We analyze the convergence rates of stochastic gradient algorithms for smooth finite-sum minimax optimization and show that, for many such algorithms, sampling the data points \emph{without replacement} leads to faster convergence compared to sampling with replacement. For the smooth and strongly convex-strongly concave setting, we consider gradient descent ascent and the proximal point method, and present a unified analysis of two popular without-replacement sampling strategies, namely \emph{Random Reshuffling} (RR), which shuffles the data every epoch, and \emph{Single Shuffling} or \emph{Shuffle Once} (SO), which shuffles only at the beginning. We obtain tight convergence rates for RR and SO and demonstrate that these strategies lead to faster convergence than uniform sampling. Moving beyond convexity, we obtain similar results for smooth nonconvex-nonconcave objectives satisfying a two-sided Polyak-\L{}ojasiewicz inequality. Finally, we demonstrate that our techniques are general enough to analyze the effect of \emph{data-ordering attacks}, where an adversary manipulates the order in which data points are supplied to the optimizer.

Predicting multimodal future behavior of traffic participants is essential for robotic vehicles to make safe decisions. Existing works explore to directly predict future trajectories based on latent features or utilize dense goal candidates to identify agent's destinations, where the former strategy converges slowly since all motion modes are derived from the same feature while the latter strategy has efficiency issue since its performance highly relies on the density of goal candidates. In this paper, we propose the Motion TRansformer (MTR) framework that models motion prediction as the joint optimization of global intention localization and local movement refinement. Instead of using goal candidates, MTR incorporates spatial intention priors by adopting a small set of learnable motion query pairs. Each motion query pair takes charge of trajectory prediction and refinement for a specific motion mode, which stabilizes the training process and facilitates better multimodal predictions.

Few-shot knowledge graph (KG) completion task aims to perform inductive reasoning over the KG: given only a few support triplets of a new relation \bowtie (e.g., (chop, \bowtie,kitchen), (read, \bowtie,library), the goal is to predict the query triplets of the same unseen relation \bowtie, e.g., (sleep, \bowtie,?). Current approaches cast the problem in a meta-learning framework, where the model needs to be first jointly trained over many training few-shot tasks, each being defined by its own relation, so that learning/prediction on the target few-shot task can be effective. However, in real-world KGs, curating many training tasks is a challenging ad hoc process. Here we propose Connection Subgraph Reasoner (CSR), which can make predictions for the target few-shot task directly without the need for pre-training on the human curated set of training tasks. The key to CSR is that we explicitly model a shared connection subgraph between support and query triplets, as inspired by the principle of eliminative induction.

The idea of using a separately trained target model (or teacher) to improve the performance of the student model has been increasingly popular in various machine learning domains, and meta-learning is no exception; a recent discovery shows that utilizing task-wise target models can significantly boost the generalization performance. However, obtaining a target model for each task can be highly expensive, especially when the number of tasks for meta-learning is large. To tackle this issue, we propose a simple yet effective method, coined Self-improving Momentum Target (SiMT). SiMT generates the target model by adapting from the temporal ensemble of the meta-learner, i.e., the momentum network. This momentum network and its task-specific adaptations enjoy a favorable generalization performance, enabling self-improving of the meta-learner through knowledge distillation.

Nonnegative (linear) least square problems are a fundamental class of problems that is well-studied in statistical learning and for which solvers have been implemented in many of the standard programming languages used within the machine learning community. The existing off-the-shelf solvers view the non-negativity constraint in these problems as an obstacle and, compared to unconstrained least squares, perform additional effort to address it. However, in many of the typical applications, the data itself is nonnegative as well, and we show that the nonnegativity in this case makes the problem easier. In particular, while the worst-case dimension-independent oracle complexity of unconstrained least squares problems necessarily scales with one of the data matrix constants (typically the spectral norm) and these problems are solved to additive error, we show that nonnegative least squares problems with nonnegative data are solvable to multiplicative error and with complexity that is independent of any matrix constants. The algorithm we introduce is accelerated and based on a primal-dual perspective.

Test-time adaptation (TTA) refers to adapting neural networks to distribution shifts, specifically with just access to unlabeled test samples from the new domain at test-time. Prior TTA methods optimize over unsupervised objectives such as the entropy of model predictions in TENT (Wang et al., 2021), but it is unclear what exactly makes a good TTA loss. In this paper, we start by presenting a surprising phenomenon: if we attempt to \textit{meta-learn} the best'' possible TTA loss over a wide class of functions, then we recover a function that is \textit{remarkably} similar to (a temperature-scaled version of) the softmax-entropy employed by TENT. This only holds, however, if the classifier we are adapting is trained via cross-entropy loss; if the classifier is trained via squared loss, a different best'' TTA loss emerges.To explain this phenomenon, we analyze test-time adaptation through the lens of the training losses's \textit{convex conjugate} . We show that under natural conditions, this (unsupervised) conjugate function can be viewed as a good local approximation to the original supervised loss and indeed, it recovers the best'' losses found by meta-learning.

Multi-Agent Reinforcement Learning (MARL) has demonstrated significant suc2 cess by virtue of collaboration across agents. Recent work, on the other hand, introduces surprise which quantifies the degree of change in an agent's environ4 ment. Surprise-based learning has received significant attention in the case of single-agent entropic settings but remains an open problem for fast-paced dynamics in multi-agent scenarios. A potential alternative to address surprise may be realized through the lens of free-energy minimization. We explore surprise minimization in multi-agent learning by utilizing the free energy across all agents in a multi-agent system.

Decentralized optimization are playing an important role in applications such as training large machine learning models, among others. Despite its superior practical performance, there has been some lack of fundamental understanding about its theoretical properties. In this work, we address the following open research question: To train an overparameterized model over a set of distributed nodes, what is the {\it minimum} communication overhead (in terms of the bits got exchanged) that the system needs to sustain, while still achieving (near) zero training loss? We show that for a class of overparameterized models where the number of parameters D is much larger than the total data samples N, the best possible communication complexity is {\Omega}(N), which is independent of the problem dimension D . Further, for a few specific overparameterized models (i.e., the linear regression, and certain multi-layer neural network with one wide layer), we develop a set of algorithms which uses certain linear compression followed by adaptive quantization, and show that they achieve dimension independent, and sometimes near optimal, communication complexity.

Graph Neural Networks (GNNs) and Graph Kernels (GKs) are two fundamental tools used to analyze graph-structured data. Efforts have been recently made in developing a composite graph learning architecture combining the expressive power of GNNs and the transparent trainability of GKs. However, learning efficiency on these models should be carefully considered as the huge computation overhead. Besides, their convolutional methods are often straightforward and introduce severe loss of graph structure information. In this paper, we design a novel quantum graph learning model to characterize the structural information while using quantum parallelism to improve computing efficiency. Specifically, a quantum algorithm is proposed to approximately estimate the neural tangent kernel of the underlying graph neural network where a multi-head quantum attention mechanism is introduced to properly incorporate semantic similarity information of nodes into the model.

In this paper, we study a large-scale multi-agent minimax optimization problem, which models many interesting applications in statistical learning and game theory, including Generative Adversarial Networks (GANs). The overall objective is a sum of agents' private local objective functions. We focus on the federated setting, where agents can perform local computation and communicate with a central server. Most existing federated minimax algorithms either require communication per iteration or lack performance guarantees with the exception of Local Stochastic Gradient Descent Ascent (SGDA), a multiple-local-update descent ascent algorithm which guarantees convergence under a diminishing stepsize. By analyzing Local SGDA under the ideal condition of no gradient noise, we show that generally it cannot guarantee exact convergence with constant stepsizes and thus suffers from slow rates of convergence.