ICML 2023 论文列表

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N+D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D=1 and to diffusion models when D$\to\infty$. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D$\to\infty$) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64$\times$64 datasets/LSUN Churches 256$\times$256, with median Ds. In class-conditional setting, D=2048 yields current state-of-the-art FID of 1.74 on CIFAR-10 without additional training. Furthermore, we demonstrate that models with smaller $D$ exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Contextual dynamic pricing is a problem of setting prices based on current contextual information and previous sales history to maximize revenue. A popular approach is to postulate a distribution of customer valuation as a function of contextual information and the baseline valuation. A semi-parametric setting, where the context effect is parametric and the baseline is nonparametric, is of growing interest due to its flexibility. A challenge is that customer valuation is almost never observable in practice and is instead *type-I interval censored* by the offered price. To address this challenge, we propose a novel semi-parametric contextual pricing algorithm for stochastic contexts, called the epoch-based Cox proportional hazards Contextual Pricing (CoxCP) algorithm. To our best knowledge, our work is the first to employ the Cox model for customer valuation. The CoxCP algorithm has a high-probability regret upper bound of $\tilde{O}( T^{\frac{2}{3}}d )$, where $T$ is the length of horizon and $d$ is the dimension of context. In addition, if the baseline is known, the regret bound can improve to $O( d \log T )$ under certain assumptions. We demonstrate empirically the proposed algorithm performs better than existing semi-parametric contextual pricing algorithms when the model assumptions of all algorithms are correct.

We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small $L^2$ error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order moment, by either employing early stopping or assuming smoothness condition on the score function of the data distribution. Our result does not rely on any log-concavity or functional inequality assumption and has a logarithmic dependence on the smoothness. In particular, we show that under only a finite second moment condition, approximating the following in reverse KL divergence in $\epsilon$-accuracy can be done in $\tilde O\left(\frac{d \log (1/\delta)}{\epsilon}\right)$ steps: 1) the variance-$\delta$ Gaussian perturbation of any data distribution; 2) data distributions with $1/\delta$-smooth score functions. Our analysis also provides a quantitative comparison between different discrete approximations and may guide the choice of discretization points in practice.

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al. (2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has $\widetilde{\mathcal{O}}(H^3S^2A/\varepsilon^2)$ sample complexity thus improving the $\varepsilon$-dependence upon existing results, where $S$ is a number of states, $A$ is a number of actions, $H$ is an episode length, and $\varepsilon$ is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order $\widetilde{\mathcal{O}}(\mathrm{poly}(S,A,H)/\varepsilon)$. Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to $\widetilde{\mathcal{O}}(H^2SA/\varepsilon^2)$, yielding a statistical separation between maximum entropy exploration and reward-free exploration.

Directed Exploration is a crucial challenge in reinforcement learning (RL), especially when rewards are sparse. Information-directed sampling (IDS), which optimizes the information ratio, seeks to do so by augmenting regret with information gain. However, estimating information gain is computationally intractable or relies on restrictive assumptions which prohibit its use in many practical instances. In this work, we posit an alternative exploration incentive in terms of the integral probability metric (IPM) between a current estimate of the transition model and the unknown optimal, which under suitable conditions, can be computed in closed form with the kernelized Stein discrepancy (KSD). Based on KSD, we develop a novel algorithm STEERING: STEin information dirEcted exploration for model-based Reinforcement LearnING. To enable its derivation, we develop fundamentally new variants of KSD for discrete conditional distributions. We further establish that STEERING archives sublinear Bayesian regret, improving upon prior learning rates of information-augmented MBRL, IDS included. Experimentally, we show that the proposed algorithm is computationally affordable and outperforms several prior approaches.

Reinforcement Learning (RL) algorithms are often known for sample inefficiency and difficult generalization. Recently, Unsupervised Environment Design (UED) emerged as a new paradigm for zero-shot generalization by simultaneously learning a task distribution and agent policies on the generated tasks. This is a non-stationary process where the task distribution evolves along with agent policies; creating an instability over time. While past works demonstrated the potential of such approaches, sampling effectively from the task space remains an open challenge, bottlenecking these approaches. To this end, we introduce CLUTR: a novel unsupervised curriculum learning algorithm that decouples task representation and curriculum learning into a two-stage optimization. It first trains a recurrent variational autoencoder on randomly generated tasks to learn a latent task manifold. Next, a teacher agent creates a curriculum by maximizing a minimax REGRET-based objective on a set of latent tasks sampled from this manifold. Using the fixed-pretrained task manifold, we show that CLUTR successfully overcomes the non-stationarity problem and improves stability. Our experimental results show CLUTR outperforms PAIRED, a principled and popular UED method, in the challenging CarRacing and navigation environments: achieving 10.6X and 45% improvement in zero-shot generalization, respectively. CLUTR also performs comparably to the non-UED state-of-the-art for CarRacing, while requiring 500X fewer environment interactions. We open source our code at https://github.com/clutr/clutr.

Recently, denoising diffusion models have led to significant breakthroughs in the generation of images, audio and text. However, it is still an open question on how to adapt their strong modeling ability to model time series. In this paper, we propose TimeDiff, a non-autoregressive diffusion model that achieves high-quality time series prediction with the introduction of two novel conditioning mechanisms: future mixup and autoregressive initialization. Similar to teacher forcing, future mixup allows parts of the ground-truth future predictions for conditioning, while autoregressive initialization helps better initialize the model with basic time series patterns such as short-term trends. Extensive experiments are performed on nine real-world datasets. Results show that TimeDiff consistently outperforms existing time series diffusion models, and also achieves the best overall performance across a variety of the existing strong baselines (including transformers and FiLM).

Graph coarsening is a dimensionality reduction technique that aims to learn a smaller-tractable graph while preserving the properties of the original input graph. However, many real-world graphs also have features or contexts associated with each node. The existing graph coarsening methods do not consider the node features and rely solely on a graph matrix(e.g., adjacency and Laplacian) to coarsen graphs. However, some recent deep learning-based graph coarsening methods are designed for specific tasks considering both node features and graph matrix. In this paper, we introduce a novel optimization-based framework for graph coarsening that takes both the graph matrix and the node features as the input and jointly learns the coarsened graph matrix and the coarsened feature matrix while ensuring desired properties. To the best of our knowledge, this is the first work that guarantees that the learned coarsened graph is $\epsilon\in[0,1)$ similar to the original graph. Extensive experiments with both real and synthetic benchmark datasets elucidate the proposed framework's efficacy and applicability for numerous graph-based applications, including graph clustering, node classification, stochastic block model identification, and graph summarization.

Consistency plays an important role in learning theory. However, in multiple kernel clustering (MKC), the consistency of kernel weights has not been sufficiently investigated. In this work, we fill this gap with a non-asymptotic analysis on the consistency of kernel weights of a novel method termed SimpleMKKM. Under the assumptions of the eigenvalue gap, we give an infinity norm bound as $\widetilde{\mathcal{O}}(k/\sqrt{n})$, where $k$ is the number of clusters and $n$ is the number of samples. On this basis, we establish an upper bound for the excess clustering risk. Moreover, we study the difference of the kernel weights learned from $n$ samples and $r$ points sampled without replacement, and derive its upper bound as $\widetilde{\mathcal{O}}(k\cdot\sqrt{1/r-1/n})$. Based on the above results, we propose a novel strategy with Nyström method to enable SimpleMKKM to handle large-scale datasets with a theoretical learning guarantee. Finally, extensive experiments are conducted to verify the theoretical results and the effectiveness of the proposed large-scale strategy.

Wider adoption of neural networks in many critical domains such as finance and healthcare is being hindered by the need to explain their predictions and to impose additional constraints on them. Monotonicity constraint is one of the most requested properties in real-world scenarios and is the focus of this paper. One of the oldest ways to construct a monotonic fully connected neural network is to constrain signs on its weights. Unfortunately, this construction does not work with popular non-saturated activation functions as it can only approximate convex functions. We show this shortcoming can be fixed by constructing two additional activation functions from a typical unsaturated monotonic activation function and employing each of them on the part of neurons. Our experiments show this approach of building monotonic neural networks has better accuracy when compared to other state-of-the-art methods, while being the simplest one in the sense of having the least number of parameters, and not requiring any modifications to the learning procedure or post-learning steps. Finally, we prove it can approximate any continuous monotone function on a compact subset of $\mathbb{R}^n$.

To deal with the challenge of high cost of annotating all relevant labels for each example in multi-label learning, single-positive multi-label learning (SPMLL) has been studied in recent years, where each example is annotated with only one positive label. By adopting pseudo-label generation, i.e., assigning pseudo-label to each example by various strategies, existing methods have empirically validated that SPMLL would significantly reduce the amount of supervision with a tolerable damage in classification performance. However, there is no existing method that can provide a theoretical guarantee for learning from pseudo-label on SPMLL. In this paper, the conditions of the effectiveness of learning from pseudo-label for SPMLL are shown and the learnability of pseudo-label-based methods is proven. Furthermore, based on the theoretical guarantee of pseudo-label for SPMLL, we propose a novel SPMLL method named MIME, i.e., Mutual label enhancement for sIngle-positive Multi-label lEarning and prove that the generated pseudo-label by MIME approximately converges to the fully-supervised case. Experiments on four image datasets and five MLL datasets show the effectiveness of our methods over several existing SPMLL approaches.

Graph neural networks (GNNs) have emerged as a powerful paradigm to learn from relational data mostly through applying the message passing mechanism. However, this approach may exhibit suboptimal performance when applied to graphs possessing various structural issues. In this work, we focus on understanding and alleviating the effect of graph structural noise on GNN performance. To evaluate the graph structural noise in real data, we propose edge signal-to-noise ratio (ESNR), a novel metric evaluating overall edge noise level with respect to data features or labels based on random matrix theory. We have found striking concordance between the proposed ESNR metric and the GNN performance in various simulated and real data. To reduce the effect of the noise, we propose GPS (Graph Propensity Score) graph rewiring, which estimates the edge likelihood for rewiring data graphs based on self-supervised link prediction. We provide a theoretical guarantee for GPS graph rewiring and demonstrate its efficacy by comprehensive benchmarks.

For many application domains, the integration of machine learning (ML) models into decision making is hindered by the poor explainability and theoretical guarantees of black box models. Although the emerging area of algorithms with predictions offers a way to leverage ML while enjoying worst-case guarantees, existing work usually assumes access to only one predictor. We demonstrate how to more effectively utilize historical datasets and application domain knowledge by intentionally using predictors of *different* quantities. By leveraging the heterogeneity in our predictors, we are able to achieve improved performance, explainability and computational efficiency over predictor-agnostic methods. Theoretical results are supplemented by large-scale empirical evaluations with production data demonstrating the success of our methods on optimization problems occurring in large distributed computing systems.

In this paper, we introduce BNN-DP, an efficient algorithmic framework for analysis of adversarial robustness of Bayesian Neural Networks (BNNs). Given a compact set of input points $T\subset \mathbb{R}^n$, BNN-DP computes lower and upper bounds on the BNN's predictions for all the points in $T$. The framework is based on an interpretation of BNNs as stochastic dynamical systems, which enables the use of Dynamic Programming (DP) algorithms to bound the prediction range along the layers of the network. Specifically, the method uses bound propagation techniques and convex relaxations to derive a backward recursion procedure to over-approximate the prediction range of the BNN with piecewise affine functions. The algorithm is general and can handle both regression and classification tasks. On a set of experiments on various regression and classification tasks and BNN architectures, we show that BNN-DP outperforms state-of-the-art methods by up to four orders of magnitude in both tightness of the bounds and computational efficiency.

In location estimation, we are given $n$ samples from a known distribution $f$ shifted by an unknown translation $\lambda$, and want to estimate $\lambda$ as precisely as possible. Asymptotically, the maximum likelihood estimate achieves the Cramér-Rao bound of error $\mathcal N(0, \frac{1}{n\mathcal I})$, where $\mathcal I$ is the Fisher information of $f$. However, the $n$ required for convergence depends on $f$, and may be arbitrarily large. We build on the theory using *smoothed* estimators to bound the error for finite $n$ in terms of $\mathcal I_r$, the Fisher information of the $r$-smoothed distribution. As $n \to \infty$, $r \to 0$ at an explicit rate and this converges to the Cramér-Rao bound. We (1) improve the prior work for 1-dimensional $f$ to converge for constant failure probability in addition to high probability, and (2) extend the theory to high-dimensional distributions. In the process, we prove a new bound on the norm of a high-dimensional random variable whose 1-dimensional projections are subgamma, which may be of independent interest.

Linear temporal logic (LTL) offers a simplified way of specifying tasks for policy optimization that may otherwise be difficult to describe with scalar reward functions. However, the standard RL framework can be too myopic to find maximally LTL satisfying policies. This paper makes two contributions. First, we develop a new value-function based proxy, using a technique we call eventual discounting, under which one can find policies that satisfy the LTL specification with highest achievable probability. Second, we develop a new experience replay method for generating off-policy data from on-policy rollouts via counterfactual reasoning on different ways of satisfying the LTL specification. Our experiments, conducted in both discrete and continuous state-action spaces, confirm the effectiveness of our counterfactual experience replay approach.

Understanding the effect of a feature vector $x\in \mathbb{R}^d$ on the response value (label) $y\in \mathbb{R}$ is the cornerstone of many statistical learning problems. Ideally, it is desired to understand how a set of collected features combine together and influence the response value, but this problem is notoriously difficult, due to the high-dimensionality of data and limited number of labeled data points, among many others. In this work, we take a new perspective on this problem, and we study the question of assessing the difference of influence that the two given features have on the response value. We first propose a notion of closeness for the influence of features, and show that our definition recovers the familiar notion of the magnitude of coefficients in the parametric model. We then propose a novel method to test for the closeness of influence in general model-free supervised learning problems. Our proposed test can be used with finite number of samples with control on type I error rate, no matter the ground truth conditional law $\mathcal{L}(Y|X)$. We analyze the power of our test for two general learning problems i) linear regression, and ii) binary classification under mixture of Gaussian models, and show that under the proper choice of score function, an internal component of our test, with sufficient number of samples will achieve full statistical power. We evaluate our findings through extensive numerical simulations, specifically we adopt the datamodel framework (Ilyas, et al., 2022) for CIFAR-10 dataset to identify pairs of training samples with different influence on the trained model via optional black box training mechanisms.

Random forests and, more generally, (decision-)tree ensembles are widely used methods for classification and regression. Recent algorithmic advances allow to compute decision trees that are optimal for various measures such as their size or depth. We are not aware of such research for tree ensembles and aim to contribute to this area. Mainly, we provide two novel algorithms and corresponding lower bounds. First, we are able to carry over and substantially improve on tractability results for decision trees, obtaining a $(6\delta D S)^S \cdot \mathrm{poly}$-time algorithm, where $S$ is the number of cuts in the tree ensemble, $D$ the largest domain size, and $\delta$ is the largest number of features in which two examples differ. To achieve this, we introduce the witness-tree technique which also seems promising for practice. Second, we show that dynamic programming, which has been successful for decision trees, may also be viable for tree ensembles, providing an $\ell^n \cdot \mathrm{poly}$-time algorithm, where $\ell$ is the number of trees and $n$ the number of examples. Finally, we compare the number of cuts necessary to classify training data sets for decision trees and tree ensembles, showing that ensembles may need exponentially fewer cuts for increasing number of trees.

Distributed training of foundation models, especially large language models (LLMs), is communication-intensive and so has heavily relied on centralized data centers with fast interconnects. Can we train on slow networks and unlock the potential of decentralized infrastructure for foundation models? In this paper, we propose CocktailSGD, a novel communication-efficient training framework that combines three distinct compression techniques -- random sparsification, top-K sparsification, and quantization -- to achieve much greater compression than each individual technique alone. We justify the benefit of such a hybrid approach through a theoretical analysis of convergence. Empirically, we show that CocktailSGD achieves up to 117$\times$ compression in fine-tuning LLMs up to 20 billion parameters without hurting convergence. On a 500Mbps network, CocktailSGD only incurs $\sim$1.2$\times$ slowdown compared with data center networks.