Autonomy via agents based on large language models (LLMs) that can carry out personalized yet standardized tasks presents a significant opportunity to drive human efficiency. There is an emerging need and interest in automating web tasks (e.g., booking a hotel for a given date within a budget). Being a practical use case itself, the web agent also serves as an important proof-of-concept example for various agent grounding scenarios, with its success promising advancements in many future applications. Meanwhile, much prior research focuses on handcrafting their web agent strategies (e.g., agent's prompting templates, reflective workflow, role-play and multi-agent systems, search or sampling methods, etc.) and the corresponding in-context examples. However, these custom strategies often struggle with generalizability across all potential real-world applications. On the other hand, there has been limited study on the misalignment between a web agent's observation and action representation, and the data on which the agent's underlying LLM has been pre-trained. This discrepancy is especially notable when LLMs are primarily trained for language completion rather than tasks involving embodied navigation actions and symbolic web elements. In our study, we enhance an LLM-based web agent by simply refining its observation and action space, aligning these more closely with the LLM's capabilities. This approach enables our base agent to significantly outperform previous methods on a wide variety of web tasks. Specifically, on WebArena, a benchmark featuring general-purpose web interaction tasks, our agent AgentOccam surpasses the previous state-of-the-art and concurrent work by 9.8 (+29.4%) and 5.9 (+15.8%) absolute points respectively, and boosts the success rate by 26.6 points (+161%) over similar plain web agents with its observation and action space alignment. Furthermore, on WebVoyager benchmark comprising tasks defined on real-world websites, AgentOccam exceeds the former best agent by 2.4 points (+4.6%) on tasks with deterministic answers. We achieve this without using in-context examples, new agent roles, online feedback or search strategies. AgentOccam's simple design highlights LLMs' impressive zero-shot performance on web tasks, and underlines the critical role of carefully tuning observation and action spaces for LLM-based agents.

Active perception approaches select future viewpoints by using some estimate of the information gain. An inaccurate estimate can be detrimental in critical situations, e.g., locating a person in distress. However the true information gained can only be calculated post hoc, i.e., after the observation is realized. We present an approach to estimate the discrepancy between the estimated information gain (which is the expectation over putative future observations while neglecting correlations among them) and the true information gain. The key idea is to analyze the mathematical relationship between active perception and the estimation error of the information gain in a gametheoretic setting. Using this, we develop an online estimation approach that achieves sub-linear regret (in the number of timesteps) for the estimation of the true information gain and reduces the sub-optimality of active perception systems. We demonstrate our approach11Code is available at https://github.com/grasp-lyd/active-perception-game. Proofs are available at https://arxiv.org/abs/2404.00769.for active perception using a comprehensive set of experiments on: (a) different types of environments, including a quadrotor in a photorealistic simulation, real-world robotic data, and real-world experiments with ground robots exploring indoor and outdoor scenes; (b) different types of robotic perception data; and (c) different map representations. On average, our approach reduces information gain estimation errors by 42%, increases the information gain by 7%, PSNR by 5%, and semantic accuracy (measured as the number of objects that are localized correctly) by 6%. In real-world experiments with a Jackal ground robot, our approach demonstrated complex trajectories to explore occluded regions.

Grid cells in the medial entorhinal cortex (MEC) and place cells in the hippocampus (HC) both form spatial representations. Grid cells fire in triangular grid patterns, while place cells fire at specific locations and respond to contextual cues. How do these interacting systems support not only spatial encoding but also internally driven path planning, such as navigating to locations recalled from cues? Here, we propose a system-level theory of MEC-HC wiring that explains how grid and place cell patterns could be connected to enable cue-triggered goal retrieval, path planning, and reconstruction of sensory experience along planned routes. We suggest that place cells autoassociate sensory inputs with grid cell patterns, allowing sensory cues to trigger recall of goal-location grid patterns. We show analytically that grid-based planning permits shortcuts through unvisited locations and generalizes local transitions to long-range paths. During planning, intermediate grid states trigger place cell pattern completion, reconstructing sensory experiences along the route. Using a single-layer RNN modeling the HC-MEC loop with a planning subnetwork, we demonstrate these effects in both biologically grounded navigation simulations using RatatouGym and visually realistic navigation tasks using Habitat Sim.

Deep Learning in Image Registration (DLIR) methods have been tremendously successful in image registration due to their speed and ability to incorporate weak label supervision at training time. However, existing DLIR methods forego many of the benefits and invariances of optimization methods. The lack of a task-specific inductive bias in DLIR methods leads to suboptimal performance, especially in the presence of domain shift. Our method aims to bridge this gap between statistical learning and optimization by explicitly incorporating optimization as a layer in a deep network. A deep network is trained to predict multi-scale dense feature images that are registered using a black box iterative optimization solver. This optimal warp is then used to minimize image and label alignment errors. By implicitly differentiating end-to-end through an iterative optimization solver, we explicitly exploit invariances of the correspondence matching problem induced by the optimization, while learning registration and label-aware features, and guaranteeing the warp functions to be a local minima of the registration objective in the feature space. Our framework shows excellent performance on in-domain datasets, and is agnostic to domain shift such as anisotropy and varying intensity profiles. For the first time, our method allows switching between arbitrary transformation representations (free-form to diffeomorphic) at test time with zero retraining. End-to-end feature learning also facilitates interpretability of features and arbitrary test-time regularization, which is not possible with existing DLIR methods.

This paper develops a real-time decentralized metric-semantic SLAM algorithm that enables a heterogeneous robot team to collaboratively construct object-based metric-semantic maps. The proposed framework integrates a data-driven front-end for instance segmentation from either RGBD cameras or LiDARs and a custom back-end for optimizing robot trajectories and object landmarks in the map. To allow multiple robots to merge their information, we design semantics-driven place recognition algorithms that leverage the informativeness and viewpoint invariance of the object-level metric-semantic map for inter-robot loop closure detection. A communication module is designed to track each robot's observations and those of other robots whenever communication links are available. The framework supports real-time, decentralized operation onboard the robots and has been integrated with three types of aerial and ground platforms. We validate its effectiveness through experiments in both indoor and outdoor environments, as well as benchmarks on public datasets and comparisons with existing methods. The framework is open-sourced and suitable for both single-agent and multi-robot real-time metric-semantic SLAM applications.

Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods to address it. This paper addresses situations when data evolves gradually. We introduce a time-varying propensity score that can detect gradual shifts in the distribution of data which allows us to selectively sample past data to update the model---not just similar data from the past like that of a standard propensity score but also data that evolved in a similar fashion in the past. The time-varying propensity score is quite general: we demonstrate different ways of implementing it and evaluate it on a variety of problems ranging from supervised learning (e.g., image classification problems) where data undergoes a sequence of gradual shifts, to reinforcement learning tasks (e.g., robotic manipulation and continuous control) where data shifts as the policy or the task changes.

Data collection for forestry, timber, and agriculture relies on manual techniques which are labor-intensive and time-consuming. We seek to demonstrate that robotics offers improvements over these techniques and can accelerate agricultural research, beginning with semantic segmentation and diameter estimation of trees in forests and orchards. We present TreeScope v1.0, the first robotics dataset for precision agriculture and forestry addressing the counting and mapping of trees in forestry and orchards. TreeScope provides LiDAR data from agricultural environments collected with robotics platforms, such as UAV and mobile robot platforms carried by vehicles and human operators. In the first release of this dataset, we provide ground-truth data with over 1,800 manually annotated semantic labels for tree stems and field-measured tree diameters. We share benchmark scripts for these tasks that researchers may use to evaluate the accuracy of their algorithms. Finally, we run our open-source diameter estimation and off-the-shelf semantic segmentation algorithms and share our baseline results.The dataset can be found at https://treescope.org, and the data pre-processing and benchmark code is available at https://github.com/KumarRobotics/treescope.

Motion planning techniques for quadrotors have advanced significantly over the past decade. Most successful planners have two stages: a front-end that determines a path that incorporates geometric (or kinematic or input) constraints and specifies the homotopy class of the trajectory, and a back-end that optimizes this path to respect dynamics and input constraints. While there are many different choices for each stage, the eventual performance depends critically not only on these choices, but also on the environment. Given a new environment, it is difficult to decide a priori how one should design a motion planner. In this work, we develop (i) a procedure to construct parametrized environments, (ii) metrics that characterize the difficulty of motion planning in these environments, and (iii) an open-source software stack that can be used to combine a wide variety of two-stage planners seamlessly. We perform experiments in simulations and a real platform. We find, somewhat conveniently, that geometric front-ends are sufficient for environments with varying complexities if combined with dynamics-aware backends. The metrics we designed faithfully capture the planning difficulty in a given environment. All code is available at https://github.com/KumarRobotics/kr_mp_design.

We study pursuit-evasion games in highly occluded urban environments, e.g. tall buildings in a city, where a scout (quadrotor) tracks multiple dynamic targets on the ground. We show that we can build a neural radiance field (NeRF) representation of the city—online—using RGB and depth images from different vantage points. This representation is used to calculate the information gain to both explore unknown parts of the city and track the targets—thereby giving a completely first-principles approach to actively tracking dynamic targets. We demonstrate, using a custom-built simulator using Open Street Maps data of Philadelphia and New York City, that we can explore and locate 20 stationary targets within 300 steps. This is slower than a greedy baseline, which does not use active perception. But for dynamic targets that actively hide behind occlusions, we show that our approach maintains, at worst, a tracking error of 200m; the greedy baseline can have a tracking error as large as 600m. We observe a number of interesting properties in the scout’s policies, e.g., it switches its attention to track a different target periodically, as the quality of the NeRF representation improves over time, the scout also becomes better in terms of target tracking.

Classical optimization and learning-based methods are the two reigning paradigms in deformable image registration. While optimization-based methods boast generalizability across modalities and robust performance, learning-based methods promise peak performance, incorporating weak supervision and amortized optimization. However, the exact conditions for either paradigm to perform well over the other are shrouded and not explicitly outlined in the existing literature. In this paper, we make an explicit correspondence between the mutual information of the distribution of per-pixel intensity and labels, and the performance of classical registration methods. This strong correlation hints to the fact that architectural designs in learning-based methods is unlikely to affect this correlation, and therefore, the performance of learning-based methods. This hypothesis is thoroughly validated with state-of-the-art classical and learning-based methods. However, learning-based methods with weak supervision can perform high-fidelity intensity and label registration, which is not possible with classical methods. Next, we show that this high-fidelity feature learning does not translate to invariance to domain shift, and learning-based methods are sensitive to such changes in the data distribution. We reassess and recalibrate performance expectations from classical and DLIR methods under access to label supervision, training time, and its generalization capabilities under minor domain shifts.

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. Code at https://github.com/neurodata/prolearn.

Correctness of instance segmentation constitutes counting the number of objects, correctly localizing all predictions and classifying each localized prediction. Average Precision is the de-facto metric used to measure all these constituents of segmentation. However, this metric does not penalize duplicate predictions in the high-recall range, and cannot distinguish instances that are localized correctly but categorized incorrectly. This weakness has inadvertently led to network designs that achieve significant gains in AP but also introduce a large number of false positives. We therefore cannot rely on AP to choose a model that provides an optimal tradeoff between false positives and high recall. To resolve this dilemma, we review alternative metrics in the literature and propose two new measures to explicitly measure the amount of both spatial and categorical duplicate predictions. We also propose a Semantic Sorting and NMS module to remove these duplicates based on a pixel occupancy matching scheme. Experiments show that modern segmentation networks have significant gains in AP, but also contain a considerable amount of duplicates. Our Semantic Sorting and NMS can be added as a plug-and-play module to mitigate hedged predictions and preserve AP.

We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the following phenomena that relate to the structure of the space of tasks: (1) the manifold of probabilistic models trained on different tasks using different representation learning methods is effectively low-dimensional; (2) supervised learning on one task results in a surprising amount of progress even on seemingly dissimilar tasks; progress on other tasks is larger if the training task has diverse classes; (3) the structure of the space of tasks indicated by our analysis is consistent with parts of the Wordnet phylogenetic tree; (4) episodic meta-learning algorithms and supervised learning traverse different trajectories during training but they fit similar models eventually; (5) contrastive and semi-supervised learning methods traverse trajectories similar to those of supervised learning. We use classification tasks constructed from the CIFAR-10 and Imagenet datasets to study these phenomena. Code is available at https://github.com/grasp-lyrl/picture_of_space_of_tasks.

Generalization error always improves with more in-distribution data. However, it is an open question what happens as we add out-of-distribution (OOD) data. Intuitively, if the OOD data is quite different, it seems more data would harm generalization error, though if the OOD data are sufficiently similar, much empirical evidence suggests that OOD data can actually improve generalization error. We show a counter-intuitive phenomenon: the generalization error of a task can be a non-monotonic function of the amount of OOD data. Specifically, we prove that generalization error can improve with small amounts of OOD data, and then get worse than no OOD data with larger amounts. In other words, there is value in training on small amounts of OOD data. We analytically demonstrate these results via Fisher’s Linear Discriminant on synthetic datasets, and empirically demonstrate them via deep networks on computer vision benchmarks such as MNIST, CIFAR-10, CINIC-10, PACS and DomainNet. In the idealistic setting where we know which samples are OOD, we show that these non-monotonic trends can be exploited using an appropriately weighted objective of the target and OOD empirical risk. While its practical utility is limited, this does suggest that if we can detect OOD samples, then there may be ways to benefit from them. When we do not know which samples are OOD, we show how a number of go-to strategies such as data-augmentation, hyper-parameter optimization and pre-training are not enough to ensure that the target generalization error does not deteriorate with the number of OOD samples in the dataset.

The main challenge of offline reinforcement learning, where data is limited, arises from a sequence of counterfactual reasoning dilemmas within the realm of potential actions: What if we were to choose a different course of action? These circumstances frequently give rise to extrapolation errors, which tend to accumulate exponentially with the problem horizon. Hence, it becomes crucial to acknowledge that not all decision steps are equally important to the final outcome, and to budget the number of counterfactual decisions a policy make in order to control the extrapolation. Contrary to existing approaches that use regularization on either the policy or value function, we propose an approach to explicitly bound the amount of out-of-distribution actions during training. Specifically, our method utilizes dynamic programming to decide where to extrapolate and where not to, with an upper bound on the decisions different from behavior policy. It balances between the potential for improvement from taking out-of-distribution actions and the risk of making errors due to extrapolation. Theoretically, we justify our method by the constrained optimality of the fixed point solution to our $Q$ updating rules. Empirically, we show that the overall performance of our method is better than the state-of-the-art offline RL methods on tasks in the widely-used D4RL benchmarks.

This paper studies the over-parameterization of deep neural networks using the Fisher Information Matrix from information geometry. We identify several surprising trends in the structure of its eigenspectrum, and how this structure relates to the eigenspectrum of the data correlation matrix. We identify how the eigenspectrum relates to the topology of the predictions of the model and develop a "model reduction'' method for deep networks. This ongoing investigation hypothesizes certain universal trends in the FIM of deep networks that may shed light on their effectiveness.

What is the best way to exploit extra data – be it unlabeled data from the same task, or labeled data from a related task – to learn a given task? This paper formalizes the question using the theory of reference priors. Reference priors are objective, uninformative Bayesian priors that maximize the mutual information between the task and the weights of the model. Such priors enable the task to maximally affect the Bayesian posterior, e.g., reference priors depend upon the number of samples available for learning the task and for very small sample sizes, the prior puts more probability mass on low-complexity models in the hypothesis space. This paper presents the first demonstration of reference priors for medium-scale deep networks and image-based data. We develop generalizations of reference priors and demonstrate applications to two problems. First, by using unlabeled data to compute the reference prior, we develop new Bayesian semi-supervised learning methods that remain effective even with very few samples per class. Second, by using labeled data from the source task to compute the reference prior, we develop a new pretraining method for transfer learning that allows data from the target task to maximally affect the Bayesian posterior. Empirical validation of these methods is conducted on image classification datasets. Code is available at https://github.com/grasp-lyrl/deep_reference_priors

We show that the input correlation matrix of typical classification datasets has an eigenspectrum where, after a sharp initial drop, a large number of small eigenvalues are distributed uniformly over an exponentially large range. This structure is mirrored in a network trained on this data: we show that the Hessian and the Fisher Information Matrix (FIM) have eigenvalues that are spread uniformly over exponentially large ranges. We call such eigenspectra “sloppy” because sets of weights corresponding to small eigenvalues can be changed by large magnitudes without affecting the loss. Networks trained on atypical datasets with non-sloppy inputs do not share these traits and deep networks trained on such datasets generalize poorly. Inspired by this, we study the hypothesis that sloppiness of inputs aids generalization in deep networks. We show that if the Hessian is sloppy, we can compute non-vacuous PAC-Bayes generalization bounds analytically. By exploiting our empirical observation that training predominantly takes place in the non-sloppy subspace of the FIM, we develop data-distribution dependent PAC-Bayes priors that lead to accurate generalization bounds using numerical optimization.

This paper prescribes a distance between learning tasks modeled as joint distributions on data and labels. Using tools in information geometry, the distance is defined to be the length of the shortest weight trajectory on a Riemannian manifold as a classifier is fitted on an interpolated task. The interpolated task evolves from the source to the target task using an optimal transport formulation. This distance, which we call the "coupled transfer distance" can be compared across different classifier architectures. We develop an algorithm to compute the distance which iteratively transports the marginal on the data of the source task to that of the target task while updating the weights of the classifier to track this evolving data distribution. We develop theory to show that our distance captures the intuitive idea that a good transfer trajectory is the one that keeps the generalization gap small during transfer, in particular at the end on the target task. We perform thorough empirical validation and analysis across diverse image classification datasets to show that the coupled transfer distance correlates strongly with the difficulty of fine-tuning.

Autonomous navigation in crowded, complex urban environments requires interacting with other agents on the road. A common solution to this problem is to use a prediction model to guess the likely future actions of other agents. While this is reasonable, it leads to overly conservative plans because it does not explicitly model the mutual influence of the actions of interacting agents. This paper builds a reinforcement learning-based method named MIDAS where an Ego agent learns to affect the control actions of other cars in urban driving scenarios. MIDAS uses an attention mechanism to handle an arbitrary number of other agents and includes a "driver-type" parameter to learn a single policy that works across different planning objectives. We build a simulation environment that enables diverse interaction experiments with a large number of agents and develop methods for quantitatively studying the safety, efficiency, and interaction among vehicles. MIDAS is validated using extensive experiments and we show that it (i) can work across different road geometries, (ii) results in an adaptive Ego policy that can be tuned easily to satisfy different performance criteria, such as aggressive or cautious driving, (iii) is robust to changes in the driving policies of external agents, and (iv) is safer and more efficient than existing approaches to interaction-aware decision-making. Code available here.

We propose a framework for deformable linear object prediction. Prediction of deformable objects (e.g., rope) is challenging due to their non-linear dynamics and infinite-dimensional configuration spaces. By mapping the dynamics from a non-linear space to a linear space, we can use the good properties of linear dynamics for easier learning and more efficient prediction. We learn a locally linear, action-conditioned dynamics model that can be used to predict future latent states. Then, we decode the predicted latent state into the predicted state. We also apply a sampling-based optimization algorithm to select the optimal control action. We empirically demonstrate that our approach can predict the rope state accurately up to ten steps into the future and that our algorithm can find the optimal action given an initial state and a goal state.

We develop a Multi-Agent Reinforcement Learning (MARL) method to learn scalable control policies for target tracking. Our method can handle an arbitrary number of pursuers and targets; we show results for tasks consisting up to 1000 pursuers tracking 1000 targets. We use a decentralized, partially-observable Markov Decision Process framework to model pursuers as agents receiving partial observations (range and bearing) about targets which move using fixed, unknown policies. An attention mechanism is used to parameterize the value function of the agents; this mechanism allows us to handle an arbitrary number of targets. Entropy-regularized off-policy RL methods are used to train a stochastic policy, and we discuss how it enables a hedging behavior between pursuers that leads to a weak form of cooperation in spite of completely decentralized control execution. We further develop a masking heuristic that allows training on smaller problems with few pursuers-targets and execution on much larger problems. Thorough simulation experiments and comparisons to state of the art algorithms are performed to study the scalability of the approach and robustness of performance to varying numbers of agents and targets.

Reliant on too many experiments to learn good actions, current Reinforcement Learning (RL) algorithms have limited applicability in real-world settings, which can be too expensive to allow exploration. We propose an algorithm for batch RL, where effective policies are learned using only a fixed offline dataset instead of online interactions with the environment. The limited data in batch RL produces inherent uncertainty in value estimates of states/actions that were insufficiently represented in the training data. This leads to particularly severe extrapolation when our candidate policies diverge from one that generated the data. We propose to mitigate this issue via two straightforward penalties: a policy-constraint to reduce this divergence and a value-constraint that discourages overly optimistic estimates. Over a comprehensive set of $32$ continuous-action batch RL benchmarks, our approach compares favorably to state-of-the-art methods, regardless of how the offline data were collected.

This paper employs a formal connection of machine learning with thermodynamics to characterize the quality of learnt representations for transfer learning. We discuss how information-theoretic functionals such as rate, distortion and classification loss of a model lie on a convex, so-called equilibrium surface. We prescribe dynamical processes to traverse this surface under constraints, e.g., an iso-classification process that trades off rate and distortion to keep the classification loss unchanged. We demonstrate how this process can be used for transferring representations from a source dataset to a target dataset while keeping the classification loss constant. Experimental validation of the theoretical results is provided on standard image-classification datasets.

This paper introduces two simple techniques to improve off-policy Reinforcement Learning (RL) algorithms. First, we formulate off-policy RL as a stochastic proximal point iteration. The target network plays the role of the variable of optimization and the value network computes the proximal operator. Second, we exploits the two value functions commonly employed in state-of-the-art off-policy algorithms to provide an improved action value estimate through bootstrapping with limited increase of computational resources. Further, we demonstrate significant performance improvement over state-of-the-art algorithms on standard continuous-control RL benchmarks.

Automated machine learning (AutoML) can produce complex model ensembles by stacking, bagging, and boosting many individual models like trees, deep networks, and nearest neighbor estimators. While highly accurate, the resulting predictors are large, slow, and opaque as compared to their constituents. To improve the deployment of AutoML on tabular data, we propose FAST-DAD to distill arbitrarily-complex ensemble predictors into individual models like boosted trees, random forests, and deep networks. At the heart of our approach is a data augmentation strategy based on Gibbs sampling from a self-attention pseudolikelihood estimator. Across 30 datasets spanning regression and binary/multiclass classification tasks, FAST-DAD distillation produces significantly better individual models than one obtains through standard training on the original data. Our individual distilled models are over 10x faster and more accurate than ensemble predictors produced by AutoML tools like H2O/AutoSklearn.

The amount of home-based exercise prescribed by a physical therapist is difficult to monitor. However, the integration of wearable inertial measurement unit (IMU) devices can aid in monitoring home exercise by analyzing exercise biomechanics. The objective of this study is to evaluate machine learning models for classifying nine different upper extremity exercises, based upon kinematic data captured from an IMU-based device. Fifty participants performed one compound and eight isolation exercises with their right arm. Each exercise was performed ten times for a total of 4500 trials. Joint angles were calculated using IMUs that were placed on the hand, forearm, upper arm, and torso. Various machine learning models were developed with different algorithms and train-test splits. Random forest models with flattened kinematic data as a feature had the greatest accuracy (98.6%). Using triaxial joint range of motion as the feature set resulted in decreased accuracy (91.9%) with faster speeds. Accuracy did not decrease below 90% until training size was decreased to 5% from 50%. Accuracy decreased (88.7%) when splitting data by participant. Upper extremity exercises can be classified accurately using kinematic data from a wearable IMU device. A random forest classification model was developed that quickly and accurately classified exercises. Sampling frequency and lower training splits had a modest effect on performance. When the data were split by subject stratification, larger training sizes were required for acceptable algorithm performance. These findings set the basis for more objective and accurate measurements of home-based exercise using emerging healthcare technologies.

This paper investigates motion-planning using formal language specifications for dynamical systems with differential constraints. In particular, we focus on process algebra as a language to specify complex task specifications motivated by autonomous electric vehicles operating in a mobility-on-demand scenario. We use ideas from sampling-based motion-planning algorithms to incrementally construct a finite abstraction of the dynamical system as a Kripke structure. Given a task specification expressed as a process graph, we use model checking techniques to construct a weighted product graph of the specification with the Kripke structure. We then devise an algorithm that provably converges to the optimal trajectory of the dynamical system that satisfies the task specification as the number of the states in the Kripke structure goes to infinity. The algorithm is demonstrated in simulation experiments, viz., charging the electric car at a busy charging station and scheduling pick-ups and drop-offs of passengers.

We consider a class of multi-robot motion planning problems where each robot is associated with multiple objectives and decoupled task specifications. The problems are formulated as an open-loop non-cooperative differential game. A distributed anytime algorithm is proposed to compute a Nash equilibrium of the game. The following properties are proven: (i) the algorithm asymptotically converges to the set of Nash equilibrium; (ii) for scalar cost functionals, the price of stability equals one; (iii) for the worst case, the computational complexity and communication cost are linear in the robot number.