ICML 2023 论文列表

Optimal transport (OT) theory focuses, among all maps $T:\mathbb{R}^d\rightarrow \mathbb{R}^d$ that can morph a probability measure $\mu$ onto another $\nu$, on those that are the ``thriftiest'', i.e. such that the average cost $c(x, T(x))$ between $x$ and its image $T(x)$ is as small as possible. Many computational approaches have been proposed to estimate such *Monge* maps when $c$ is the squared-Euclidean distance, e.g., using entropic maps [Pooladian+2021], or input convex neural networks [Makkuva+2020, Korotin+2020]. We propose a new research direction, that leverages a specific translation invariant cost $c(x, y):=h(x-y)$ inspired by the elastic net. Here, $h:=\tfrac{1}{2}\|\cdot\|_2^2+\tau(\cdot)$, where $\tau$ is a convex function. We highlight a surprising link tying together a generalized entropic map for $h$, *Bregman* centroids induced by $h$, and the proximal operator of $\tau$. We show how setting $\tau$ to be a sparsity-inducing norm results in the first application of *Occam*'s razor to transport. These maps yield, mechanically, displacement vectors $\Delta(x):= T(x)-x$ that are sparse, with sparsity patterns that vary depending on $x$. We showcase the ability of our method to estimate meaningful OT maps for high-dimensional single-cell transcription data. We use our methods in the $34000$-d space of gene counts for cells, *without* using a prior dimensionality reduction, thus retaining the ability to interpret all displacements at the gene level.

General function approximation is a powerful tool to handle large state and action spaces in a broad range of reinforcement learning (RL) scenarios. However, theoretical understanding of non-stationary MDPs with general function approximation is still limited. In this paper, we make the first such an attempt. We first propose a new complexity metric called dynamic Bellman Eluder (DBE) dimension for non-stationary MDPs, which subsumes majority of existing tractable RL problems in static MDPs as well as non-stationary MDPs. Based on the proposed complexity metric, we propose a novel confidence-set based model-free algorithm called SW-OPEA, which features a sliding window mechanism and a new confidence set design for non-stationary MDPs. We then establish an upper bound on the dynamic regret for the proposed algorithm, and show that SW-OPEA is provably efficient as long as the variation budget is not significantly large. We further demonstrate via examples of non-stationary linear and tabular MDPs that our algorithm performs better in small variation budget scenario than the existing UCB-type algorithms. To the best of our knowledge, this is the first dynamic regret analysis in non-stationary MDPs with general function approximation.

We consider a non-stationary Bandits with Knapsack problem. The outcome distribution at each time is scaled by a non-stationary quantity that signifies changing demand volumes. Instead of studying settings with limited non-stationarity, we investigate how online predictions on the total demand volume $Q$ allows us to improve our performance guarantees. We show that, without any prediction, any online algorithm incurs a linear-in-$T$ regret. In contrast, with online predictions on $Q$, we propose an online algorithm that judiciously incorporates the predictions, and achieve regret bounds that depends on the accuracy of the predictions. These bounds are shown to be tight in settings when prediction accuracy improves across time. Our theoretical results are corroborated by our numerical findings.

Real-world graphs generally have only one kind of tendency in their connections. These connections are either homophilic-prone or heterophily-prone. While graphs with homophily-prone edges tend to connect nodes with the same class (i.e., intra-class nodes), heterophily-prone edges tend to build relationships between nodes with different classes (i.e., inter-class nodes). Existing GNNs only take the original graph as input during training. The problem with this approach is that it forgets to take into consideration the ''missing-half'' structural information, that is, heterophily-prone topology for homophily-prone graphs and homophily-prone topology for heterophily-prone graphs. In our paper, we introduce Graph cOmplementAry Learning, namely GOAL, which consists of two components: graph complementation and complemented graph convolution. The first component finds the missing-half structural information for a given graph to complement it. The complemented graph has two sets of graphs including both homophily- and heterophily-prone topology. In the latter component, to handle complemented graphs, we design a new graph convolution from the perspective of optimisation. The experiment results show that GOAL consistently outperforms all baselines in eight real-world datasets.

We propose *iterative inversion* - an algorithm for learning an inverse function without input-output pairs, but only with samples from the desired output distribution and access to the forward function. The key challenge is a *distribution shift* between the desired outputs and the outputs of an initial random guess, and we prove that iterative inversion can steer the learning correctly, under rather strict conditions on the function. We apply iterative inversion to learn control. Our input is a set of demonstrations of desired behavior, given as video embeddings of trajectories (without actions), and our method iteratively learns to imitate trajectories generated by the current policy, perturbed by random exploration noise. Our approach does not require rewards, and only employs supervised learning, which can be easily scaled to use state-of-the-art trajectory embedding techniques and policy representations. Indeed, with a VQ-VAE embedding, and a transformer-based policy, we demonstrate non-trivial continuous control on several tasks (videos available at https://sites.google.com/view/iter-inver). Further, we report an improved performance on imitating diverse behaviors compared to reward based methods.

In the misspecified kernel ridge regression problem, researchers usually assume the underground true function $f_{\rho}^{\star} \in [\mathcal{H}]^{s}$, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) $\mathcal{H}$ for some $s\in (0,1)$. The existing minimax optimal results require $\left\Vert f_{\rho}^{\star} \right \Vert_{L^{\infty}} < \infty$ which implicitly requires $s > \alpha_{0}$ where $\alpha_{0} \in (0,1) $ is the embedding index, a constant depending on $\mathcal{H}$. Whether the KRR is optimal for all $s\in (0,1)$ is an outstanding problem lasting for years. In this paper, we show that KRR is minimax optimal for any $s\in (0,1)$ when the $\mathcal{H}$ is a Sobolev RKHS.

We introduce a new mechanism for stochastic convex optimization (SCO) with user-level differential privacy guarantees. The convergence rates of this mechanism are similar to those in the prior work of Levy et al. 2021 and Narayanan et al. 2022, but with two important improvements. Our mechanism does not require any smoothness assumptions on the loss. Furthermore, our bounds are also the first where the minimum number of users needed for user-level privacy has no dependence on the dimension and only a logarithmic dependence on the desired excess error. The main idea underlying the new mechanism is to show that the optimizers of strongly convex losses have low local deletion sensitivity, along with a new output perturbation method for functions with low local deletion sensitivity, which could be of independent interest.

Deep learning methods are highly accurate, yet their opaque decision process prevents them from earning full human trust. Concept-based models aim to address this issue by learning tasks based on a set of human-understandable concepts. However, state-of-the-art concept-based models rely on high-dimensional concept embedding representations which lack a clear semantic meaning, thus questioning the interpretability of their decision process. To overcome this limitation, we propose the Deep Concept Reasoner (DCR), the first interpretable concept-based model that builds upon concept embeddings. In DCR, neural networks do not make task predictions directly, but they build syntactic rule structures using concept embeddings. DCR then executes these rules on meaningful concept truth degrees to provide a final interpretable and semantically-consistent prediction in a differentiable manner. Our experiments show that DCR: (i) improves up to +25% w.r.t. state-of-the-art interpretable concept-based models on challenging benchmarks (ii) discovers meaningful logic rules matching known ground truths even in the absence of concept supervision during training, and (iii), facilitates the generation of counterfactual examples providing the learnt rules as guidance.

Despite the widespread application of latent factor analysis, existing methods suffer from the following weaknesses: requiring the number of factors to be known, lack of theoretical guarantees for learning the model structure, and nonidentifiability of the parameters due to rotation invariance properties of the likelihood. We address these concerns by proposing a fast correlation thresholding (CT) algorithm that simultaneously learns the number of latent factors and a rotationally identifiable model structure. Our novel approach translates this structure learning problem into the search for so-called independent maximal cliques in a thresholded correlation graph that can be easily constructed from the observed data. Our clique analysis technique scales well up to thousands of variables, while competing methods are not applicable in a reasonable amount of running time. We establish a finite-sample error bound and high-dimensional consistency for the structure learning of our method. Through a series of simulation studies and a real data example, we show that the CT algorithm is an accurate method for learning the structure of factor analysis models and is robust to violations of its assumptions.

We present Kernel QuantTree (KQT), a non-parametric change detection algorithm that monitors multivariate data through a histogram. KQT constructs a nonlinear partition of the input space that matches pre-defined target probabilities and specifically promotes compact bins adhering to the data distribution, resulting in a powerful detection algorithm. We prove two key theoretical advantages of KQT: *i*) statistics defined over the KQT histogram do not depend on the stationary data distribution $\phi_0$, so detection thresholds can be set a priori to control false positive rate, and *ii*) thanks to the kernel functions adopted, the KQT monitoring scheme is invariant to the roto-translation of the input data. Consequently, KQT does not require any preprocessing step like PCA. Our experiments show that KQT achieves superior detection power than non-parametric state-of-the-art change detection methods, and can reliably control the false positive rate.

The cost of vision-and-language pre-training has become increasingly prohibitive due to end-to-end training of large-scale models. This paper proposes BLIP-2, a generic and efficient pre-training strategy that bootstraps vision-language pre-training from off-the-shelf frozen pre-trained image encoders and frozen large language models. BLIP-2 bridges the modality gap with a lightweight Querying Transformer, which is pre-trained in two stages. The first stage bootstraps vision-language representation learning from a frozen image encoder. The second stage bootstraps vision-to-language generative learning from a frozen language model. BLIP-2 achieves state-of-the-art performance on various vision-language tasks, despite having significantly fewer trainable parameters than existing methods. For example, our model outperforms Flamingo80B by 8.7% on zero-shot VQAv2 with 54x fewer trainable parameters. We also demonstrate the model's emerging capabilities of zero-shot image-to-text generation that can follow natural language instructions.

Answering complex logical queries on incomplete knowledge graphs is a challenging task, and has been widely studied. Embedding-based methods require training on complex queries and may not generalize well to out-of-distribution query structures. Recent work frames this task as an end-to-end optimization problem, and it only requires a pretrained link predictor. However, due to the exponentially large combinatorial search space, the optimal solution can only be approximated, limiting the final accuracy. In this work, we propose QTO (Query Computation Tree Optimization) that can efficiently find the exact optimal solution. QTO finds the optimal solution by a forward-backward propagation on the tree-like computation graph, i.e., query computation tree. In particular, QTO utilizes the independence encoded in the query computation tree to reduce the search space, where only local computations are involved during the optimization procedure. Experiments on 3 datasets show that QTO obtains state-of-the-art performance on complex query answering, outperforming previous best results by an average of 22%. Moreover, QTO can interpret the intermediate solutions for each of the one-hop atoms in the query with over 90% accuracy.

Probabilistic modeling is a central task in machine learning. Probabilistic models should be tractable, i.e., allowing tractable probabilistic inference, but also efficient, i.e., being able to represent a large set of probability distributions. Zhang et al. (ICML 2021) recently proposed a new model, probabilistic generating circuits. They raised the question whether every strongly Rayleigh distribution can be efficiently represented by such circuits. We prove that this question has a negative answer, there are strongly Rayleigh distributions that cannot be represented by polynomial-sized probabilistic generating circuits, assuming a widely accepted complexity theoretic conjecture.

Competitions for shareable and limited resources have long been studied with strategic agents. In reality, agents often have to learn and maximize the rewards of the resources at the same time. To design an individualized competing policy, we model the competition between agents in a novel multi-player multi-armed bandit (MPMAB) setting where players are selfish and aim to maximize their own rewards. In addition, when several players pull the same arm, we assume that these players averagely share the arms' rewards by expectation. Under this setting, we first analyze the Nash equilibrium when arms' rewards are known. Subsequently, we propose a novel Selfish MPMAB with Averaging Allocation (SMAA) approach based on the equilibrium. We theoretically demonstrate that SMAA could achieve a good regret guarantee for each player when all players follow the algorithm. Additionally, we establish that no single selfish player can significantly increase their rewards through deviation, nor can they detrimentally affect other players' rewards without incurring substantial losses for themselves. We finally validate the effectiveness of the method in extensive synthetic experiments.

We study the design of loss functions for click-through rates (CTR) to optimize (social) welfare in advertising auctions. Existing works either only focus on CTR predictions without consideration of business objectives (e.g., welfare) in auctions or assume that the distribution over the participants' expected cost-per-impression (eCPM) is known a priori, then use various additional assumptions on the parametric form of the distribution to derive loss functions for predicting CTRs. In this work, we bring back the welfare objectives of ad auctions into CTR predictions and propose a novel weighted rankloss to train the CTR model. Compared to existing literature, our approach provides a provable guarantee on welfare but without assumptions on the eCPMs' distribution while also avoiding the intractability of naively applying existing learning-to-rank methods. Further, we propose a theoretically justifiable technique for calibrating the losses using labels generated from a teacher network, only assuming that the teacher network has bounded $\ell_2$ generalization error. Finally, we demonstrate the advantages of the proposed loss on synthetic and real-world data.

Counterfactual explanations have been widely studied in explainability, with a range of application dependent methods prominent in fairness, recourse and model understanding. The major shortcoming associated with these methods, however, is their inability to provide explanations beyond the local or instance-level. While many works touch upon the notion of a global explanation, typically suggesting to aggregate masses of local explanations in the hope of ascertaining global properties, few provide frameworks that are both reliable and computationally tractable. Meanwhile, practitioners are requesting more efficient and interactive explainability tools. We take this opportunity to propose Global & Efficient Counterfactual Explanations (GLOBE-CE), a flexible framework that tackles the reliability and scalability issues associated with current state-of-the-art, particularly on higher dimensional datasets and in the presence of continuous features. Furthermore, we provide a unique mathematical analysis of categorical feature translations, utilising it in our method. Experimental evaluation with publicly available datasets and user studies demonstrate that GLOBE-CE performs significantly better than the current state-of-the-art across multiple metrics (e.g., speed, reliability).

We investigate the expressive power of depth-2 bandlimited random neural networks. A random net is a neural network where the hidden layer parameters are frozen with random assignment, and only the output layer parameters are trained by loss minimization. Using random weights for a hidden layer is an effective method to avoid non-convex optimization in standard gradient descent learning. It has also been adopted in recent deep learning theories. Despite the well-known fact that a neural network is a universal approximator, in this study, we mathematically show that when hidden parameters are distributed in a bounded domain, the network may not achieve zero approximation error. In particular, we derive a new nontrivial approximation error lower bound. The proof utilizes the technique of ridgelet analysis, a harmonic analysis method designed for neural networks. This method is inspired by fundamental principles in classical signal processing, specifically the idea that signals with limited bandwidth may not always be able to perfectly reconstruct the original signal. We corroborate our theoretical results with various simulation studies, and generally, two main take-home messages are offered: (i) Not any distribution for selecting random weights is feasible to build a universal approximator; (ii) A suitable assignment of random weights exists but to some degree is associated with the complexity of the target function.

In this paper, we introduce neural network accelerated implicit filtering (NNAIF), a novel family of methods for solving noisy derivative free (i.e. black box, zeroth order) optimization problems. NNAIF intelligently combines the established literature on implicit filtering (IF) optimization methods with a neural network (NN) surrogate model of the objective function, resulting in accelerated derivative free methods for unconstrained optimization problems. The NN surrogate model consists of a fixed number of parameters, which can be as few as $\approx 1.3 \times 10^{4}$, that are updated as NNAIF progresses. We show that NNAIF directly inherits the convergence properties of IF optimization methods, and thus NNAIF is guaranteed to converge towards a critical point of the objective function under appropriate assumptions. Numerical experiments with $31$ noisy problems from the CUTEst optimization benchmark set demonstrate the benefits and costs associated with NNAIF. These benefits include NNAIF's ability to minimize structured functions of several thousand variables much more rapidly than well-known alternatives, such as Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and finite difference based variants of gradient descent (GD) and BFGS, as well as its namesake IF.

In recent years, decentralized bilevel optimization has gained significant attention thanks to its versatility in modeling a wide range of multi-agent learning problems, such as multi-agent reinforcement learning and multi-agent meta-learning. However, one unexplored and fundamental problem in this area is how to solve decentralized stochastic bilevel optimization problems with **domain constraints** while achieving low sample and communication complexities. This problem often arises from multi-agent learning problems with safety constraints. As shown in this paper, constrained decentralized bilevel optimization is far more challenging than its unconstrained counterpart due to the complex coupling structure, which necessitates new algorithm design and analysis techniques. Toward this end, we investigate a class of constrained decentralized bilevel optimization problems, where multiple agents collectively solve a nonconvex-strongly-convex bilevel problem with constraints in the upper-level variables. We propose an algorithm called Prometheus (proximal tracked stochastic recursive estimator) that achieves the first $\mathcal{O}(\epsilon^{-1})$ results in both sample and communication complexities for constrained decentralized bilevel optimization, where $\epsilon>0$ is a desired stationarity error. Collectively, the results in this work contribute to a theoretical foundation for low sample- and communication-complexity constrained decentralized bilevel learning.