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Optimization · Bilevel optimization

Ieva Petrulionytė, Julien Mairal, Michael Arbel

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods developed in the parametric setting, where the inner objective is strongly convex with respect to the parameters of the prediction function. The functional point of view does not rely on this assumption and notably allows using over-parameterized neural networks as the inner prediction function. We propose scalable and efficient algorithms for the functional bilevel optimization problem and illustrate the benefits of our approach on instrumental regression and reinforcement learning tasks.

Probabilistic Methods · Gaussian Processes

Yunyue Wei, Vincent Zhuang, Saraswati Soedarmadji, Yanan Sui

Bayesian optimization is an effective technique for black-box optimization, but its applicability is typically limited to low-dimensional and small-budget problems due to the cubic complexity of computing the Gaussian process (GP) surrogate. While various approximate GP models have been employed to scale Bayesian optimization to larger sample sizes, most suffer from overly-smooth estimation and focus primarily on problems that allow for large online samples. In this work, we argue that Bayesian optimization algorithms with sparse GPs can more efficiently allocate their representational power to relevant regions of the search space. To achieve this, we propose focalized GP, which leverages a novel variational loss function to achieve stronger local prediction, as well as FocalBO, which hierarchically optimizes the focalized GP acquisition function over progressively smaller search spaces. Experimental results demonstrate that FocalBO can efficiently leverage large amounts of offline and online data to achieve state-of-the-art performance on robot morphology design and to control a 585-dimensional musculoskeletal system.

Optimization · Convex

Youyuan Long, Tolga Ok, Pedro Zattoni Scroccaro, Peyman Mohajerin Esfahani

Inverse Optimization (IO) is a framework for learning the unknown objective function of an expert decision-maker from a past dataset.In this paper, we extend the hypothesis class of IO objective functions to a reproducing kernel Hilbert space (RKHS), thereby enhancing feature representation to an infinite-dimensional space.We demonstrate that a variant of the representer theorem holds for a specific training loss, allowing the reformulation of the problem as a finite-dimensional convex optimization program.To address scalability issues commonly associated with kernel methods, we propose the Sequential Selection Optimization (SSO) algorithm to efficiently train the proposed Kernel Inverse Optimization (KIO) model.Finally, we validate the generalization capabilities of the proposed KIO model and the effectiveness of the SSO algorithm through learning-from-demonstration tasks on the MuJoCo benchmark.

Privacy

Bonwoo Lee, Jeongyoun Ahn, Cheolwoo Park

As the volume of data invested in statistical learning increases and concerns regarding privacy grow, the privacy leakage issue has drawn significant attention. Differential privacy has emerged as a widely accepted concept capable of mitigating privacy concerns, and numerous differentially private (DP) versions of machine learning algorithms have been developed. However, existing works on DP kernel learning algorithms have exhibited practical limitations, including scalability, restricted choice of kernels, or dependence on test data availability. We propose DP scalable kernel empirical risk minimization (ERM) algorithms and a DP kernel mean embedding (KME) release algorithm suitable for general kernels. Our approaches address the shortcomings of previous algorithms by employing Nyström methods, classical techniques in non-private scalable kernel learning. These methods provide data-dependent low-rank approximations of the kernel matrix for general kernels in a DP manner. We present excess empirical risk bounds and computational complexities for the scalable kernel DP ERM, KME algorithms, contrasting them with established methodologies. Furthermore, we develop a private data-generating algorithm capable of learning diverse kernel models. We conduct experiments to demonstrate the performance of our algorithms, comparing them with existing methods to highlight their superiority.

Trustworthy Machine Learning

Edwige Cyffers, Muni Sreenivas Pydi, Jamal Atif, Olivier Cappé

Performative learning addresses the increasingly pervasive situations in which algorithmic decisions may induce changes in the data distribution as a consequence of their public deployment. We propose a novel view in which these performative effects are modelled as push forward measures. This general framework encompasses existing models and enables novel performative gradient estimation methods, leading to more efficient and scalable learning strategies. For distribution shifts, unlike previous models which require full specification of the data distribution, we only assume knowledge of the shift operator that represents the performative changes. This approach can also be integrated into various change-of-variable-based models, such as VAEs or normalizing flows. Focusing on classification with a linear-in-parameters performative effect, we prove the convexity of the performative risk under a new set of assumptions. Notably, we do not limit the strength of performative effects but rather their direction, requiring only that classification becomes harder when deploying more accurate models. In this case, we also establish a connection with adversarially robust classification by reformulating the performative risk as a min-max variational problem. Finally, we illustrate our approach on synthetic and real datasets.

Reinforcement Learning · Planning

Bharath Muppasani, Protik Nag, Vignesh Narayanan, Biplav Srivastava, Michael Huhns

In this study, we investigate the under-explored intervention planning aimed at disseminating accurate information within dynamic opinion networks by leveraging learning strategies. Intervention planning involves identifying key nodes (search) and exerting control (e.g., disseminating accurate/official information through the nodes) to mitigate the influence of misinformation. However, as the network size increases, the problem becomes computationally intractable. To address this, we first introduce a ranking algorithm to identify key nodes for disseminating accurate information, which facilitates the training of neural network (NN) classifiers that provide generalized solutions for the search and planning problems. Second, we mitigate the complexity of label generation—which becomes challenging as the network grows—by developing a reinforcement learning (RL)-based centralized dynamic planning framework. We analyze these NN-based planners for opinion networks governed by two dynamic propagation models. Each model incorporates both binary and continuous opinion and trust representations. Our experimental results demonstrate that the ranking algorithm-based classifiers provide plans that enhance infection rate control, especially with increased action budgets for small networks. Further, we observe that the reward strategies focusing on key metrics, such as the number of susceptible nodes and infection rates, outperform those prioritizing faster blocking strategies. Additionally, our findings reveal that graph convolutional network (GCN)-based planners facilitate scalable centralized plans that achieve lower infection rates (higher control) across various network configurations (e.g., Watts-Strogatz topology, varying action budgets, varying initial infected nodes, and varying degree of infected nodes).

Reinforcement Learning · Everything Else

Marcel Hussing, Michael Kearns, Aaron Roth, Sikata Sengupta, Jessica Sorrell

Reinforcement learning (RL) in large or infinite state spaces is notoriously challenging, both theoretically (where worst-case sample and computational complexities must scale with state space cardinality) and experimentally (where function approximation and policy gradient techniques often scale poorly and suffer from instability and high variance). One line of research attempting to address these difficultiesmakes the natural assumption that we are given a collection of base or *constituent* policies (possibly heuristic) upon which we would like to improve in a scalable manner. In this work we aim to compete with the *max-following policy*, which at each state follows the action of whichever constituent policy has the highest value. The max-following policy is always at least as good as the best constituent policy, and may be considerably better. Our main result is an efficient algorithm that learns to compete with the max-following policy, given only access to the constituent policies (but not their value functions). In contrast to prior work in similar settings, our theoretical results require only the minimal assumption of an ERM oracle for value function approximation for the constituent policies (and not the global optimal policy or the max-following policy itself) on samplable distributions. We illustrate our algorithm's experimental effectiveness and behavior on several robotic simulation testbeds.

Graph Neural Networks

Eric Zhao, Pranjal Awasthi, Zhengdao Chen, Sreenivas Gollapudi, Daniel Delling

We study learning-based approaches to semantic route planning, which concerns producing routes in response to rich queries that specify various criteria and preferences. Semantic routing is already widely found in industry applications, especially navigational services like Google Maps; however, existing implementations only support limited route criteria and narrow query sets as they rely on repurposing classical route optimization algorithms. We argue for a learning-based approach to semantic routing as a more scalable and general alternative. To foster interest in this important application of graph learning, we are releasing a large-scale publicly-licensed benchmark for semantic routing consisting of real-world multi-objective navigation problems---expressed via natural language queries---on the richly annotated road networks of US cities. In addition to being intractable with existing approaches to semantic routing, our benchmark poses a significant scaling challenge for graph learning methods. As a proof-of-concept, we show that---at scale---even a standard transformer network is a powerful semantic routing system and achieves non-trivial performance on our benchmark. In the process, we demonstrate a simple solution to the challenge of scaling up graph learning: an autoregressive approach that decomposes semantic routing into smaller ``next-edge'' prediction problems.

Probabilistic Methods

Marvin Schmitt, Valentin Pratz, Ullrich Köthe, Paul-Christian Bürkner, Stefan Radev

Simulation-based inference (SBI) is constantly in search of more expressive and efficient algorithms to accurately infer the parameters of complex simulation models.In line with this goal, we present consistency models for posterior estimation (CMPE), a new conditional sampler for SBI that inherits the advantages of recent unconstrained architectures and overcomes their sampling inefficiency at inference time.CMPE essentially distills a continuous probability flow and enables rapid few-shot inference with an unconstrained architecture that can be flexibly tailored to the structure of the estimation problem.We provide hyperparameters and default architectures that support consistency training over a wide range of different dimensions, including low-dimensional ones which are important in SBI workflows but were previously difficult to tackle even with unconditional consistency models. Our empirical evaluation demonstrates that CMPE not only outperforms current state-of-the-art algorithms on hard low-dimensional benchmarks, but also achieves competitive performance with much faster sampling speed on two realistic estimation problems with high data and/or parameter dimensions.

Optimization · Large Scale, Parallel and Distributed

Ilya Kuruzov, Gesualdo Scutari, Alexander Gasnikov

This paper addresses the minimization of the sum of strongly convex, smoothfunctions over a network of agents without a centralized server. Existing decentralized algorithms require knowledge of functions and network parameters, such as the Lipschitz constant of the global gradient and/or network connectivity, forhyperparameter tuning. Agents usually cannot access this information, leadingto conservative selections and slow convergence or divergence. This paper introduces a decentralized algorithm that eliminates the need for specific parametertuning. Our approach employs an operator splitting technique with a novel variablemetric, enabling a local backtracking line-search to adaptively select the stepsizewithout global information or extensive communications. This results in favorableconvergence guarantees and dependence on optimization and network parameterscompared to existing nonadaptive methods. Notably, our method is the first adaptive decentralized algorithm that achieves linear convergence for strongly convex,smooth objectives. Preliminary numerical experiments support our theoreticalfindings, demonstrating superior performance in convergence speed and scalability.

Applications

Xinhao Zheng, Yang Li, Cunxin Fan, Huaijin Wu, Xinhao Song, Junchi Yan

Cryptographic problems, operating within binary variable spaces, can be routinely transformed into Boolean Satisfiability (SAT) problems regarding specific cryptographic conditions like plaintext-ciphertext matching. With the fast development of learning for discrete data, this SAT representation also facilitates the utilization of machine-learning approaches with the hope of automatically capturing patterns and strategies inherent in cryptographic structures in a data-driven manner. Existing neural SAT solvers consistently adopt conjunctive normal form (CNF) for instance representation, which in the cryptographic context can lead to scale explosion and a loss of high-level semantics. In particular, extensively used XOR operations in cryptographic problems can incur an exponential number of clauses. In this paper, we propose a graph structure based on Arithmetic Normal Form (ANF) to efficiently handle the XOR operation bottleneck. Additionally, we design an encoding method for AND operations in these ANF-based graphs, demonstrating improved efficiency over alternative general graph forms for SAT. We then propose CryptoANFNet, a graph learning approach that trains a classifier based on a message-passing scheme to predict plaintext-ciphertext satisfiability. Using ANF-based SAT instances, CryptoANFNet demonstrates superior scalability and can naturally capture higher-order operational information. Empirically, CryptoANFNet achieves a 50x speedup over heuristic solvers and outperforms SOTA learning-based SAT solver NeuroSAT, with 96\% vs. 91\% accuracy on small-scale and 72\% vs. 55\% on large-scale datasets from real encryption algorithms. We also introduce a key-solving algorithm that simplifies ANF-based SAT instances from plaintext and ciphertext, enhancing key decryption accuracy from 76.5\% to 82\% and from 72\% to 75\% for datasets generated from two real encryption algorithms.

Deep Learning · Robustness

Duo Zhou, Christopher Brix, Grani A. Hanasusanto, Huan Zhang

Recently, cutting-plane methods such as GCP-CROWN have been explored to enhance neural network verifiers and made significant advancements. However, GCP-CROWN currently relies on ${\it generic}$ cutting planes ("cuts") generated from external mixed integer programming (MIP) solvers. Due to the poor scalability of MIP solvers, large neural networks cannot benefit from these cutting planes. In this paper, we exploit the structure of the neural network verification problem to generate efficient and scalable cutting planes ${\it specific}$ to this problem setting. We propose a novel approach, Branch-and-bound Inferred Cuts with COnstraint Strengthening (BICCOS), that leverages the logical relationships of neurons within verified subproblems in the branch-and-bound search tree, and we introduce cuts that preclude these relationships in other subproblems. We develop a mechanism that assigns influence scores to neurons in each path to allow the strengthening of these cuts. Furthermore, we design a multi-tree search technique to identify more cuts, effectively narrowing the search space and accelerating the BaB algorithm. Our results demonstrate that BICCOS can generate hundreds of useful cuts during the branch-and-bound process and consistently increase the number of verifiable instances compared to other state-of-the-art neural network verifiers on a wide range of benchmarks, including large networks that previous cutting plane methods could not scale to.

Generative Models · New Approaches

Xinyu Yang, Jixuan Leng, Geyang Guo, Jiawei Zhao, Ryumei Nakada, Linjun Zhang, Huaxiu Yao, Beidi Chen

Current PEFT methods for LLMs can achieve high quality, efficient training, or scalable serving, but not all three simultaneously. To address this limitation, we investigate sparse fine-tuning and observe a remarkable improvement in generalization ability. Utilizing this key insight, we propose a family of Structured Sparse Fine-Tuning (S${^2}$FT) methods for LLMs, which concurrently achieve state-of-the-art fine-tuning performance, training efficiency, and inference scalability. S${^2}$FT accomplishes this by "selecting sparsely and computing densely". Based on the coupled structures in LLMs, \model selects a few attention heads and channels in the MHA and FFN modules for each Transformer block, respectively. Next, it co-permutes the weight matrices on both sides of all coupled structures to connect the selected subsets in each layer into a dense submatrix. Finally, S${^2}$FT performs in-place gradient updates on all selected submatrices.Through theoretical analyses and empirical results, our method prevents forgetting while simplifying optimization, delivers SOTA performance on both commonsense and arithmetic reasoning with 4.6% and 1.3% average improvements compared to LoRA, and surpasses full FT by 11.5% when generalizing to various domains after instruction tuning. Using our partial back-propagation algorithm, S${^2}$FT saves training memory up to 3$\times$ and improves latency by 1.5-2.7$\times$ compared to full FT, while achieving an average 10\% improvement over LoRA on both metrics. We further demonstrate that the weight updates in S${^2}$FT can be decoupled into adapters, enabling effective fusion, fast switch, and efficient parallelism when serving multiple fine-tuned models.

Multimodal Models

Yixia Li, Boya Xiong, Guanhua Chen, Yun Chen

Out-of-distribution (OOD) detection is crucial for the safe deployment of neural networks. Existing CLIP-based approaches perform OOD detection by devising novel scoring functions or sophisticated fine-tuning methods. In this work, we propose SeTAR, a novel, training-free OOD detection method that leverages selective low-rank approximation of weight matrices in vision-language and vision-only models. SeTAR enhances OOD detection via post-hoc modification of the model's weight matrices using a simple greedy search algorithm. Based on SeTAR, we further propose SeTAR+FT, a fine-tuning extension optimizing model performance for OOD detection tasks. Extensive evaluations on ImageNet1K and Pascal-VOC benchmarks show SeTAR's superior performance, reducing the relatively false positive rate by up to 18.95\% and 36.80\% compared to zero-shot and fine-tuning baselines. Ablation studies further validate our approach's effectiveness, robustness, and generalizability across different model backbones. Our work offers a scalable, efficient solution for OOD detection, setting a new state-of-the-art in this area.

Theory · Reinforcement Learning and Planning

Tom Yan, Zachary Lipton

A key source of complexity in next-generation AI models is the size of model outputs, making it time-consuming to parse and provide reliable feedback on. To ensure such models are aligned, we will need to bolster our understanding of scalable oversight and how to scale up human feedback. To this end, we study the challenges of scalable oversight in the context of goal-conditioned hierarchical reinforcement learning. Hierarchical structure is a promising entrypoint into studying how to scale up human feedback, which in this work we assume can only be provided for model outputs below a threshold size. In the cardinal feedback setting, we develop an apt sub-MDP reward and algorithm that allows us to acquire and scale up low-level feedback for learning with sublinear regret. In the ordinal feedback setting, we show the necessity of both high- and low-level feedback, and develop a hierarchical experimental design algorithm that efficiently acquires both types of feedback for learning. Altogether, our work aims to consolidate the foundations of scalable oversight, formalizing and studying the various challenges thereof.

Theory · Game Theory

Zhiyuan Fan, Christian Kroer, Gabriele Farina

First-order methods (FOMs) are arguably the most scalable algorithms for equilibrium computation in large extensive-form games. To operationalize these methods, a distance-generating function, acting as a regularizer for the strategy space, must be chosen. The ratio between the strong convexity modulus and the diameter of the regularizer is a key parameter in the analysis of FOMs.A natural question is then: what is the optimal distance-generating function for extensive-form decision spaces? In this paper, we make a number of contributions, ultimately establishing that the weight-one dilated entropy (DilEnt) distance-generating function is optimal up to logarithmic factors. The DilEnt regularizer is notable due to its iterate-equivalence with Kernelized OMWU (KOMWU)---the algorithm with state-of-the-art dependence on the game tree size in extensive-form games---when used in conjunction with the online mirror descent (OMD) algorithm. However, the standard analysis for OMD is unable to establish such a result; the only current analysis is by appealing to the iterate equivalence to KOMWU. We close this gap by introducing a pair of primal-dual treeplex norms, which we contend form the natural analytic viewpoint for studying the strong convexity of DilEnt. Using these norm pairs, we recover the diameter-to-strong-convexity ratio that predicts the same performance as KOMWU. Along with a new regret lower bound for online learning in sequence-form strategy spaces, we show that this ratio is nearly optimal.Finally, we showcase our analytic techniques by refining the analysis of Clairvoyant OMD when paired with DilEnt, establishing an $\mathcal{O}(n \log |\mathcal{V}| \log T/T)$ approximation rate to coarse correlated equilibrium in $n$-player games, where $|\mathcal{V}|$ is the number of reduced normal-form strategies of the players, establishing the new state of the art.

Miscellaneous Aspects of Machine Learning

Elias Jääsaari, Ville Hyvönen, Teemu Roos

Approximate nearest neighbor (ANN) search is a key component in many modern machine learning pipelines; recent use cases include retrieval-augmented generation (RAG) and vector databases. Clustering-based ANN algorithms, that use score computation methods based on product quantization (PQ), are often used in industrial-scale applications due to their scalability and suitability for distributed and disk-based implementations. However, they have slower query times than the leading graph-based ANN algorithms. In this work, we propose a new supervised score computation method based on the observation that inner product approximation is a multivariate (multi-output) regression problem that can be solved efficiently by reduced-rank regression. Our experiments show that on modern high-dimensional data sets, the proposed reduced-rank regression (RRR) method is superior to PQ in both query latency and memory usage. We also introduce LoRANN, a clustering-based ANN library that leverages the proposed score computation method. LoRANN is competitive with the leading graph-based algorithms and outperforms the state-of-the-art GPU ANN methods on high-dimensional data sets.

Zhuoming Chen, Avner May, Ruslan Svirschevski, Yu-Hsun Huang, Max Ryabinin, Zhihao Jia, Beidi Chen

As the usage of large language models (LLMs) grows, it becomes increasingly important to serve them quickly and efficiently. While speculative decoding has recently emerged as a promising direction for accelerating LLM serving, existing methods are limited in their ability to scale to larger speculation budgets and adapt to different hyperparameters. This paper introduces Sequoia, a scalable and robust algorithm for speculative decoding. To improve scalability, Sequoia introduces a dynamic programming algorithm to find an optimal tree structure for the speculated tokens. To achieve robust speculative decoding, Sequoia uses a novel sampling and verification method that outperforms prior work across different decoding temperatures. Sequoia improves the decoding speed of Llama2-7B, Llama2-13B, and Vicuna-33B on an A100 GPU by up to $4.04\times$, $3.73\times$, and $2.27 \times$. To serve Llama3-70B-Instruct on a single L40 GPU through offloading, Sequoia reduces the per-token decoding latency to 0.60 s/token, $9.5\times$ faster than DeepSpeed-Zero-Inference.

Optimization

Ipsita Ghosh, Abiy Tasissa, Christian Kümmerle

The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this paper, we aim to solve this problem given a minimal number of distance samples. To this end, we leverage continuous and non-convex rank minimization formulations of the problem and establish a local convergence guarantee for a variant of iteratively reweighted least squares (IRLS), which applies if a minimal random set of observed distances is provided. As a technical tool, we establish a restricted isometry property (RIP) restricted to a tangent space of the manifold of symmetric rank-$r$ matrices given random Euclidean distance measurements, which might be of independent interest for the analysis of other non-convex approaches. Furthermore, we assess data efficiency, scalability and generalizability of different reconstruction algorithms through numerical experiments with simulated data as well as real-world data, demonstrating the proposed algorithm's ability to identify the underlying geometry from fewer distance samples compared to the state-of-the-art. The Matlab code can be found at \href{https://github.com/ipsita-ghosh-1/EDG-IRLS}{github\_SEGRED}

Fairness

Oyku Kose, Yanning Shen

Machine learning over graphs has recently attracted growing attention due to its ability to analyze and learn complex relations within critical interconnected systems. However, the disparate impact that is amplified by the use of biased graph structures in these algorithms has raised significant concerns for their deployment in real-world decision systems. In addition, while synthetic graph generation has become pivotal for privacy and scalability considerations, the impact of generative learning algorithms on structural bias has not yet been investigated. Motivated by this, this work focuses on the analysis and mitigation of structural bias for both real and synthetic graphs. Specifically, we first theoretically analyze the sources of structural bias that result in disparity for the predictions of dyadic relations. To alleviate the identified bias factors, we design a novel fairness regularizer that offers a versatile use. Faced with the bias amplification in graph generation models brought to light in this work, we further propose a fair graph generation framework, FairWire, by leveraging our fair regularizer design in a generative model. Experimental results on real-world networks validate that the proposed tools herein deliver effective structural bias mitigation for both real and synthetic graphs.