A Nearly Optimal Single Loop Algorithm for Stochastic Bilevel Optimization under Unbounded Smoothness

This paper studies the problem of stochastic bilevel optimization where the upper-level function is nonconvex with potentially unbounded smoothness and the lower-level function is strongly convex. This problem is motivated by meta-learning applied to sequential data, such as text classification using recurrent neural networks, where the smoothness constant of the upper-level loss function scales linearly with the gradient norm and can be potentially unbounded. Existing algorithm crucially relies on the nested loop design, which requires significant tuning efforts and is not practical. In this paper, we address this issue by proposing a Single Loop bIlevel oPtimizer (SLIP). The proposed algorithm first updates the lower-level variable by a few steps of stochastic gradient descent, and then simultaneously updates the upper-level variable by normalized stochastic gradient descent with momentum and the lower-level variable by stochastic gradient descent. Under standard assumptions, we show that our algorithm finds an $\epsilon$-stationary point within $\widetilde{O}(1/\epsilon^4)$\footnote{Here $\widetilde{O}(\cdot)$ compresses logarithmic factors of $1/\epsilon$ and $1/\delta$, where $\delta\in(0,1)$ denotes the failure probability.} oracle calls of stochastic gradient or Hessian-vector product, both in expectation and with high probability. This complexity result is nearly optimal up to logarithmic factors without mean-square smoothness of the stochastic gradient oracle. Our proof relies on (i) a refined characterization and control of the lower-level variable and (ii) establishing a novel connection between bilevel optimization and stochastic optimization under distributional drift. Our experiments on various tasks show that our algorithm significantly outperforms strong baselines in bilevel optimization.

Facet-Aware Multi-Head Mixture-of-Experts Model for Sequential Recommendation

Sequential recommendation (SR) systems excel at capturing users' dynamic preferences by leveraging their interaction histories. Most existing SR systems assign a single embedding vector to each item to represent its features, and various types of models are adopted to combine these item embeddings into a sequence representation vector to capture the user intent. However, we argue that this representation alone is insufficient to capture an item's multi-faceted nature (e.g., movie genres, starring actors). Besides, users often exhibit complex and varied preferences within these facets (e.g., liking both action and musical films in the facet of genre), which are challenging to fully represent. To address the issues above, we propose a novel structure called Facet-Aware Multi-Head Mixture-of-Experts Model for Sequential Recommendation (FAME). We leverage sub-embeddings from each head in the last multi-head attention layer to predict the next item separately. This approach captures the potential multi-faceted nature of items without increasing model complexity. A gating mechanism integrates recommendations from each head and dynamically determines their importance. Furthermore, we introduce a Mixture-of-Experts (MoE) network in each attention head to disentangle various user preferences within each facet. Each expert within the MoE focuses on a specific preference. A learnable router network is adopted to compute the importance weight for each expert and aggregate them. We conduct extensive experiments on four public sequential recommendation datasets and the results demonstrate the effectiveness of our method over existing baseline models.

Federated Learning under Periodic Client Participation and Heterogeneous Data: A New Communication-Efficient Algorithm and Analysis

In federated learning, it is common to assume that clients are always available to participate in training, which may not be feasible with user devices in practice. Recent works analyze federated learning under more realistic participation patterns, such as cyclic client availability or arbitrary participation. However, all such works either require strong assumptions (e.g., all clients participate almost surely within a bounded window), do not achieve linear speedup and reduced communication rounds, or are not applicable in the general non-convex setting. In this work, we focus on nonconvex optimization and consider participation patterns in which the chance of participation over a fixed window of rounds is equal among all clients, which includes cyclic client availability as a special case. Under this setting, we propose a new algorithm, named Amplified SCAFFOLD, and prove that it achieves linear speedup, reduced communication, and resilience to data heterogeneity simultaneously. In particular, for cyclic participation, our algorithm is proved to enjoy $\mathcal{O}(\epsilon^{-2})$ communication rounds to find an $\epsilon$-stationary point in the non-convex stochastic setting. In contrast, the prior work under the same setting requires $\mathcal{O}(\kappa^2 \epsilon^{-4})$ communication rounds, where $\kappa$ denotes the data heterogeneity. Therefore, our algorithm significantly reduces communication rounds due to better dependency in terms of $\epsilon$ and $\kappa$. Our analysis relies on a fine-grained treatment of the nested dependence between client participation and errors in the control variates, which results in tighter guarantees than previous work. We also provide experimental results with (1) synthetic data and (2) real-world data with a large number of clients $(N = 250)$, demonstrating the effectiveness of our algorithm under periodic client participation.

Mask-based Membership Inference Attacks for Retrieval-Augmented Generation

Retrieval-Augmented Generation (RAG) has been an effective approach to mitigate hallucinations in large language models (LLMs) by incorporating up-to-date and domain-specific knowledge. Recently, there has been a trend of storing up-to-date or copyrighted data in RAG knowledge databases instead of using it for LLM training. This practice has raised concerns about Membership Inference Attacks (MIAs), which aim to detect if a specific target document is stored in the RAG system's knowledge database so as to protect the rights of data producers. While research has focused on enhancing the trustworthiness of RAG systems, existing MIAs for RAG systems remain largely insufficient. Previous work either relies solely on the RAG system's judgment or is easily influenced by other documents or the LLM's internal knowledge, which is unreliable and lacks explainability. To address these limitations, we propose a Mask-Based Membership Inference Attacks (MBA) framework. Our framework first employs a masking algorithm that effectively masks a certain number of words in the target document. The masked text is then used to prompt the RAG system, and the RAG system is required to predict the mask values. If the target document appears in the knowledge database, the masked text will retrieve the complete target document as context, allowing for accurate mask prediction. Finally, we adopt a simple yet effective threshold-based method to infer the membership of target document by analyzing the accuracy of mask prediction. Our mask-based approach is more document-specific, making the RAG system's generation less susceptible to distractions from other documents or the LLM's internal knowledge. Extensive experiments demonstrate the effectiveness of our approach compared to existing baseline models.

An Accelerated Algorithm for Stochastic Bilevel Optimization under Unbounded Smoothness

This paper investigates a class of stochastic bilevel optimization problems where the upper-level function is nonconvex with potentially unbounded smoothness and the lower-level problem is strongly convex. These problems have significant applications in sequential data learning, such as text classification using recurrent neural networks. The unbounded smoothness is characterized by the smoothness constant of the upper-level function scaling linearly with the gradient norm, lacking a uniform upper bound. Existing state-of-the-art algorithms require $\widetilde{O}(1/\epsilon^4)$ oracle calls of stochastic gradient or Hessian/Jacobian-vector product to find an $\epsilon$-stationary point. However, it remains unclear if we can further improve the convergence rate when the assumptions for the function in the population level also hold for each random realization almost surely (e.g., Lipschitzness of each realization of the stochastic gradient). To address this issue, we propose a new Accelerated Bilevel Optimization algorithm named AccBO. The algorithm updates the upper-level variable by normalized stochastic gradient descent with recursive momentum and the lower-level variable by the stochastic Nesterov accelerated gradient descent algorithm with averaging. We prove that our algorithm achieves an oracle complexity of $\widetilde{O}(1/\epsilon^3)$ to find an $\epsilon$-stationary point. Our proof relies on a novel lemma characterizing the dynamics of stochastic Nesterov accelerated gradient descent algorithm under distribution drift with high probability for the lower-level variable, which is of independent interest and also plays a crucial role in analyzing the hypergradient estimation error over time. Experimental results on various tasks confirm that our proposed algorithm achieves the predicted theoretical acceleration and significantly outperforms baselines in bilevel optimization.

Beyond Single-Model Views for Deep Learning: Optimization versus Generalizability of Stochastic Optimization Algorithms

Despite an extensive body of literature on deep learning optimization, our current understanding of what makes an optimization algorithm effective is fragmented. In particular, we do not understand well whether enhanced optimization translates to improved generalizability. Current research overlooks the inherent stochastic nature of stochastic gradient descent (SGD) and its variants, resulting in a lack of comprehensive benchmarking and insight into their statistical performance. This paper aims to address this gap by adopting a novel approach. Rather than solely evaluating the endpoint of individual optimization trajectories, we draw from an ensemble of trajectories to estimate the stationary distribution of stochastic optimizers. Our investigation encompasses a wide array of techniques, including SGD and its variants, flat-minima optimizers, and new algorithms we propose under the Basin Hopping framework. Through our evaluation, which encompasses synthetic functions with known minima and real-world problems in computer vision and natural language processing, we emphasize fair benchmarking under a statistical framework, comparing stationary distributions and establishing statistical significance. Our study uncovers several key findings regarding the relationship between training loss and hold-out accuracy, as well as the comparable performance of SGD, noise-enabled variants, and novel optimizers utilizing the BH framework. Notably, these algorithms demonstrate performance on par with flat-minima optimizers like SAM, albeit with half the gradient evaluations. We anticipate that our work will catalyze further exploration in deep learning optimization, encouraging a shift away from single-model approaches towards methodologies that acknowledge and leverage the stochastic nature of optimizers.

Bilevel Optimization under Unbounded Smoothness: A New Algorithm and Convergence Analysis

Bilevel optimization is an important formulation for many machine learning problems. Current bilevel optimization algorithms assume that the gradient of the upper-level function is Lipschitz. However, recent studies reveal that certain neural networks such as recurrent neural networks (RNNs) and long-short-term memory networks (LSTMs) exhibit potential unbounded smoothness, rendering conventional bilevel optimization algorithms unsuitable. In this paper, we design a new bilevel optimization algorithm, namely BO-REP, to address this challenge. This algorithm updates the upper-level variable using normalized momentum and incorporates two novel techniques for updating the lower-level variable: \textit{initialization refinement} and \textit{periodic updates}. Specifically, once the upper-level variable is initialized, a subroutine is invoked to obtain a refined estimate of the corresponding optimal lower-level variable, and the lower-level variable is updated only after every specific period instead of each iteration. When the upper-level problem is nonconvex and unbounded smooth, and the lower-level problem is strongly convex, we prove that our algorithm requires $\widetilde{\mathcal{O}}(1/\epsilon^4)$ iterations to find an $\epsilon$-stationary point in the stochastic setting, where each iteration involves calling a stochastic gradient or Hessian-vector product oracle. Notably, this result matches the state-of-the-art complexity results under the bounded smoothness setting and without mean-squared smoothness of the stochastic gradient, up to logarithmic factors. Our proof relies on novel technical lemmas for the periodically updated lower-level variable, which are of independent interest. Our experiments on hyper-representation learning, hyperparameter optimization, and data hyper-cleaning for text classification tasks demonstrate the effectiveness of our proposed algorithm.

LESS-Map: Lightweight and Evolving Semantic Map in Parking Lots for Long-term Self-Localization

Precise and long-term stable localization is essential in parking lots for tasks like autonomous driving or autonomous valet parking, \textit{etc}. Existing methods rely on a fixed and memory-inefficient map, which lacks robust data association approaches. And it is not suitable for precise localization or long-term map maintenance. In this paper, we propose a novel mapping, localization, and map update system based on ground semantic features, utilizing low-cost cameras. We present a precise and lightweight parameterization method to establish improved data association and achieve accurate localization at centimeter-level. Furthermore, we propose a novel map update approach by implementing high-quality data association for parameterized semantic features, allowing continuous map update and refinement during re-localization, while maintaining centimeter-level accuracy. We validate the performance of the proposed method in real-world experiments and compare it against state-of-the-art algorithms. The proposed method achieves an average accuracy improvement of 5cm during the registration process. The generated maps consume only a compact size of 450 KB/km and remain adaptable to evolving environments through continuous update.

Stability and Generalization for Minibatch SGD and Local SGD

The increasing scale of data propels the popularity of leveraging parallelism to speed up the optimization. Minibatch stochastic gradient descent (minibatch SGD) and local SGD are two popular methods for parallel optimization. The existing theoretical studies show a linear speedup of these methods with respect to the number of machines, which, however, is measured by optimization errors. As a comparison, the stability and generalization of these methods are much less studied. In this paper, we pioneer the stability and generalization analysis of minibatch and local SGD to understand their learnability. We incorporate training errors into the stability analysis, which shows how small training errors help generalization for overparameterized models. Our stability bounds imply optimistic risk bounds which decay fast under a low noise condition. We show both minibatch and local SGD achieve a linear speedup to attain the optimal risk bounds.

EPISODE: Episodic Gradient Clipping with Periodic Resampled Corrections for Federated Learning with Heterogeneous Data

Gradient clipping is an important technique for deep neural networks with exploding gradients, such as recurrent neural networks. Recent studies have shown that the loss functions of these networks do not satisfy the conventional smoothness condition, but instead satisfy a relaxed smoothness condition, i.e., the Lipschitz constant of the gradient scales linearly in terms of the gradient norm. Due to this observation, several gradient clipping algorithms have been developed for nonconvex and relaxed-smooth functions. However, the existing algorithms only apply to the single-machine or multiple-machine setting with homogeneous data across machines. It remains unclear how to design provably efficient gradient clipping algorithms in the general Federated Learning (FL) setting with heterogeneous data and limited communication rounds. In this paper, we design EPISODE, the very first algorithm to solve FL problems with heterogeneous data in the nonconvex and relaxed smoothness setting. The key ingredients of the algorithm are two new techniques called \textit{episodic gradient clipping} and \textit{periodic resampled corrections}. At the beginning of each round, EPISODE resamples stochastic gradients from each client and obtains the global averaged gradient, which is used to (1) determine whether to apply gradient clipping for the entire round and (2) construct local gradient corrections for each client. Notably, our algorithm and analysis provide a unified framework for both homogeneous and heterogeneous data under any noise level of the stochastic gradient, and it achieves state-of-the-art complexity results. In particular, we prove that EPISODE can achieve linear speedup in the number of machines, and it requires significantly fewer communication rounds. Experiments on several heterogeneous datasets show the superior performance of EPISODE over several strong baselines in FL.