ICML 2019 论文列表

We consider the PAC learnability of the local functions at the vertices of a discrete networked dynamical system, assuming that the underlying network is known. Our focus is on the learnability of threshold functions. We show that several variants of threshold functions are PAC learnable and provide tight bounds on the sample complexity. In general, when the input consists of positive and negative examples, we show that the concept class of threshold functions is not efficiently PAC learnable, unless NP = RP. Using a dynamic programming approach, we show efficient PAC learnability when the number of negative examples is small. We also present an efficient learner which is consistent with all the positive examples and at least (1-1/e) fraction of the negative examples. This algorithm is based on maximizing a submodular function under matroid constraints. By performing experiments on both synthetic and real-world networks, we study how the network structure and sample complexity influence the quality of the inferred system.

We consider the problem of identifying any k out of the best m arms in an n-armed stochastic multi-armed bandit; framed in the PAC setting, this particular problem generalises both the problem of “best subset selection” (Kalyanakrishnan & Stone, 2010) and that of selecting “one out of the best m” arms (Roy Chaudhuri & Kalyanakrishnan, 2017). We present a lower bound on the worst-case sample complexity for general k, and a fully sequential PAC algorithm, LUCB-k-m, which is more sample-efficient on easy instances. Also, extending our analysis to infinite-armed bandits, we present a PAC algorithm that is independent of n, which identifies an arm from the best $\rho$ fraction of arms using at most an additive poly-log number of samples than compared to the lower bound, thereby improving over Roy Chaudhuri & Kalyanakrishnan (2017) and Aziz et al. (2018). The problem of identifying k > 1 distinct arms from the best $\rho$ fraction is not always well-defined; for a special class of this problem, we present lower and upper bounds. Finally, through a reduction, we establish a relation between upper bounds for the “one out of the best $\rho$” problem for infinite instances and the “one out of the best m” problem for finite instances. We conjecture that it is more efficient to solve “small” finite instances using the latter formulation, rather than going through the former.

Alternating gradient descent (A-GD) is a simple but popular algorithm in machine learning, which updates two blocks of variables in an alternating manner using gradient descent steps. In this paper, we consider a smooth unconstrained nonconvex optimization problem, and propose a perturbed A-GD (PA-GD) which is able to converge (with high probability) to the second-order stationary points (SOSPs) with a global sublinear rate. Existing analysis on A-GD type algorithm either only guarantees convergence to first-order solutions, or converges to second-order solutions asymptotically (without rates). To the best of our knowledge, this is the first alternating type algorithm that takes $\mathcal{O}(\text{polylog}(d)/\epsilon^2)$ iterations to achieve an ($\epsilon,\sqrt{\epsilon}$)-SOSP with high probability, where polylog$(d)$ denotes the polynomial of the logarithm with respect to problem dimension $d$.

Many modern learning tasks involve fitting nonlinear models which are trained in an overparameterized regime where the parameters of the model exceed the size of the training dataset. Due to this overparameterization, the training loss may have infinitely many global minima and it is critical to understand the properties of the solutions found by first-order optimization schemes such as (stochastic) gradient descent starting from different initializations. In this paper we demonstrate that when the loss has certain properties over a minimally small neighborhood of the initial point, first order methods such as (stochastic) gradient descent have a few intriguing properties: (1) the iterates converge at a geometric rate to a global optima even when the loss is nonconvex, (2) among all global optima of the loss the iterates converge to one with a near minimal distance to the initial point, (3) the iterates take a near direct route from the initial point to this global optimum. As part of our proof technique, we introduce a new potential function which captures the tradeoff between the loss function and the distance to the initial point as the iterations progress. The utility of our general theory is demonstrated for a variety of problem domains spanning low-rank matrix recovery to shallow neural network training.

We identify a phenomenon, which we refer to as multi-model forgetting, that occurs when sequentially training multiple deep networks with partially-shared parameters; the performance of previously-trained models degrades as one optimizes a subsequent one, due to the overwriting of shared parameters. To overcome this, we introduce a statistically-justified weight plasticity loss that regularizes the learning of a model’s shared parameters according to their importance for the previous models, and demonstrate its effectiveness when training two models sequentially and for neural architecture search. Adding weight plasticity in neural architecture search preserves the best models to the end of the search and yields improved results in both natural language processing and computer vision tasks.

We identify a new variational inference scheme for dynamical systems whose transition function is modelled by a Gaussian process. Inference in this setting has either employed computationally intensive MCMC methods, or relied on factorisations of the variational posterior. As we demonstrate in our experiments, the factorisation between latent system states and transition function can lead to a miscalibrated posterior and to learning unnecessarily large noise terms. We eliminate this factorisation by explicitly modelling the dependence between state trajectories and the low-rank representation of our Gaussian process posterior. Samples of the latent states can then be tractably generated by conditioning on this representation. The method we obtain gives better predictive performance and more calibrated estimates of the transition function, yet maintains the same time and space complexities as mean-field methods.

We propose the orthogonal random forest, an algorithm that combines Neyman-orthogonality to reduce sensitivity with respect to estimation error of nuisance parameters with generalized random forests (Athey et al., 2017)—a flexible non-parametric method for statistical estimation of conditional moment models using random forests. We provide a consistency rate and establish asymptotic normality for our estimator. We show that under mild assumptions on the consistency rate of the nuisance estimator, we can achieve the same error rate as an oracle with a priori knowledge of these nuisance parameters. We show that when the nuisance functions have a locally sparse parametrization, then a local ell_1-penalized regression achieves the required rate. We apply our method to estimate heterogeneous treatment effects from observational data with discrete treatments or continuous treatments, and we show that, unlike prior work, our method provably allows to control for a high-dimensional set of variables under standard sparsity conditions. We also provide a comprehensive empirical evaluation of our algorithm on both synthetic and real data.

Policy Search (PS) is an effective approach to Reinforcement Learning (RL) for solving control tasks with continuous state-action spaces. In this paper, we address the exploration-exploitation trade-off in PS by proposing an approach based on Optimism in the Face of Uncertainty. We cast the PS problem as a suitable Multi Armed Bandit (MAB) problem, defined over the policy parameter space, and we propose a class of algorithms that effectively exploit the problem structure, by leveraging Multiple Importance Sampling to perform an off-policy estimation of the expected return. We show that the regret of the proposed approach is bounded by $\widetilde{\mathcal{O}}(\sqrt{T})$ for both discrete and continuous parameter spaces. Finally, we evaluate our algorithms on tasks of varying difficulty, comparing them with existing MAB and RL algorithms.

We propose a novel combination of optimization tools with learning theory bounds in order to analyze the sample complexity of optimal kernel sum classifiers. This contrasts the typical learning theoretic results which hold for all (potentially suboptimal) classifiers. Our work also justifies assumptions made in prior work on multiple kernel learning. As a byproduct of our analysis, we also provide a new form of Rademacher complexity for hypothesis classes containing only optimal classifiers.

This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance ( i.e. that minimizes a total cost of transporting probability masses) that unveils the geometric nature of the structured objects space. Unlike Wasserstein or Gromov-Wasserstein metrics that focus solely and respectively on features (by considering a metric in the feature space) or structure (by seeing structure as a metric space), our new distance exploits jointly both information, and is consequently called Fused Gromov-Wasserstein (FGW). After discussing its properties and computational aspects, we show results on a graph classification task, where our method outperforms both graph kernels and deep graph convolutional networks. Exploiting further on the metric properties of FGW, interesting geometric objects such as Fr{é}chet means or barycenters of graphs are illustrated and discussed in a clustering context.

Boosting algorithms iteratively produce linear combinations of more and more base hypotheses and it has been observed experimentally that the generalization error keeps improving even after achieving zero training error. One popular explanation attributes this to improvements in margins. A common goal in a long line of research, is to obtain large margins using as few base hypotheses as possible, culminating with the AdaBoostV algorithm by R{ä}tsch and Warmuth [JMLR’05]. The AdaBoostV algorithm was later conjectured to yield an optimal trade-off between number of hypotheses trained and the minimal margin over all training points (Nie, Warmuth, Vishwanathan and Zhang [JMLR’13]). Our main contribution is a new algorithm refuting this conjecture. Furthermore, we prove a lower bound which implies that our new algorithm is optimal.

Recently it has been shown that the step sizes of a family of variance reduced gradient methods called the JacSketch methods depend on the expected smoothness constant. In particular, if this expected smoothness constant could be calculated a priori, then one could safely set much larger step sizes which would result in a much faster convergence rate. We fill in this gap, and provide simple closed form expressions for the expected smoothness constant and careful numerical experiments verifying these bounds. Using these bounds, and since the SAGA algorithm is part of this JacSketch family, we suggest a new standard practice for setting the step and mini-batch sizes for SAGA that are competitive with a numerical grid search. Furthermore, we can now show that the total complexity of the SAGA algorithm decreases linearly in the mini-batch size up to a pre-defined value: the optimal mini-batch size. This is a rare result in the stochastic variance reduced literature, only previously shown for the Katyusha algorithm. Finally we conjecture that this is the case for many other stochastic variance reduced methods and that our bounds and analysis of the expected smoothness constant is key to extending these results.

One of the central goals of Recurrent Neural Networks (RNNs) is to learn long-term dependencies in sequential data. Nevertheless, the most popular training method, Truncated Backpropagation through Time (TBPTT), categorically forbids learning dependencies beyond the truncation horizon. In contrast, the online training algorithm Real Time Recurrent Learning (RTRL) provides untruncated gradients, with the disadvantage of impractically large computational costs. Recently published approaches reduce these costs by providing noisy approximations of RTRL. We present a new approximation algorithm of RTRL, Optimal Kronecker-Sum Approximation (OK). We prove that OK is optimal for a class of approximations of RTRL, which includes all approaches published so far. Additionally, we show that OK has empirically negligible noise: Unlike previous algorithms it matches TBPTT in a real world task (character-level Penn TreeBank) and can exploit online parameter updates to outperform TBPTT in a synthetic string memorization task. Code available at GitHub.

Mean field inference for discrete graphical models is generally a highly nonconvex problem, which also holds for the class of probabilistic log-submodular models. Existing optimization methods, e.g., coordinate ascent algorithms, typically only find local optima. In this work we propose provable mean filed methods for probabilistic log-submodular models and its posterior agreement (PA) with strong approximation guarantees. The main algorithmic technique is a new Double Greedy scheme, termed DR-DoubleGreedy, for continuous DR-submodular maximization with box-constraints. It is a one-pass algorithm with linear time complexity, reaching the optimal 1/2 approximation ratio, which may be of independent interest. We validate the superior performance of our algorithms against baselines on both synthetic and real-world datasets.

Designing an incentive compatible auction that maximizes expected revenue is an intricate task. The single-item case was resolved in a seminal piece of work by Myerson in 1981. Even after 30-40 years of intense research the problem remains unsolved for seemingly simple multi-bidder, multi-item settings. In this work, we initiate the exploration of the use of tools from deep learning for the automated design of optimal auctions. We model an auction as a multi-layer neural network, frame optimal auction design as a constrained learning problem, and show how it can be solved using standard pipelines. We prove generalization bounds and present extensive experiments, recovering essentially all known analytical solutions for multi-item settings, and obtaining novel mechanisms for settings in which the optimal mechanism is unknown.

We study Lipschitz bandits, where a learner repeatedly plays one arm from an infinite arm set and then receives a stochastic reward whose expectation is a Lipschitz function of the chosen arm. Most of existing work assume the reward distributions are bounded or at least sub-Gaussian, and thus do not apply to heavy-tailed rewards arising in many real-world scenarios such as web advertising and financial markets. To address this limitation, in this paper we relax the assumption on rewards to allow arbitrary distributions that have finite $(1+\epsilon)$-th moments for some $\epsilon \in (0, 1]$, and propose algorithms that enjoy a sublinear regret of $\widetilde{O}(T^{(d_z\epsilon + 1)/(d_z \epsilon + \epsilon + 1)})$ where $T$ is the time horizon and $d_z$ is the zooming dimension. The key idea is to exploit the Lipschitz property of the expected reward function by adaptively discretizing the arm set, and employ upper confidence bound policies with robust mean estimators designed for heavy-tailed distributions. Furthermore, we provide a lower bound for Lipschitz bandits with heavy-tailed rewards, and show that our algorithms are optimal in terms of $T$. Finally, we conduct numerical experiments to demonstrate the effectiveness of our algorithms.

Zero-sum games such as chess and poker are, abstractly, functions that evaluate pairs of agents, for example labeling them ‘winner’ and ‘loser’. If the game is approximately transitive, then self-play generates sequences of agents of increasing strength. However, nontransitive games, such as rock-paper-scissors, can exhibit strategic cycles, and there is no longer a clear objective – we want agents to increase in strength, but against whom is unclear. In this paper, we introduce a geometric framework for formulating agent objectives in zero-sum games, in order to construct adaptive sequences of objectives that yield open-ended learning. The framework allows us to reason about population performance in nontransitive games, and enables the development of a new algorithm (rectified Nash response, PSRO_rN) that uses game-theoretic niching to construct diverse populations of effective agents, producing a stronger set of agents than existing algorithms. We apply PSRO_rN to two highly nontransitive resource allocation games and find that PSRO_rN consistently outperforms the existing alternatives.

Machine learning models that take computer program source code as input typically use Natural Language Processing (NLP) techniques. However, a major challenge is that code is written using an open, rapidly changing vocabulary due to, e.g., the coinage of new variable and method names. Reasoning over such a vocabulary is not something for which most NLP methods are designed. We introduce a Graph-Structured Cache to address this problem; this cache contains a node for each new word the model encounters with edges connecting each word to its occurrences in the code. We find that combining this graph-structured cache strategy with recent Graph-Neural-Network-based models for supervised learning on code improves the models’ performance on a code completion task and a variable naming task — with over 100% relative improvement on the latter — at the cost of a moderate increase in computation time.

We present a generalization of the adversarial linear bandits framework, where the underlying losses are kernel functions (with an associated reproducing kernel Hilbert space) rather than linear functions. We study a version of the exponential weights algorithm and bound its regret in this setting. Under conditions on the eigen-decay of the kernel we provide a sharp characterization of the regret for this algorithm. When we have polynomial eigen-decay ($\mu_j \le \mathcal{O}(j^{-\beta})$), we find that the regret is bounded by $\mathcal{R}_n \le \mathcal{O}(n^{\beta/2(\beta-1)})$. While under the assumption of exponential eigen-decay ($\mu_j \le \mathcal{O}(e^{-\beta j })$) we get an even tighter bound on the regret $\mathcal{R}_n \le \tilde{\mathcal{O}}(n^{1/2})$. When the eigen-decay is polynomial we also show a