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Reinforcement Learning

Thomas Rupf, Marco Bagatella, Nico Gürtler, Jonas Frey, Georg Martius

Zero-shot imitation learning algorithms hold the promise of reproducing unseen behavior from as little as a single demonstration at test time. Existing practical approaches view the expert demonstration as a sequence of goals, enabling imitation with a high-level goal selector, and a low-level goal-conditioned policy. However, this framework can suffer from myopic behavior: the agent's immediate actions towards achieving individual goals may undermine long-term objectives. We introduce a novel method that mitigates this issue by directly optimizing the occupancy matching objective that is intrinsic to imitation learning. We propose to lift a goal-conditioned value function to a distance between occupancies, which are in turn approximated via a learned world model. The resulting method can learn from offline, suboptimal data, and is capable of non-myopic, zero-shot imitation, as we demonstrate in complex, continuous benchmarks. The code is available at https://github.com/martius-lab/zilot.

Theory · Optimization

Chansophea Wathanak In, Yi Li, David Woodruff, Xuan Wu

Robustness to outliers is important in machine learning. Many classical problems, including subspace embedding, clustering, and low-rank approximation, lack scalable, outlier-resilient algorithms. This paper considers machine learning problems of the form $\min_{x\in \mathbb{R}^d} F(x)$, where $F(x)=\sum_{i=1}^n F_i(x)$, and their robust counterparts $\min_{x\in\mathbb{R}^d} F^{(m)}(x)$, where $F^{(m)}(x)$ denotes the sum of all but the $m$ largest $F_i(x)$ values. We develop a general framework for constructing $\epsilon$-coresets for such robust problems, where an $\epsilon$-coreset is a weighted subset of functions $\{F_1(x),\dots,F_n(x)\}$ that provides a $(1+\epsilon)$-approximation to $F(x)$. Specifically, if the original problem $F$ has total sensitivity $T$ and admits a vanilla $\epsilon$-coreset of size $S$, our algorithm constructs an $\epsilon$-coreset of size $\tilde{O}(\frac{mT}{\epsilon})+S$ for the robust objective $F^{(m)}$. This coreset size can be shown to be near-tight for $\ell_2$ subspace embedding. Our coreset algorithm has scalable running time and leads to new or improved algorithms for the robust optimization problems. Empirical evaluations demonstrate that our coresets outperform uniform sampling on real-world data sets.

Deep Learning · Graph Neural Networks

Juwei Yue, Haikuo Li, Jiawei Sheng, Xiaodong Li, Taoyu Su, Tingwen Liu, Li Guo

Graph neural networks (GNNs) leverage message passing mechanisms to learn the topological features of graph data. Traditional GNNs learns node features in a spatial domain unrelated to the topology, which can hardly ensure topological features. In this paper, we formulates message passing as a system of hyperbolic partial differential equations (hyperbolic PDEs), constituting a dynamical system that explicitly maps node representations into a particular solution space. This solution space is spanned by a set of eigenvectors describing the topological structure of graphs. Within this system, for any moment in time, a node features can be decomposed into a superposition of the basis of eigenvectors. This not only enhances the interpretability of message passing but also enables the explicit extraction of fundamental characteristics about the topological structure. Furthermore, by solving this system of hyperbolic partial differential equations, we establish a connection with spectral graph neural networks (spectral GNNs), serving as a message passing enhancement paradigm for spectral GNNs.We further introduce polynomials to approximate arbitrary filter functions. Extensive experiments demonstrate that the paradigm of hyperbolic PDEs not only exhibits strong flexibility but also significantly enhances the performance of various spectral GNNs across diverse graph tasks.

Reinforcement Learning

Zachary Roch, George Atia, Yue Wang

Robust reinforcement learning (RL) under the average reward criterion, which seeks to optimize long-term system performance in uncertain environments, remains a largely unexplored area. To address this challenge, we propose a reduction-based framework that transforms robust average reward optimization into the more extensively studied robust discounted reward optimization by employing a specific discount factor. Our framework provides two key advantages. **Data Efficiency**: We design a model-based reduction algorithm that achieves near-optimal sample complexity, enabling efficient identification of optimal robust policies; **Scalability**: By bypassing the inherent challenges of scaling up average reward optimization, our framework facilitates the design of scalable, convergent algorithms for robust average reward optimization leveraging function approximation. Our algorithmic design, supported by theoretical and empirical analyses, provides a concrete solution to robust average reward RL with the first data efficiency and scalability guarantees, highlighting the framework’s potential to optimize long-term performance under model uncertainty in practical problems.

Reinforcement Learning · Multi-agent

Zhiyao Zhang, Myeung Suk Oh, Hairi, Ziyue Luo, Alvaro Velasquez, Jia (Kevin) Liu

Actor-critic methods for decentralized multi-agent reinforcement learning (MARL) facilitate collaborative optimal decision making without centralized coordination, thus enabling a wide range of applications in practice. To date, however, most theoretical convergence studies for existing actor-critic decentralized MARL methods are limited to the guarantee of a stationary solution under the linear function approximation. This leaves a significant gap between the highly successful use of deep neural actor-critic for decentralized MARL in practice and the current theoretical understanding. To bridge this gap, in this paper, we make the first attempt to develop a deep neural actor-critic method for decentralized MARL, where both the actor and critic components are inherently non-linear. We show that our proposed method enjoys a global optimality guarantee with a finite-time convergence rate of $\mathcal{O}(1/T)$, where $T$ is the total iteration times. This marks the first global convergence result for deep neural actor-critic methods in the MARL literature. We also conduct extensive numerical experiments, which verify our theoretical results.

Applications · Language, Speech and Dialog

Zhongweiyang Xu, Xulin Fan, Zhong-Qiu Wang, Xilin Jiang, Romit Roy Choudhury

Blind Speech Separation (BSS) aims to separate multiple speech sources from audio mixturesrecorded by a microphone array. The problem ischallenging because it is a blind inverse problem,i.e., the microphone array geometry, the room impulse response (RIR), and the speech sources, areall unknown. We propose ArrayDPS to solve theBSS problem in an unsupervised, array-agnostic,and generative manner. The core idea builds ondiffusion posterior sampling (DPS), but unlikeDPS where the likelihood is tractable, ArrayDPSmust approximate the likelihood by formulatinga separate optimization problem. The solution to the optimization approximates room acousticsand the relative transfer functions between microphones. These approximations, along with thediffusion priors, iterate through the ArrayDPSsampling process and ultimately yield separatedvoice sources. We only need a simple single-speaker speech diffusion model as a prior, alongwith the mixtures recorded at the microphones; nomicrophone array information is necessary. Evaluation results show that ArrayDPS outperformsall baseline unsupervised methods while beingcomparable to supervised methods in terms ofSDR. Audio demos and codes are provided at:https://arraydps.github.io/ArrayDPSDemo/ andhttps://github.com/ArrayDPS/ArrayDPS.

Deep Learning · Generative Models and Autoencoders

Eric Frankel, Sitan Chen, Jerry Li, Pang Wei Koh, Lillian Ratliff, Sewoong Oh

Diffusion models (DMs) create samples from a data distribution by starting from random noise and iteratively solving a reverse-time ordinary differential equation (ODE).Because each step in the iterative solution requires an expensive neural function evaluation (NFE), there has been significant interest in approximately solving these diffusion ODEs with only a few NFEs without modifying the underlying model.However, in the few NFE regime, we observe that tracking the true ODE evolution is fundamentally impossible using traditional ODE solvers.In this work, we propose a new method that learns a good solver for the DM, which we call **S**olving **for** the **S**olver (**S4S**).S4S directly optimizes a solver to obtain good generation quality by learning to match the output of a strong teacher solver.We evaluate S4S on six different pre-trained DMs, including pixel-space and latent-space DMs for both conditional and unconditional sampling.In all settings, S4S uniformly improves the sample quality relative to traditional ODE solvers. Moreover, our method is lightweight, data-free, and can be plugged in black-box on top of any discretization schedule or architecture to improve performance.Building on top of this, we also propose **S4S-Alt**, which optimizes both the solver and the discretization schedule.By exploiting the full design space of DM solvers, with 5 NFEs, we achieve an FID of 3.73 on CIFAR10 and 13.26 on MS-COCO, representing a $1.5\times$ improvement over previous training-free ODE methods.

Optimization · Zero-order and Black-box Optimization

Mujin Cheon, Jay Lee, Dong-Yeun Koh, Calvin Tsay

To avoid myopic behavior, multi-step lookahead Bayesian optimization (BO) algorithms consider the sequential nature of BO and have demonstrated promising results in recent years. However, owing to the curse of dimensionality, most of these methods make significant approximations or suffer scalability issues. This paper presents a novel reinforcement learning (RL)-based framework for multi-step lookahead BO in high-dimensional black-box optimization problems. The proposed method enhances the scalability and decision-making quality of multi-step lookahead BO by efficiently solving the sequential dynamic program of the BO process in a near-optimal manner using RL. We first introduce an Attention-DeepSets encoder to represent the state of knowledge to the RL agent and subsequently propose a multi-task, fine-tuning procedure based on end-to-end (encoder-RL) on-policy learning. We evaluate the proposed method, EARL-BO (Encoder Augmented RL for BO), on synthetic benchmark functions and hyperparameter tuning problems, finding significantly improved performance compared to existing multi-step lookahead and high-dimensional BO methods.

Applications · Neuroscience, Cognitive Science

Bariscan Kurtkaya, Fatih Dinc, Mert Yuksekgonul, Marta Blanco-Pozo, Ege Cirakman, Mark Schnitzer, Yucel Yemez, Hidenori Tanaka, Yuan, Nina Miolane

Short-term memory is essential for cognitive processing, yet our understanding of its neural mechanisms remains unclear. Neuroscience has long focused on how sequential activity patterns, where neurons fire one after another within large networks, can explain how information is maintained. While recurrent connections were shown to drive sequential dynamics, a mechanistic understanding of this process still remains unknown. In this work, we introduce two unique mechanisms that can support this form of short-term memory: slow-point manifolds generating direct sequences or limit cycles providing temporally localized approximations. Using analytical models, we identify fundamental properties that govern the selection of each mechanism. Precisely, on short-term memory tasks (delayed cue-discrimination tasks), we derive theoretical scaling laws for critical learning rates as a function of the delay period length, beyond which no learning is possible. We empirically verify these results by training and evaluating approximately 80,000 recurrent neural networks (RNNs), which are publicly available for further analysis. Overall, our work provides new insights into short-term memory mechanisms and proposes experimentally testable predictions for systems neuroscience.

Optimization · Discrete and Combinatorial Optimization

Yixin Chen, Wenjing Chen, Alan Kuhnle

With the rapid growth of data in modern applications, parallel combinatorial algorithms for maximizing non-monotone submodular functions have gained significant attention. In the parallel computation setting, the state-of-the-art approximation ratio of $1/e$ is achieved by a continuous algorithm (Ene & Nguyen, 2020) with adaptivity $\mathcal O (log(n))$. In this work, we focus on size constraints and present the first combinatorial algorithm matching this bound – a randomized parallel approach achieving $1/e − \epsilon$ approximation ratio. This result bridgesthe gap between continuous and combinatorial approaches for this problem. As a byproduct, we also develop a simpler $(1/4 − \epsilon)$-approximation algorithm with high probability $(\ge 1 − 1/n)$. Both algorithms achieve $\mathcal O (log(n) log(k))$ adaptivity and $\mathcal O (n log(n) log(k)) query complexity. Empirical results show our algorithms achieve competitive objective values, with the $(1/4 − \epsilon)$-approximation algorithm particularly efficient in queries.

Theory

Yiding Chen, Yiyi Zhang, Owen Oertell, Wen Sun

Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from noise to data directly, which allows one-step fast data generation and multistep sampling to improve sample quality. In this paper, we study the convergence of consistency models when the self-consistency property holds approximately under the training distribution. Our analysis requires only mild data assumption and applies to a family of forward processes. When the target data distribution has bounded support or has tails that decay sufficiently fast, we show that the samples generated by the consistency model are close to the target distribution in Wasserstein distance; when the target distribution satisfies some smoothness assumption, we show that with an additional perturbation step for smoothing, the generated samples are close to the target distribution in total variation distance. We provide two case studies with commonly chosen forward processes to demonstrate the benefit of multistep sampling.

Deep Learning · Generative Models and Autoencoders

Alexander Lobashev, Dmitry Guskov, Maria Larchenko, Mikhail Tamm

This paper presents a novel method for analyzing the latent space geometry of generative models, including statistical physics models and diffusion models, by reconstructing the Fisher information metric. The method approximates the posterior distribution of latent variables given generated samples and uses this to learn the log-partition function, which defines the Fisher metric for exponential families. Theoretical convergence guarantees are provided, and the method is validated on the Ising and TASEP models, outperforming existing baselines in reconstructing thermodynamic quantities. Applied to diffusion models, the method reveals a fractal structure of phase transitions in the latent space, characterized by abrupt changes in the Fisher metric. We demonstrate that while geodesic interpolations are approximately linear within individual phases, this linearity breaks down at phase boundaries, where the diffusion model exhibits a divergent Lipschitz constant with respect to the latent space. These findings provide new insights into the complex structure of diffusion model latent spaces and their connection to phenomena like phase transitions.Our source code is available at \url{https://github.com/alobashev/hessian-geometry-of-diffusion-models}.

Theory · Learning Theory

Ari Karchmer, Eran Malach

We study the relationship between gradient-based optimization of parametric models (e.g., neural networks) and optimization of linear combinations of random features. Our main result shows that if a parametric model can be learned using mini-batch stochastic gradient descent (bSGD) without making assumptions about the data distribution, then with high probability, the target function can also be approximated using a polynomial-sized combination of random features. The size of this combination depends on the number of gradient steps and numerical precision used in the bSGD process. This finding reveals fundamental limitations of distribution-free learning in neural networks trained by gradient descent, highlighting why making assumptions about data distributions is often crucial in practice.Along the way, we also introduce a new theoretical framework called average probabilistic dimension complexity (adc), which extends the probabilistic dimension complexity developed by Kamath et al. (2020). We prove that adc has a polynomial relationship with statistical query dimension, and use this relationship to demonstrate an infinite separation between adc and standard dimension complexity.

Applications · Everything Else

Mengmeng Chen, Xiaohu Wu, QIQI LIU, Tiantian He, Yew Soon ONG, Yaochu Jin, Qicheng Lao, Han Yu

Multi-objective optimization (MOO) exists extensively in machine learning, and aims to find a set of Pareto-optimal solutions, called the Pareto front, e.g., it is fundamental for multiple avenues of research in federated learning (FL). Pareto-Front Learning (PFL) is a powerful method implemented using Hypernetworks (PHNs) to approximate the Pareto front. This method enables the acquisition of a mapping function from a given preference vector to the solutions on the Pareto front. However, most existing PFL approaches still face two challenges: (a) sampling rays in high-dimensional spaces; (b) failing to cover the entire Pareto Front which has a convex shape. Here, we introduce a novel PFL framework, called as PHN-HVVS, which decomposes the design space into Voronoi grids and deploys a genetic algorithm (GA) for Voronoi grid partitioning within high-dimensional space. We put forward a new loss function, which effectively contributes to more extensive coverage of the resultant Pareto front and maximizes the HV Indicator. Experimental results on multiple MOO machine learning tasks demonstrate that PHN-HVVS outperforms the baselines significantly in generating Pareto front. Also, we illustrate that PHN-HVVS advances the methodologies of several recent problems in the FL field. The code is available athttps://github.com/buptcmm/phnhvvs.

General Machine Learning · Clustering

Steinar Laenen, Peter Macgregor, He Sun

In the kernel density estimation (KDE) problem, we are given a set $X$ of data points in $\mathbb{R}^d$, a kernel function $k: \mathbb{R}^d \times \mathbb{R}^d \rightarrow \mathbb{R}$, and a query point $\mathbf{q} \in \mathbb{R}^d$, and the objective is to quickly output an estimate of $\sum_{\mathbf{x} \in X} k(\mathbf{q}, \mathbf{x})$.In this paper, we consider $\textsf{KDE}$ in the dynamic setting, and introduce a data structure that efficiently maintains the _estimates_ for a set of query points as data points are added to $X$ over time.Based on this, we design a dynamic data structure that maintains a sparse approximation of the fully connected similarity graph on $X$, and develop a fast dynamic spectral clustering algorithm.We further evaluate the effectiveness of our algorithms on both synthetic and real-world datasets.

Probabilistic Methods · Bayesian Models and Methods

Jacopo Talpini, Marco Savi, Giovanni Neglia

One-Shot Federated Learning (FL) is a recent paradigm that enables multiple clients to cooperatively learn a global model in a single round of communication with a central server. In this paper, we analyze the One-Shot FL problem through the lens of Bayesian inference and propose FedBEns, an algorithm that leverages the inherent multimodality of local loss functions to find better global models.Our algorithm leverages a mixture of Laplace approximations for the clients' local posteriors, which the server then aggregates to infer the global model. We conduct extensive experiments on various datasets, demonstrating that the proposed method outperforms competing baselines that typically rely on unimodal approximations of the local losses.

Reinforcement Learning

David Pfau, Ian Davies, Diana Borsa, João Madeira Araujo, Brendan Tracey, Hado van Hasselt

We introduce Wasserstein Policy Optimization (WPO), an actor-critic algorithm for reinforcement learning in continuous action spaces. WPO can be derived as an approximation to Wasserstein gradient flow over the space of all policies projected into a finite-dimensional parameter space (e.g., the weights of a neural network), leading to a simple and completely general closed-form update. The resulting algorithm combines many properties of deterministic and classic policy gradient methods. Like deterministic policy gradients, it exploits knowledge of the *gradient* of the action-value function with respect to the action. Like classic policy gradients, it can be applied to stochastic policies with arbitrary distributions over actions -- without using the reparameterization trick. We show results on the DeepMind Control Suite and a magnetic confinement fusion task which compare favorably with state-of-the-art continuous control methods.

Position · Understanding

David A. Danhofer, Davide DAscenzo, Rafael Dubach, Tomaso A Poggio

Overparametrized Deep Neural Networks (DNNs) have demonstrated remarkable success in a wide variety of domains too high-dimensional for classical shallow networks subject to the curse of dimensionality. However, open questions about fundamental principles, that govern the learning dynamics of DNNs, remain. In this position paper we argue that it is the ability of DNNs to exploit the compositionally sparse structure of the target function driving their success. As such, DNNs can leverage the property that most practically relevant functions can be composed from a small set of constituent functions, each of which relies only on a low-dimensional subset of all inputs. We show that this property is shared by all efficiently Turing-computable functions and is therefore highly likely present in all current learning problems. While some promising theoretical insights on questions concerned with approximation and generalization exist in the setting of compositionally sparse functions, several important questions on the learnability and optimization of DNNs remain. Completing the picture of the role of compositional sparsity in deep learning is essential to a comprehensive theory of artificial—and even general—intelligence.

Social Aspects · Privacy

Leo de Castro, Daniel Escudero, Adya Agrawal, Antigoni Polychroniadou, Manuela Veloso

As large language models (LLMs) become more powerful, the computation required to run these models is increasingly outsourced to a third-party cloud. While this saves clients' computation, it risks leaking the clients' LLM queries to the cloud provider. Fully homomorphic encryption (FHE) presents a natural solution to this problem: simply encrypt the query and evaluate the LLM homomorphically on the cloud machine. The result remains encrypted and can only be learned by the client who holds the secret key. In this work, we present a GPU-accelerated implementation of FHE and use this implementation to benchmark an encrypted GPT-2 forward pass, with runtimes over $200\times$ faster than the CPU baseline. We also present novel and extensive experimental analysis of approximations of LLM activation functions to maintain accuracy while achieving this performance.

Deep Learning · Sequential Models, Time series

Yitian Zhang, Liheng Ma, Antonios Valkanas, Boris Oreshkin, Mark Coates

Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the advantage of linearity, the operator is generally infinite-dimensional. Therefore, the objective is to learn measurement functions that yield a tractable finite-dimensional Koopman operator approximation. In this work, we establish a connection between Koopman operator approximation and linear Recurrent Neural Networks (RNNs), which have recently demonstrated remarkable success in sequence modeling. We show that by considering an extended state consisting of lagged observations, we can establish an equivalence between a structured Koopman operator and linear RNN updates. Building on this connection, we present SKOLR, which integrates a learnable spectral decomposition of the input signal with a multilayer perceptron (MLP) as the measurement functions and implements a structured Koopman operator via a highly parallel linear RNN stack. Numerical experiments on various forecasting benchmarks and dynamical systems show that this streamlined, Koopman-theory-based design delivers exceptional performance. Our code is available at: https://github.com/networkslab/SKOLR.