Motivated by the surge of interest in Koopman operator theory, we propose a machine-learning alternative based on a functional Bayesian perspective for operator-theoretic modeling of unknown, data-driven, nonlinear dynamical systems. This formulation is directly done in an infinite-dimensional space of linear operators or Hilbert space with universal approximation property. The theory of reproducing kernel Hilbert space (RKHS) allows the lifting of nonlinear dynamics to a potentially infinite-dimensional space via linear embeddings, where a general nonlinear function is represented as a set of linear functions or operators in the functional space. This allows us to apply classical linear Bayesian methods such as the Kalman filter directly in the Hilbert space, yielding nonlinear solutions in the original input space. This kernel perspective on the Koopman operator offers two compelling advantages. First, the Hilbert space can be constructed deterministically, agnostic to the nonlinear dynamics. The Gaussian kernel is universal, approximating uniformly an arbitrary continuous target function over any compact domain. Second, Bayesian filter is an adaptive, linear minimum-variance algorithm, allowing the system to update the Koopman operator and continuously track the changes across an extended period of time, ideally suited for modern data-driven applications such as real-time machine learning using streaming data. In this paper, we present several practical implementations to obtain a finite-dimensional approximation of the functional Bayesian filter (FBF). Due to the rapid decay of the Gaussian kernel, excellent approximation is obtained with a small dimension. We demonstrate that this practical approach can obtain accurate results and outperform finite-dimensional Koopman decomposition.

In real-world applications, the distribution of the data, and our goals, evolve over time. The prevailing theoretical framework for studying machine learning, namely probably approximately correct (PAC) learning, largely ignores time. As a consequence, existing strategies to address the dynamic nature of data and goals exhibit poor real-world performance. This paper develops a theoretical framework called "Prospective Learning" that is tailored for situations when the optimal hypothesis changes over time. In PAC learning, empirical risk minimization (ERM) is known to be consistent. We develop a learner called Prospective ERM, which returns a sequence of predictors that make predictions on future data. We prove that the risk of prospective ERM converges to the Bayes risk under certain assumptions on the stochastic process generating the data. Prospective ERM, roughly speaking, incorporates time as an input in addition to the data. We show that standard ERM as done in PAC learning, without incorporating time, can result in failure to learn when distributions are dynamic. Numerical experiments illustrate that prospective ERM can learn synthetic and visual recognition problems constructed from MNIST and CIFAR-10.

Model Compression has drawn much attention within the deep learning community recently. Compressing a dense neural network offers many advantages including lower computation cost, deployability to devices of limited storage and memories, and resistance to adversarial attacks. This may be achieved via weight pruning or fully discarding certain input features. Here we demonstrate a novel strategy to emulate principles of Bayesian model selection in a deep learning setup. Given a fully connected Bayesian neural network with spike-and-slab priors trained via a variational algorithm, we obtain the posterior inclusion probability for every node that typically gets lost. We employ these probabilities for pruning and feature selection on a host of simulated and real-world benchmark data and find evidence of better generalizability of the pruned model in all our experiments.

Conventional methods for Bayesian optimization (BO) primarily involve one-step optimal decisions (e.g., maximizing expected improvement of the next step). To avoid myopic behavior, multi-step lookahead BO algorithms such as rollout strategies consider the sequential decision-making nature of BO, i.e., as a stochastic dynamic programming (SDP) problem, demonstrating promising results in recent years. However, owing to the curse of dimensionality, most of these methods make significant approximations or suffer scalability issues, e.g., being limited to two-step lookahead. 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 SDP 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 employ off-policy learning to accelerate its initial training. We then 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 Bayesian Optimization), on both synthetic benchmark functions and real-world hyperparameter optimization problems, demonstrating significantly improved performance compared to existing multi-step lookahead and high-dimensional BO methods.

Federated learning (FL) is a distributed learning framework that leverages commonalities between distributed client datasets to train a global model. Under heterogeneous clients, however, FL can fail to produce stable training results. Personalized federated learning (PFL) seeks to address this by learning individual models tailored to each client. One approach is to decompose model training into shared representation learning and personalized classifier training. Nonetheless, previous works struggle to navigate the bias-variance trade-off in classifier learning, relying solely on limited local datasets or introducing costly techniques to improve generalization. In this work, we frame representation learning as a generative modeling task, where representations are trained with a classifier based on the global feature distribution. We then propose an algorithm, pFedFDA, that efficiently generates personalized models by adapting global generative classifiers to their local feature distributions. Through extensive computer vision benchmarks, we demonstrate that our method can adjust to complex distribution shifts with significant improvements over current state-of-the-art in data-scarce settings.

Recent advances in Large Language Models (LLMs) have helped facilitate exciting progress for robotic planning in real, open-world environments. 3D scene graphs (3DSGs) offer a promising environment representation for grounding such LLM-based planners as they are compact and semantically rich. However, as the robot's environment scales (e.g., number of entities tracked) and the complexity of scene graph information increases (e.g., maintaining more attributes), providing the 3DSG as-is to an LLM-based planner quickly becomes infeasible due to input token count limits and attentional biases present in LLMs. Inspired by the successes of Retrieval-Augmented Generation (RAG) methods that retrieve query-relevant document chunks for LLM question and answering, we adapt the paradigm for our embodied domain. Specifically, we propose a 3D scene subgraph retrieval framework, called EmbodiedRAG, that we augment an LLM-based planner with for executing natural language robotic tasks. Notably, our retrieved subgraphs adapt to changes in the environment as well as changes in task-relevancy as the robot executes its plan. We demonstrate EmbodiedRAG's ability to significantly reduce input token counts (by an order of magnitude) and planning time (up to 70% reduction in average time per planning step) while improving success rates on AI2Thor simulated household tasks with a single-arm, mobile manipulator. Additionally, we implement EmbodiedRAG on a quadruped with a manipulator to highlight the performance benefits for robot deployment at the edge in real environments.

We establish a new theoretical framework for learning under multi-class, instance-dependent label noise. This framework casts learning with label noise as a form of domain adaptation, in particular, domain adaptation under posterior drift. We introduce the concept of \emph{relative signal strength} (RSS), a pointwise measure that quantifies the transferability from noisy to clean posterior. Using RSS, we establish nearly matching upper and lower bounds on the excess risk. Our theoretical findings support the simple \emph{Noise Ignorant Empirical Risk Minimization (NI-ERM)} principle, which minimizes empirical risk while ignoring label noise. Finally, we translate this theoretical insight into practice: by using NI-ERM to fit a linear classifier on top of a self-supervised feature extractor, we achieve state-of-the-art performance on the CIFAR-N data challenge.

Imitation learning from human demonstrations is an effective means to teach robots manipulation skills. But data acquisition is a major bottleneck in applying this paradigm more broadly, due to the amount of cost and human effort involved. There has been significant interest in imitation learning for bimanual dexterous robots, like humanoids. Unfortunately, data collection is even more challenging here due to the challenges of simultaneously controlling multiple arms and multi-fingered hands. Automated data generation in simulation is a compelling, scalable alternative to fuel this need for data. To this end, we introduce DexMimicGen, a large-scale automated data generation system that synthesizes trajectories from a handful of human demonstrations for humanoid robots with dexterous hands. We present a collection of simulation environments in the setting of bimanual dexterous manipulation, spanning a range of manipulation behaviors and different requirements for coordination among the two arms. We generate 21K demos across these tasks from just 60 source human demos and study the effect of several data generation and policy learning decisions on agent performance. Finally, we present a real-to-sim-to-real pipeline and deploy it on a real-world humanoid can sorting task. Videos and more are at https://dexmimicgen.github.io/

The cooperative driving technology of Connected and Autonomous Vehicles (CAVs) is crucial for improving the efficiency and safety of transportation systems. Learning-based methods, such as Multi-Agent Reinforcement Learning (MARL), have demonstrated strong capabilities in cooperative decision-making tasks. However, existing MARL approaches still face challenges in terms of learning efficiency and performance. In recent years, Large Language Models (LLMs) have rapidly advanced and shown remarkable abilities in various sequential decision-making tasks. To enhance the learning capabilities of cooperative agents while ensuring decision-making efficiency and cost-effectiveness, we propose LDPD, a language-driven policy distillation method for guiding MARL exploration. In this framework, a teacher agent based on LLM trains smaller student agents to achieve cooperative decision-making through its own decision-making demonstrations. The teacher agent enhances the observation information of CAVs and utilizes LLMs to perform complex cooperative decision-making reasoning, which also leverages carefully designed decision-making tools to achieve expert-level decisions, providing high-quality teaching experiences. The student agent then refines the teacher's prior knowledge into its own model through gradient policy updates. The experiments demonstrate that the students can rapidly improve their capabilities with minimal guidance from the teacher and eventually surpass the teacher's performance. Extensive experiments show that our approach demonstrates better performance and learning efficiency compared to baseline methods.

In this paper we propose a formal, model-agnostic meta-learning framework for safe reinforcement learning. Our framework is inspired by how parents safeguard their children across a progression of increasingly riskier tasks, imparting a sense of safety that is carried over from task to task. We model this as a meta-learning process where each task is synchronized with a safeguard that monitors safety and provides a reward signal to the agent. The safeguard is implemented as a finite-state machine based on a safety specification; the reward signal is formally shaped around this specification. The safety specification and its corresponding safeguard can be arbitrarily complex and non-Markovian, which adds flexibility to the training process and explainability to the learned policy. The design of the safeguard is manual but it is high-level and model-agnostic, which gives rise to an end-to-end safe learning approach with wide applicability, from pixel-level game control to language model fine-tuning. Starting from a given set of safety specifications (tasks), we train a model such that it can adapt to new specifications using only a small number of training samples. This is made possible by our method for efficiently transferring safety bias between tasks, which effectively minimizes the number of safety violations. We evaluate our framework in a Minecraft-inspired Gridworld, a VizDoom game environment, and an LLM fine-tuning application. Agents trained with our approach achieve near-minimal safety violations, while baselines are shown to underperform.