ICML 2021 Papers

Since the Message Passing (Graph) Neural Networks (MPNNs) have a linear complexity with respect to the number of nodes when applied to sparse graphs, they have been widely implemented and still raise a lot of interest even though their theoretical expressive power is limited to the first order Weisfeiler-Lehman test (1-WL). In this paper, we show that if the graph convolution supports are designed in spectral-domain by a non-linear custom function of eigenvalues and masked with an arbitrary large receptive field, the MPNN is theoretically more powerful than the 1-WL test and experimentally as powerful as a 3-WL existing models, while remaining spatially localized. Moreover, by designing custom filter functions, outputs can have various frequency components that allow the convolution process to learn different relationships between a given input graph signal and its associated properties. So far, the best 3-WL equivalent graph neural networks have a computational complexity in $\mathcal{O}(n^3)$ with memory usage in $\mathcal{O}(n^2)$, consider non-local update mechanism and do not provide the spectral richness of output profile. The proposed method overcomes all these aforementioned problems and reaches state-of-the-art results in many downstream tasks.

The deadly triad refers to the instability of a reinforcement learning algorithm when it employs off-policy learning, function approximation, and bootstrapping simultaneously. In this paper, we investigate the target network as a tool for breaking the deadly triad, providing theoretical support for the conventional wisdom that a target network stabilizes training. We first propose and analyze a novel target network update rule which augments the commonly used Polyak-averaging style update with two projections. We then apply the target network and ridge regularization in several divergent algorithms and show their convergence to regularized TD fixed points. Those algorithms are off-policy with linear function approximation and bootstrapping, spanning both policy evaluation and control, as well as both discounted and average-reward settings. In particular, we provide the first convergent linear $Q$-learning algorithms under nonrestrictive and changing behavior policies without bi-level optimization.

We consider repair tasks: given a critic (e.g., compiler) that assesses the quality of an input, the goal is to train a fixer that converts a bad example (e.g., code with syntax errors) into a good one (e.g., code with no errors). Existing works create training data consisting of (bad, good) pairs by corrupting good examples using heuristics (e.g., dropping tokens). However, fixers trained on this synthetically-generated data do not extrapolate well to the real distribution of bad inputs. To bridge this gap, we propose a new training approach, Break-It-Fix-It (BIFI), which has two key ideas: (i) we use the critic to check a fixer’s output on real bad inputs and add good (fixed) outputs to the training data, and (ii) we train a breaker to generate realistic bad code from good code. Based on these ideas, we iteratively update the breaker and the fixer while using them in conjunction to generate more paired data. We evaluate BIFI on two code repair datasets: GitHub-Python, a new dataset we introduce where the goal is to repair Python code with AST parse errors; and DeepFix, where the goal is to repair C code with compiler errors. BIFI outperforms existing methods, obtaining 90.5% repair accuracy on GitHub-Python (+28.5%) and 71.7% on DeepFix (+5.6%). Notably, BIFI does not require any labeled data; we hope it will be a strong starting point for unsupervised learning of various repair tasks.

Bootstrapping provides a flexible and effective approach for assessing the quality of batch reinforcement learning, yet its theoretical properties are poorly understood. In this paper, we study the use of bootstrapping in off-policy evaluation (OPE), and in particular, we focus on the fitted Q-evaluation (FQE) that is known to be minimax-optimal in the tabular and linear-model cases. We propose a bootstrapping FQE method for inferring the distribution of the policy evaluation error and show that this method is asymptotically efficient and distributionally consistent for off-policy statistical inference. To overcome the computation limit of bootstrapping, we further adapt a subsampling procedure that improves the runtime by an order of magnitude. We numerically evaluate the bootrapping method in classical RL environments for confidence interval estimation, estimating the variance of off-policy evaluator, and estimating the correlation between multiple off-policy evaluators.

Datacenter vision systems widely use small, specialized convolutional neural networks (CNNs) trained on specific tasks for high-throughput inference. These settings employ accelerators with massive computational capacity, but which specialized CNNs underutilize due to having low arithmetic intensity. This results in suboptimal application-level throughput and poor returns on accelerator investment. Increasing batch size is the only known way to increase both application-level throughput and accelerator utilization for inference, but yields diminishing returns; specialized CNNs poorly utilize accelerators even with large batch size. We propose FoldedCNNs, a new approach to CNN design that increases inference throughput and utilization beyond large batch size. FoldedCNNs rethink the structure of inputs and layers of specialized CNNs to boost arithmetic intensity: in FoldedCNNs, f images with C channels each are concatenated into a single input with fC channels and jointly classified by a wider CNN. Increased arithmetic intensity in FoldedCNNs increases the throughput and GPU utilization of specialized CNN inference by up to 2.5x and 2.8x, with accuracy close to the original CNN in most cases.

We consider the decision-making framework of online convex optimization with a very large number of experts. This setting is ubiquitous in contextual and reinforcement learning problems, where the size of the policy class renders enumeration and search within the policy class infeasible. Instead, we consider generalizing the methodology of online boosting. We define a weak learning algorithm as a mechanism that guarantees multiplicatively approximate regret against a base class of experts. In this access model, we give an efficient boosting algorithm that guarantees near-optimal regret against the convex hull of the base class. We consider both full and partial (a.k.a. bandit) information feedback models. We also give an analogous efficient boosting algorithm for the i.i.d. statistical setting. Our results simultaneously generalize online boosting and gradient boosting guarantees to contextual learning model, online convex optimization and bandit linear optimization settings.

Much of the work in the field of group fairness addresses disparities between predefined groups based on protected features such as gender, age, and race, which need to be available at train, and often also at test, time. These approaches are static and retrospective, since algorithms designed to protect groups identified a priori cannot anticipate and protect the needs of different at-risk groups in the future. In this work we analyze the space of solutions for worst-case fairness beyond demographics, and propose Blind Pareto Fairness (BPF), a method that leverages no-regret dynamics to recover a fair minimax classifier that reduces worst-case risk of any potential subgroup of sufficient size, and guarantees that the remaining population receives the best possible level of service. BPF addresses fairness beyond demographics, that is, it does not rely on predefined notions of at-risk groups, neither at train nor at test time. Our experimental results show that the proposed framework improves worst-case risk in multiple standard datasets, while simultaneously providing better levels of service for the remaining population. The code is available at github.com/natalialmg/BlindParetoFairness

We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor requires any problem-specific tuning, and is asymptotically exact for any density function with a bounded domain. The output is an approximation to the whole density function including the normalisation constant, via partitions organised in efficient data structures. Such approximations may be used for evidence estimation or fast posterior sampling, but also as building blocks to treat a larger class of estimation problems. The algorithm shows competitive performance to recent state-of-the-art methods on synthetic and real-world problems including parameter inference for gravitational-wave physics.

To cope with high annotation costs, training a classifier only from weakly supervised data has attracted a great deal of attention these days. Among various approaches, strengthening supervision from completely unsupervised classification is a promising direction, which typically employs class priors as the only supervision and trains a binary classifier from unlabeled (U) datasets. While existing risk-consistent methods are theoretically grounded with high flexibility, they can learn only from two U sets. In this paper, we propose a new approach for binary classification from $m$ U-sets for $m\ge2$. Our key idea is to consider an auxiliary classification task called surrogate set classification (SSC), which is aimed at predicting from which U set each observed sample is drawn. SSC can be solved by a standard (multi-class) classification method, and we use the SSC solution to obtain the final binary classifier through a certain linear-fractional transformation. We built our method in a flexible and efficient end-to-end deep learning framework and prove it to be classifier-consistent. Through experiments, we demonstrate the superiority of our proposed method over state-of-the-art methods.

This work introduces Bilinear Classes, a new structural framework, which permit generalization in reinforcement learning in a wide variety of settings through the use of function approximation. The framework incorporates nearly all existing models in which a polynomial sample complexity is achievable, and, notably, also includes new models, such as the Linear Q*/V* model in which both the optimal Q-function and the optimal V-function are linear in some known feature space. Our main result provides an RL algorithm which has polynomial sample complexity for Bilinear Classes; notably, this sample complexity is stated in terms of a reduction to the generalization error of an underlying supervised learning sub-problem. These bounds nearly match the best known sample complexity bounds for existing models. Furthermore, this framework also extends to the infinite dimensional (RKHS) setting: for the the Linear Q*/V* model, linear MDPs, and linear mixture MDPs, we provide sample complexities that have no explicit dependence on the explicit feature dimension (which could be infinite), but instead depends only on information theoretic quantities.

Bilevel optimization has arisen as a powerful tool for many machine learning problems such as meta-learning, hyperparameter optimization, and reinforcement learning. In this paper, we investigate the nonconvex-strongly-convex bilevel optimization problem. For deterministic bilevel optimization, we provide a comprehensive convergence rate analysis for two popular algorithms respectively based on approximate implicit differentiation (AID) and iterative differentiation (ITD). For the AID-based method, we orderwisely improve the previous convergence rate analysis due to a more practical parameter selection as well as a warm start strategy, and for the ITD-based method we establish the first theoretical convergence rate. Our analysis also provides a quantitative comparison between ITD and AID based approaches. For stochastic bilevel optimization, we propose a novel algorithm named stocBiO, which features a sample-efficient hypergradient estimator using efficient Jacobian- and Hessian-vector product computations. We provide the convergence rate guarantee for stocBiO, and show that stocBiO outperforms the best known computational complexities orderwisely with respect to the condition number $\kappa$ and the target accuracy $\epsilon$. We further validate our theoretical results and demonstrate the efficiency of bilevel optimization algorithms by the experiments on meta-learning and hyperparameter optimization.

Recently, local SGD has got much attention and been extensively studied in the distributed learning community to overcome the communication bottleneck problem. However, the superiority of local SGD to minibatch SGD only holds in quite limited situations. In this paper, we study a new local algorithm called Bias-Variance Reduced Local SGD (BVR-L-SGD) for nonconvex distributed optimization. Algorithmically, our proposed bias and variance reduced local gradient estimator fully utilizes small second-order heterogeneity of local objectives and suggests randomly picking up one of the local models instead of taking the average of them when workers are synchronized. Theoretically, under small heterogeneity of local objectives, we show that BVR-L-SGD achieves better communication complexity than both the previous non-local and local methods under mild conditions, and particularly BVR-L-SGD is the first method that breaks the barrier of communication complexity $\Theta(1/\varepsilon)$ for general nonconvex smooth objectives when the heterogeneity is small and the local computation budget is large. Numerical results are given to verify the theoretical findings and give empirical evidence of the superiority of our method.

We consider Bayesian optimization in settings where observations can be adversarially biased, for example by an uncontrolled hidden confounder. Our first contribution is a reduction of the confounded setting to the dueling bandit model. Then we propose a novel approach for dueling bandits based on information-directed sampling (IDS). Thereby, we obtain the first efficient kernelized algorithm for dueling bandits that comes with cumulative regret guarantees. Our analysis further generalizes a previously proposed semi-parametric linear bandit model to non-linear reward functions, and uncovers interesting links to doubly-robust estimation.

Scalable Gaussian Process methods are computationally attractive, yet introduce modeling biases that require rigorous study. This paper analyzes two common techniques: early truncated conjugate gradients (CG) and random Fourier features (RFF). We find that both methods introduce a systematic bias on the learned hyperparameters: CG tends to underfit while RFF tends to overfit. We address these issues using randomized truncation estimators that eliminate bias in exchange for increased variance. In the case of RFF, we show that the bias-to-variance conversion is indeed a trade-off: the additional variance proves detrimental to optimization. However, in the case of CG, our unbiased learning procedure meaningfully outperforms its biased counterpart with minimal additional computation. Our code is available at https://github.com/ cunningham-lab/RTGPS.

Many problems in engineering design and simulation require balancing competing objectives under the presence of uncertainty. Sample-efficient multiobjective optimization methods focus on the objective function values in metric space and ignore the sampling behavior of the design configurations in parameter space. Consequently, they may provide little actionable insight on how to choose designs in the presence of metric uncertainty or limited precision when implementing a chosen design. We propose a new formulation that accounts for the importance of the parameter space and is thus more suitable for multiobjective design problems; instead of searching for the Pareto-efficient frontier, we solicit the desired minimum performance thresholds on all objectives to define regions of satisfaction. We introduce an active search algorithm called Expected Coverage Improvement (ECI) to efficiently discover the region of satisfaction and simultaneously sample diverse acceptable configurations. We demonstrate our algorithm on several design and simulation domains: mechanical design, additive manufacturing, medical monitoring, and plasma physics.

Bandit and reinforcement learning (RL) problems can often be framed as optimization problems where the goal is to maximize average performance while having access only to stochastic estimates of the true gradient. Traditionally, stochastic optimization theory predicts that learning dynamics are governed by the curvature of the loss function and the noise of the gradient estimates. In this paper we demonstrate that the standard view is too limited for bandit and RL problems. To allow our analysis to be interpreted in light of multi-step MDPs, we focus on techniques derived from stochastic optimization principles (e.g., natural policy gradient and EXP3) and we show that some standard assumptions from optimization theory are violated in these problems. We present theoretical results showing that, at least for bandit problems, curvature and noise are not sufficient to explain the learning dynamics and that seemingly innocuous choices like the baseline can determine whether an algorithm converges. These theoretical findings match our empirical evaluation, which we extend to multi-state MDPs.

We design decentralized algorithms for regret minimization in the two sided matching market with one-sided bandit feedback that significantly improves upon the prior works (Liu et al.\,2020a, Sankararaman et al.\,2020, Liu et al.\,2020b). First, for general markets, for any $\varepsilon > 0$, we design an algorithm that achieves a $O(\log^{1+\varepsilon}(T))$ regret to the agent-optimal stable matching, with unknown time horizon $T$, improving upon the $O(\log^{2}(T))$ regret achieved in (Liu et al.\,2020b). Second, we provide the optimal $\Theta(\log(T))$ agent-optimal regret for markets satisfying {\em uniqueness consistency} – markets where leaving participants don’t alter the original stable matching. Previously, $\Theta(\log(T))$ regret was achievable (Sankararaman et al.\,2020, Liu et al.\,2020b) in the much restricted {\em serial dictatorship} setting, when all arms have the same preference over the agents. We propose a phase based algorithm, where in each phase, besides deleting the globally communicated dominated arms the agents locally delete arms with which they collide often. This \emph{local deletion} is pivotal in breaking deadlocks arising from rank heterogeneity of agents across arms. We further demonstrate superiority of our algorithm over existing works through simulations.

We employ constraints to control the parameter space of deep neural networks throughout training. The use of customised, appropriately designed constraints can reduce the vanishing/exploding gradients problem, improve smoothness of classification boundaries, control weight magnitudes and stabilize deep neural networks, and thus enhance the robustness of training algorithms and the generalization capabilities of neural networks. We provide a general approach to efficiently incorporate constraints into a stochastic gradient Langevin framework, allowing enhanced exploration of the loss landscape. We also present specific examples of constrained training methods motivated by orthogonality preservation for weight matrices and explicit weight normalizations. Discretization schemes are provided both for the overdamped formulation of Langevin dynamics and the underdamped form, in which momenta further improve sampling efficiency. These optimisation schemes can be used directly, without needing to adapt neural network architecture design choices or to modify the objective with regularization terms, and see performance improvements in classification tasks.

We introduce and analyze a best arm identification problem in the rested bandit setting, wherein arms are themselves learning algorithms whose expected losses decrease with the number of times the arm has been played. The shape of the expected loss functions is similar across arms, and is assumed to be available up to unknown parameters that have to be learned on the fly. We define a novel notion of regret for this problem, where we compare to the policy that always plays the arm having the smallest expected loss at the end of the game. We analyze an arm elimination algorithm whose regret vanishes as the time horizon increases. The actual rate of convergence depends in a detailed way on the postulated functional form of the expected losses. We complement our analysis with lower bounds, indicating strengths and limitations of the proposed solution.