In this paper, we study planning in stochastic systems, modeled as Markov decision processes (MDPs), with preferences over temporally extended goals. Prior work on temporal planning with preferences assumes that the user preferences form a total order, meaning that every pair of outcomes are comparable with each other. In this work, we consider the case where the preferences over possible outcomes are a partial order rather than a total order. We first introduce a variant of deterministic finite automaton, referred to as a preference DFA, for specifying the user's preferences over temporally extended goals. Based on the order theory, we translate the preference DFA to a preference relation over policies for probabilistic planning in a labeled MDP. In this treatment, a most preferred policy induces a weak-stochastic nondominated probability distribution over the finite paths in the MDP. The proposed planning algorithm hinges on the construction of a multi-objective MDP. We prove that a weak-stochastic nondominated policy given the preference specification is Pareto-optimal in the constructed multi-objective MDP, and vice versa. Throughout the paper, we employ a running example to demonstrate the proposed preference specification and solution approaches. We show the efficacy of our algorithm using the example with detailed analysis, and then discuss possible future directions.

Federated learning (FL) is a promising framework that models distributed machine learning while protecting the privacy of clients. However, FL suffers performance degradation from heterogeneous and limited data. To alleviate the degradation, we present a novel personalized Bayesian FL approach named pFedBayes. By using the trained global distribution from the server as the prior distribution of each client, each client adjusts its own distribution by minimizing the sum of the reconstruction error over its personalized data and the KL divergence with the downloaded global distribution. Then, we propose a sparse personalized Bayesian FL approach named sFedBayes. To overcome the extreme heterogeneity in non-i.i.d. data, we propose a clustered Bayesian FL model named cFedbayes by learning different prior distributions for different clients. Theoretical analysis gives the generalization error bound of three approaches and shows that the generalization error convergence rates of the proposed approaches achieve minimax optimality up to a logarithmic factor. Moreover, the analysis presents that cFedbayes has a tighter generalization error rate than pFedBayes. Numerous experiments are provided to demonstrate that the proposed approaches have better performance than other advanced personalized methods on private models in the presence of heterogeneous and limited data.

Benefitting from UAVs' characteristics of flexible deployment and controllable movement in 3D space, odor source localization with multiple UAVs has been a hot research area in recent years. Considering the limited resources and insufficient battery capacities of UAVs, it is necessary to fast locate the odor source with low-complexity computation and minimal interaction under complicated environmental states. To this end, we propose a multi-UAV collaboration based odor source localization (\textit{MUC-OSL}) method, where source estimation and UAV navigation are iteratively performed, aiming to accelerate the searching process and reduce the resource consumption of UAVs. Specifically, in the source estimation phase, we present a collaborative particle filter algorithm on the basis of UAVs' cognitive difference and Gaussian fitting to improve source estimation accuracy. In the following navigation phase, an adaptive path planning algorithm is designed based on Partially Observable Markov Decision Process (POMDP) to distributedly determine the subsequent flying direction and moving steps of each UAV. The results of experiments conducted on two simulation platforms demonstrate that \textit{MUC-OSL} outperforms existing efforts in terms of mean search time and success rate, and effectively reduces the resource consumption of UAVs.

This study proposes a hierarchically integrated framework for safe task and motion planning (TAMP) of bipedal locomotion in a partially observable environment with dynamic obstacles and uneven terrain. The high-level task planner employs linear temporal logic (LTL) for a reactive game synthesis between the robot and its environment and provides a formal guarantee on navigation safety and task completion. To address environmental partial observability, a belief abstraction is employed at the high-level navigation planner to estimate the dynamic obstacles' location. Accordingly, a synthesized action planner sends a set of locomotion actions to the middle-level motion planner, while incorporating safe locomotion specifications extracted from safety theorems based on a reduced-order model (ROM) of the locomotion process. The motion planner employs the ROM to design safety criteria and a sampling algorithm to generate non-periodic motion plans that accurately track high-level actions. At the low level, a foot placement controller based on an angular-momentum linear inverted pendulum model is implemented and integrated with an ankle-actuated passivity-based controller for full-body trajectory tracking. To address external perturbations, this study also investigates safe sequential composition of the keyframe locomotion state and achieves robust transitions against external perturbations through reachability analysis. The overall TAMP framework is validated with extensive simulations and hardware experiments on bipedal walking robots Cassie and Digit designed by Agility Robotics.

The recently proposed Joint Energy-based Model (JEM) interprets discriminatively trained classifier $p(y|x)$ as an energy model, which is also trained as a generative model describing the distribution of the input observations $p(x)$. The JEM training relies on "positive examples" (i.e. examples from the training data set) as well as on "negative examples", which are samples from the modeled distribution $p(x)$ generated by means of Stochastic Gradient Langevin Dynamics (SGLD). Unfortunately, SGLD often fails to deliver negative samples of sufficient quality during the standard JEM training, which causes a very unbalanced contribution from the positive and negative examples when calculating gradients for JEM updates. As a consequence, the standard JEM training is quite unstable requiring careful tuning of hyper-parameters and frequent restarts when the training starts diverging. This makes it difficult to apply JEM to different neural network architectures, modalities, and tasks. In this work, we propose a training procedure that stabilizes SGLD-based JEM training (ST-JEM) by balancing the contribution from the positive and negative examples. We also propose to add an additional "regularization" term to the training objective -- MI between the input observations $x$ and output labels $y$ -- which encourages the JEM classifier to make more certain decisions about output labels. We demonstrate the effectiveness of our approach on the CIFAR10 and CIFAR100 tasks. We also consider the task of classifying phonemes in a speech signal, for which we were not able to train JEM without the proposed stabilization. We show that a convincing speech can be generated from the trained model. Alternatively, corrupted speech can be de-noised by bringing it closer to the modeled speech distribution using a few SGLD iterations. We also propose and discuss additional applications of the trained model.

As autonomous agents enter complex environments, it becomes more difficult to adequately model the interactions between the two. Agents must therefore cope with greater ambiguity (e.g., unknown environments, underdefined models, and vague problem definitions). Despite the consequences of ignoring ambiguity, tools for decision making under ambiguity are understudied. The general approach has been to avoid ambiguity (exploit known information) using robust methods. This work contributes ambiguity attitude graph search (AAGS), generalizing robust methods with ambiguity attitudes--the ability to trade-off between seeking and avoiding ambiguity in the problem. AAGS solves online decision making problems with limited budget to learn about their environment. To evaluate this approach AAGS is tasked with path planning in static and dynamic environments. Results demonstrate that appropriate ambiguity attitudes are dependent on the quality of information from the environment. In relatively certain environments, AAGS can readily exploit information with robust policies. Conversely, model complexity reduces the information conveyed by individual samples; this allows the risks taken by optimistic policies to achieve better performance.

Foundation models pretrained on diverse data at scale have demonstrated extraordinary capabilities in a wide range of vision and language tasks. When such models are deployed in real world environments, they inevitably interface with other entities and agents. For example, language models are often used to interact with human beings through dialogue, and visual perception models are used to autonomously navigate neighborhood streets. In response to these developments, new paradigms are emerging for training foundation models to interact with other agents and perform long-term reasoning. These paradigms leverage the existence of ever-larger datasets curated for multimodal, multitask, and generalist interaction. Research at the intersection of foundation models and decision making holds tremendous promise for creating powerful new systems that can interact effectively across a diverse range of applications such as dialogue, autonomous driving, healthcare, education, and robotics. In this manuscript, we examine the scope of foundation models for decision making, and provide conceptual tools and technical background for understanding the problem space and exploring new research directions. We review recent approaches that ground foundation models in practical decision making applications through a variety of methods such as prompting, conditional generative modeling, planning, optimal control, and reinforcement learning, and discuss common challenges and open problems in the field.

Deep latent variable models have achieved significant empirical successes in model-based reinforcement learning (RL) due to their expressiveness in modeling complex transition dynamics. On the other hand, it remains unclear theoretically and empirically how latent variable models may facilitate learning, planning, and exploration to improve the sample efficiency of RL. In this paper, we provide a representation view of the latent variable models for state-action value functions, which allows both tractable variational learning algorithm and effective implementation of the optimism/pessimism principle in the face of uncertainty for exploration. In particular, we propose a computationally efficient planning algorithm with UCB exploration by incorporating kernel embeddings of latent variable models. Theoretically, we establish the sample complexity of the proposed approach in the online and offline settings. Empirically, we demonstrate superior performance over current state-of-the-art algorithms across various benchmarks.

Data cleaning is crucial but often laborious in most machine learning (ML) applications. However, task-agnostic data cleaning is sometimes unnecessary if certain inconsistencies in the dirty data will not affect the prediction of ML models to the test points. A test point is certifiably robust for an ML classifier if the prediction remains the same regardless of which (among exponentially many) cleaned dataset it is trained on. In this paper, we study certifiable robustness for the Naive Bayes classifier (NBC) on dirty datasets with missing values. We present (i) a linear time algorithm in the number of entries in the dataset that decides whether a test point is certifiably robust for NBC, (ii) an algorithm that counts for each label, the number of cleaned datasets on which the NBC can be trained to predict that label, and (iii) an efficient optimal algorithm that poisons a clean dataset by inserting the minimum number of missing values such that a test point is not certifiably robust for NBC. We prove that (iv) poisoning a clean dataset such that multiple test points become certifiably non-robust is NP-hard for any dataset with at least three features. Our experiments demonstrate that our algorithms for the decision and data poisoning problems achieve up to $19.5\times$ and $3.06\times$ speed-up over the baseline algorithms across different real-world datasets.

Causal representation learning is the task of identifying the underlying causal variables and their relations from high-dimensional observations, such as images. Recent work has shown that one can reconstruct the causal variables from temporal sequences of observations under the assumption that there are no instantaneous causal relations between them. In practical applications, however, our measurement or frame rate might be slower than many of the causal effects. This effectively creates "instantaneous" effects and invalidates previous identifiability results. To address this issue, we propose iCITRIS, a causal representation learning method that allows for instantaneous effects in intervened temporal sequences when intervention targets can be observed, e.g., as actions of an agent. iCITRIS identifies the potentially multidimensional causal variables from temporal observations, while simultaneously using a differentiable causal discovery method to learn their causal graph. In experiments on three datasets of interactive systems, iCITRIS accurately identifies the causal variables and their causal graph.