networks in particular). They argue against inherently interpretable models because the good interpretability of these models is often at the cost of their prediction accuracy. However, those post-hoc methods often fail to provide stable interpretation and may extract features that are spuriously correlated with the task. In this work, we address these issues by proposing Graph Stochastic Attention (GSAT). Derived from the information bottleneck principle, GSAT injects stochasticity to the attention weights to block the information from task-irrelevant graph components while learning stochasticity-reduced attention to select task-relevant subgraphs for interpretation. The selected subgraphs provably do not contain patterns that are spuriously correlated with the task under some assumptions. Extensive experiments on eight datasets show that GSAT outperforms the state-of-the-art methods by up to 20% in interpretation AUC and 5% in prediction accuracy. Our code is available at https://github.com/Graph-COM/GSAT.
Modeling Structure with Undirected Neural Networks
Authors: Tsvetomila Mihaylova, Vlad Niculae, Andre Martins
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem – e.g., factor graphs – neural networks are usually monolithic mappings from inputs to outputs, with a fixed computation order. This limitation prevents them from capturing different directions of computation and interaction between the modeled variables. In this paper, we combine the representational strengths of factor graphs and of neural networks, proposing undirected neural networks (UNNs): a flexible framework for specifying computations that can be performed in any order. For particular choices, our proposed models subsume and extend many existing architectures: feed-forward, recurrent, self-attention networks, auto-encoders, and networks with implicit layers. We demonstrate the effectiveness of undirected neural architectures, both unstructured and structured, on a range of tasks: tree-constrained dependency parsing, convolutional image classification, and sequence completion with attention. By varying the computation order, we show how a single UNN can be used both as a classifier and a prototype generator, and how it can fill in missing parts of an input sequence, making them a promising field for further research.
Universal Hopfield Networks: A General Framework for Single-Shot Associative Memory Models
Authors: Beren Millidge, Tommaso Salvatori, Yuhang Song, Thomas Lukasiewicz, Rafal Bogacz
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: A large number of neural network models of associative memory have been proposed in the literature. These include the classical Hopfield networks (HNs), sparse distributed memories (SDMs), and more recently the modern continuous Hopfield networks (MCHNs), which possess close links with self-attention in machine learning. In this paper, we propose a general framework for understanding the operation of such memory networks as a sequence of three operations: similarity, separation, and projection. We derive all these memory models as instances of our general framework with differing similarity and separation functions. We extend the mathematical framework of Krotov et al (2020) to express general associative memory models using neural network dynamics with local computation, and derive a general energy function that is a Lyapunov function of the dynamics. Finally, using our framework, we empirically investigate the capacity of using different similarity functions for these associative memory models, beyond the dot product similarity measure, and demonstrate empirically that Euclidean or Manhattan distance similarity metrics perform substantially better in practice on many tasks, enabling a more robust retrieval and higher memory capacity than existing models.
Learning Stochastic Shortest Path with Linear Function Approximation
Authors: Yifei Min, Jiafan He, Tianhao Wang, Quanquan Gu
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: We study the stochastic shortest path (SSP) problem in reinforcement learning with linear function approximation, where the transition kernel is represented as a linear mixture of unknown models. We call this class of SSP problems as linear mixture SSPs. We propose a novel algorithm with Hoeffding-type confidence sets for learning the linear mixture SSP, which can attain an $\tilde\mathcalO(d B_⋆^1.5\sqrtK/c_\min)$ regret. Here $K$ is the number of episodes, $d$ is the dimension of the feature mapping in the mixture model, $B_⋆$ bounds the expected cumulative cost of the optimal policy, and $c_\min>0$ is the lower bound of the cost function. Our algorithm also applies to the case when $c_\min = 0$, and an $\tilde\mathcalO(K^2/3)$ regret is guaranteed. To the best of our knowledge, this is the first algorithm with a sublinear regret guarantee for learning linear mixture SSP. Moreover, we design a refined Bernstein-type confidence set and propose an improved algorithm, which provably achieves an $\tilde\mathcalO(d B_⋆\sqrtK/c_\min)$ regret. In complement to the regret upper bounds, we also prove a lower bound of $Ømega(dB_⋆ \sqrtK)$. Hence, our improved algorithm matches the lower bound up to a $1/\sqrtc_\min$ factor and poly-logarithmic factors, achieving a near-optimal regret guarantee.
Prioritized Training on Points that are Learnable, Worth Learning, and not yet Learnt
Authors: Sören Mindermann, Jan M Brauner, Muhammed T Razzak, Mrinank Sharma, Andreas Kirsch, Winnie Xu, Benedikt Höltgen, Aidan N Gomez, Adrien Morisot, Sebastian Farquhar, Yarin Gal
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Training on web-scale data can take months. But much computation and time is wasted on redundant and noisy points that are already learnt or not learnable. To accelerate training, we introduce Reducible Holdout Loss Selection (RHO-LOSS), a simple but principled technique which selects approximately those points for training that most reduce the model’s generalization loss. As a result, RHO-LOSS mitigates the weaknesses of existing data selection methods: techniques from the optimization literature typically select "hard" (e.g. high loss) points, but such points are often noisy (not learnable) or less task-relevant. Conversely, curriculum learning prioritizes "easy" points, but such points need not be trained on once learned. In contrast, RHO-LOSS selects points that are learnable, worth learning, and not yet learnt. RHO-LOSS trains in far fewer steps than prior art, improves accuracy, and speeds up training on a wide range of datasets, hyperparameters, and architectures (MLPs, CNNs, and BERT). On the large web-scraped image dataset Clothing-1M, RHO-LOSS trains in 18x fewer steps and reaches 2% higher final accuracy than uniform data shuffling.
POEM: Out-of-Distribution Detection with Posterior Sampling
Authors: Yifei Ming, Ying Fan, Yixuan Li
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Out-of-distribution (OOD) detection is indispensable for machine learning models deployed in the open world. Recently, the use of an auxiliary outlier dataset during training (also known as outlier exposure) has shown promising performance. As the sample space for potential OOD data can be prohibitively large, sampling informative outliers is essential. In this work, we propose a novel posterior sampling based outlier mining framework, POEM, which facilitates efficient use of outlier data and promotes learning a compact decision boundary between ID and OOD data for improved detection. We show that POEM establishes state-of-the-art performance on common benchmarks. Compared to the current best method that uses a greedy sampling strategy, POEM improves the relative performance by 42.0% and 24.2% (FPR95) on CIFAR-10 and CIFAR-100, respectively. We further provide theoretical insights on the effectiveness of POEM for OOD detection.
A Simple Reward-free Approach to Constrained Reinforcement Learning
Authors: Sobhan Miryoosefi, Chi Jin
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: In constrained reinforcement learning (RL), a learning agent seeks to not only optimize the overall reward but also satisfy the additional safety, diversity, or budget constraints. Consequently, existing constrained RL solutions require several new algorithmic ingredients that are notably different from standard RL. On the other hand, reward-free RL is independently developed in the unconstrained literature, which learns the transition dynamics without using the reward information, and thus naturally capable of addressing RL with multiple objectives under the common dynamics. This paper bridges reward-free RL and constrained RL. Particularly, we propose a simple meta-algorithm such that given any reward-free RL oracle, the approachability and constrained RL problems can be directly solved with negligible overheads in sample complexity. Utilizing the existing reward-free RL solvers, our framework provides sharp sample complexity results for constrained RL in the tabular MDP setting, matching the best existing results up to a factor of horizon dependence; our framework directly extends to a setting of tabular two-player Markov games, and gives a new result for constrained RL with linear function approximation.
Wide Neural Networks Forget Less Catastrophically
Authors: Seyed Iman Mirzadeh, Arslan Chaudhry, Dong Yin, Huiyi Hu, Razvan Pascanu, Dilan Gorur, Mehrdad Farajtabar
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: A primary focus area in continual learning research is alleviating the "catastrophic forgetting" problem in neural networks by designing new algorithms that are more robust to the distribution shifts. While the recent progress in continual learning literature is encouraging, our understanding of what properties of neural networks contribute to catastrophic forgetting is still limited. To address this, instead of focusing on continual learning algorithms, in this work, we focus on the model itself and study the impact of "width" of the neural network architecture on catastrophic forgetting, and show that width has a surprisingly significant effect on forgetting. To explain this effect, we study the learning dynamics of the network from various perspectives such as gradient orthogonality, sparsity, and lazy training regime. We provide potential explanations that are consistent with the empirical results across different architectures and continual learning benchmarks.
Proximal and Federated Random Reshuffling
Authors: Konstantin Mishchenko, Ahmed Khaled, Peter Richtarik
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Random Reshuffling (RR), also known as Stochastic Gradient Descent (SGD) without replacement, is a popular and theoretically grounded method for finite-sum minimization. We propose two new algorithms: Proximal and Federated Random Reshuffling (ProxRR and FedRR). The first algorithm, ProxRR, solves composite finite-sum minimization problems in which the objective is the sum of a (potentially non-smooth) convex regularizer and an average of $n$ smooth objectives. ProxRR evaluates the proximal operator once per epoch only. When the proximal operator is expensive to compute, this small difference makes ProxRR up to $n$ times faster than algorithms that evaluate the proximal operator in every iteration, such as proximal (stochastic) gradient descent. We give examples of practical optimization tasks where the proximal operator is difficult to compute and ProxRR has a clear advantage. One such task is federated or distributed optimization, where the evaluation of the proximal operator corresponds to communication across the network. We obtain our second algorithm, FedRR, as a special case of ProxRR applied to federated optimization, and prove it has a smaller communication footprint than either distributed gradient descent or Local SGD. Our theory covers both constant and decreasing stepsizes, and allows for importance resampling schemes that can improve conditioning, which may be of independent interest. Our theory covers both convex and nonconvex regimes. Finally, we corroborate our results with experiments on real data sets.
ProxSkip: Yes! Local Gradient Steps Provably Lead to Communication Acceleration! Finally!
Authors: Konstantin Mishchenko, Grigory Malinovsky, Sebastian Stich, Peter Richtarik
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: We introduce ProxSkip—a surprisingly simple and provably efficient method for minimizing the sum of a smooth ($f$) and an expensive nonsmooth proximable ($ψ$) function. The canonical approach to solving such problems is via the proximal gradient descent (ProxGD) algorithm, which is based on the evaluation of the gradient of $f$ and the prox operator of $ψ$ in each iteration. In this work we are specifically interested in the regime in which the evaluation of prox is costly relative to the evaluation of the gradient, which is the case in many applications. ProxSkip allows for the expensive prox operator to be skipped in most iterations: while its iteration complexity is $\mathcalO(ąppa łog ∋cefrac1ɛ)$, where $\p̨pa$ is the condition number of $f$, the number of prox evaluations is $\mathcalO(\sqrt\kp̨a łog ∋cefrac1ɛ)$ only. Our main motivation comes from federated learning, where evaluation of the gradient operator corresponds to taking a local GD step independently on all devices, and evaluation of prox corresponds to (expensive) communication in the form of gradient averaging. In this context, ProxSkip offers an effective <em>acceleration</em> of communication complexity. Unlike other local gradient-type methods, such as FedAvg, SCAFFOLD, S-Local-GD and FedLin, whose theoretical communication complexity is worse than, or at best matching, that of vanilla GD in the heterogeneous data regime, we obtain a provable and large improvement without any heterogeneity-bounding assumptions.
Fast Convex Optimization for Two-Layer ReLU Networks: Equivalent Model Classes and Cone Decompositions
Authors: Aaron Mishkin, Arda Sahiner, Mert Pilanci
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: We develop fast algorithms and robust software for convex optimization of two-layer neural networks with ReLU activation functions. Our work leverages a convex re-formulation of the standard weight-decay penalized training problem as a set of group-l1-regularized data-local models, where locality is enforced by polyhedral cone constraints. In the special case of zero-regularization, we show that this problem is exactly equivalent to unconstrained optimization of a convex "gated ReLU" network. For problems with non-zero regularization, we show that convex gated ReLU models obtain data-dependent approximation bounds for the ReLU training problem. To optimize the convex re-formulations, we develop an accelerated proximal gradient method and a practical augmented Lagrangian solver. We show that these approaches are faster than standard training heuristics for the non-convex problem, such as SGD, and outperform commercial interior-point solvers. Experimentally, we verify our theoretical results, explore the group-l1 regularization path, and scale convex optimization for neural networks to image classification on MNIST and CIFAR-10.
Memory-Based Model Editing at Scale
Authors: Eric Mitchell, Charles Lin, Antoine Bosselut, Christopher D Manning, Chelsea Finn
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Even the largest neural networks make errors, and once-correct predictions can become invalid as the world changes. Model editors make local updates to the behavior of base (pre-trained) models to inject updated knowledge or correct undesirable behaviors. Existing model editors have shown promise, but also suffer from insufficient expressiveness: they struggle to accurately model an edit’s intended scope (examples affected by the edit), leading to inaccurate predictions for test inputs loosely related to the edit, and they often fail altogether after many edits. As a higher-capacity alternative, we propose Semi-Parametric Editing with a Retrieval-Augmented Counterfactual Model (SERAC), which stores edits in an explicit memory and learns to reason over them to modulate the base model’s predictions as needed. To enable more rigorous evaluation of model editors, we introduce three challenging language model editing problems based on question answering, fact-checking, and dialogue generation. We find that only SERAC achieves high performance on all three problems, consistently outperforming existing approaches to model editing by a significant margin. Code, data, and additional project information will be made available at https://sites.google.com/view/serac-editing.
Invariant Ancestry Search
Authors: Phillip B Mogensen, Nikolaj Thams, Jonas Peters
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Recently, methods have been proposed that exploit the invariance of prediction models with respect to changing environments to infer subsets of the causal parents of a response variable. If the environments influence only few of the underlying mechanisms, the subset identified by invariant causal prediction (ICP), for example, may be small, or even empty. We introduce the concept of minimal invariance and propose invariant ancestry search (IAS). In its population version, IAS outputs a set which contains only ancestors of the response and is a superset of the output of ICP. When applied to data, corresponding guarantees hold asymptotically if the underlying test for invariance has asymptotic level and power. We develop scalable algorithms and perform experiments on simulated and real data.
Differentially Private Community Detection for Stochastic Block Models
Authors: Mohamed S Mohamed, Dung Nguyen, Anil Vullikanti, Ravi Tandon
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: The goal of community detection over graphs is to recover underlying labels/attributes of users (e.g., political affiliation) given the connectivity between users. There has been significant recent progress on understanding the fundamental limits of community detection when the graph is generated from a stochastic block model (SBM). Specifically, sharp information theoretic limits and efficient algorithms have been obtained for SBMs as a function of $p$ and $q$, which represent the intra-community and inter-community connection probabilities. In this paper, we study the community detection problem while preserving the privacy of the individual connections between the vertices. Focusing on the notion of $(ε, δ)$-edge differential privacy (DP), we seek to understand the fundamental tradeoffs between $(p, q)$, DP budget $(ε, δ)$, and computational efficiency for exact recovery of community labels. To this end, we present and analyze the associated information-theoretic tradeoffs for three differentially private community recovery mechanisms: a) stability based mechanism; b) sampling based mechanisms; and c) graph perturbation mechanisms. Our main findings are that stability and sampling based mechanisms lead to a superior tradeoff between $(p,q)$ and the privacy budget $(ε, δ)$; however this comes at the expense of higher computational complexity. On the other hand, albeit low complexity, graph perturbation mechanisms require the privacy budget $ε$ to scale as $Ømega(łog(n))$ for exact recovery.
A Multi-objective / Multi-task Learning Framework Induced by Pareto Stationarity
Authors: Michinari Momma, Chaosheng Dong, Jia Liu
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Multi-objective optimization (MOO) and multi-task learning (MTL) have gained much popularity with prevalent use cases such as production model development of regression / classification / ranking models with MOO, and training deep learning models with MTL. Despite the long history of research in MOO, its application to machine learning requires development of solution strategy, and algorithms have recently been developed to solve specific problems such as discovery of any Pareto optimal (PO) solution, and that with a particular form of preference. In this paper, we develop a novel and generic framework to discover a PO solution with multiple forms of preferences. It allows us to formulate a generic MOO / MTL problem to express a preference, which is solved to achieve both alignment with the preference and PO, at the same time. Specifically, we apply the framework to solve the weighted Chebyshev problem and an extension of that. The former is known as a method to discover the Pareto front, the latter helps to find a model that outperforms an existing model with only one run. Experimental results demonstrate not only the method achieves competitive performance with existing methods, but also it allows us to achieve the performance from different forms of preferences.
EqR: Equivariant Representations for Data-Efficient Reinforcement Learning
Authors: Arnab Kumar Mondal, Vineet Jain, Kaleem Siddiqi, Siamak Ravanbakhsh
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: We study a variety of notions of equivariance as an inductive bias in Reinforcement Learning (RL). In particular, we propose new mechanisms for learning representations that are equivariant to both the agent’s action, as well as symmetry transformations of the state-action pairs. Whereas prior work on exploiting symmetries in deep RL can only incorporate predefined linear transformations, our approach allows non-linear symmetry transformations of state-action pairs to be learned from the data. This is achieved through 1) equivariant Lie algebraic parameterization of state and action encodings, 2) equivariant latent transition models, and 3) the incorporation of symmetry-based losses. We demonstrate the advantages of our method, which we call Equivariant representations for RL (EqR), for Atari games in a data-efficient setting limited to 100K steps of interactions with the environment.
Feature and Parameter Selection in Stochastic Linear Bandits
Authors: Ahmadreza Moradipari, Berkay Turan, Yasin Abbasi-Yadkori, Mahnoosh Alizadeh, Mohammad Ghavamzadeh
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: We study two model selection settings in stochastic linear bandits (LB). In the first setting, which we refer to as feature selection, the expected reward of the LB problem is in the linear span of at least one of $M$ feature maps (models). In the second setting, the reward parameter of the LB problem is arbitrarily selected from $M$ models represented as (possibly) overlapping balls in $\mathbb R^d$. However, the agent only has access to misspecified models, i.e., estimates of the centers and radii of the balls. We refer to this setting as parameter selection. For each setting, we develop and analyze a computationally efficient algorithm that is based on a reduction from bandits to full-information problems. This allows us to obtain regret bounds that are not worse (up to a $\sqrtłog M$ factor) than the case where the true model is known. This is the best reported dependence on the number of models $M$ in these settings. Finally, we empirically show the effectiveness of our algorithms using synthetic and real-world experiments.
Power-Law Escape Rate of SGD
Authors: Takashi Mori, Liu Ziyin, Kangqiao Liu, Masahito Ueda
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Stochastic gradient descent (SGD) undergoes complicated multiplicative noise for the mean-square loss. We use this property of SGD noise to derive a stochastic differential equation (SDE) with simpler additive noise by performing a random time change. Using this formalism, we show that the log loss barrier $Δłog L=łog[L(þeta^s)/L(þeta^*)]$ between a local minimum $þeta^*$ and a saddle $þeta^s$ determines the escape rate of SGD from the local minimum, contrary to the previous results borrowing from physics that the linear loss barrier $Δ L=L(þeta^s)-L(þeta^*)$ decides the escape rate. Our escape-rate formula strongly depends on the typical magnitude $h^*$ and the number $n$ of the outlier eigenvalues of the Hessian. This result explains an empirical fact that SGD prefers flat minima with low effective dimensions, giving an insight into implicit biases of SGD.
Rethinking Fano’s Inequality in Ensemble Learning
Authors: Terufumi Morishita, Gaku Morio, Shota Horiguchi, Hiroaki Ozaki, Nobuo Nukaga
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: We propose a fundamental theory on ensemble learning that evaluates a given ensemble system by a well-grounded set of metrics. Previous studies used a variant of Fano’s inequality of information theory and derived a lower bound of the classification error rate on the basis of the accuracy and diversity of models. We revisit the original Fano’s inequality and argue that the studies did not take into account the information lost when multiple model predictions are combined into a final prediction. To address this issue, we generalize the previous theory to incorporate the information loss. Further, we empirically validate and demonstrate the proposed theory through extensive experiments on actual systems. The theory reveals the strengths and weaknesses of systems on each metric, which will push the theoretical understanding of ensemble learning and give us insights into designing systems.
SpeqNets: Sparsity-aware permutation-equivariant graph networks
Authors: Christopher Morris, Gaurav Rattan, Sandra Kiefer, Siamak Ravanbakhsh
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: While message-passing graph neural networks have clear limitations in approximating permutation-equivariant functions over graphs or general relational data, more expressive, higher-order graph neural networks do not scale to large graphs. They either operate on $k$-order tensors or consider all $k$-node subgraphs, implying an exponential dependence on $k$ in memory requirements, and do not adapt to the sparsity of the graph. By introducing new heuristics for the graph isomorphism problem, we devise a class of universal, permutation-equivariant graph networks, which, unlike previous architectures, offer a fine-grained control between expressivity and scalability and adapt to the sparsity of the graph. These architectures lead to vastly reduced computation times compared to standard higher-order graph networks in the supervised node- and graph-level classification and regression regime while significantly improving standard graph neural network and graph kernel architectures in terms of predictive performance.
CtrlFormer: Learning Transferable State Representation for Visual Control via Transformer
Authors: Yao Mark Mu, Shoufa Chen, Mingyu Ding, Jianyu Chen, Runjian Chen, Ping Luo
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Transformer has achieved great successes in learning vision and language representation, which is general across various downstream tasks. In visual control, learning transferable state representation that can transfer between different control tasks is important to reduce the training sample size. However, porting Transformer to sample-efficient visual control remains a challenging and unsolved problem. To this end, we propose a novel Control Transformer (CtrlFormer), possessing many appealing benefits that prior arts do not have. Firstly, CtrlFormer jointly learns self-attention mechanisms between visual tokens and policy tokens among different control tasks, where multitask representation can be learned and transferred without catastrophic forgetting. Secondly, we carefully design a contrastive reinforcement learning paradigm to train CtrlFormer, enabling it to achieve high sample efficiency, which is important in control problems. For example, in the DMControl benchmark, unlike recent advanced methods that failed by producing a zero score in the “Cartpole” task after transfer learning with 100k samples, CtrlFormer can achieve a state-of-the-art score with only 100k samples while maintaining the performance of previous tasks. The code and models are released in our project homepage.
Generalized Beliefs for Cooperative AI
Authors: Darius Muglich, Luisa M Zintgraf, Christian A Schroeder De Witt, Shimon Whiteson, Jakob Foerster
Published in: Proceedings of the 39th International Conference on Machine Learning (Main Conference Track), 2022

Abstract: Self-play is a common method for constructing solutions in Markov games that can yield optimal policies in collaborative settings. However, these policies often adopt highly-specialized conventions that make playing with a novel partner difficult. To address this, recent approaches rely on encoding symmetry and convention-awareness into policy training, but these require strong environmental assumptions and can complicate policy training. To overcome this, we propose moving the learning of conventions to the belief space. Specifically, we propose a belief learning paradigm that can maintain beliefs over rollouts of policies not seen at training time, and can thus decode and adapt to novel conventions at test time. We show how to leverage this belief model for both search and training of a best response over a pool of policies to greatly improve zero-shot coordination. We also show how our paradigm promotes explainability and interpretability of nuanced agent conventions.