We introduce a cooperative Bayesian optimization problem for optimizing black-box functions of two variables where two agents choose together at which points to query the function but have only control over one variable each. This setting is inspired by human-AI teamwork, where an AI-assistant helps its human user solve a problem, in this simplest case, collaborative optimization. We formulate the solution as sequential decision-making, where the agent we control models the user as a computationally rational agent with prior knowledge about the function. We show that strategic planning of the queries enables better identification of the global maximum of the function as long as the user avoids excessive exploration. This planning is made possible by using Bayes Adaptive Monte Carlo planning and by endowing the agent with a user model that accounts for conservative belief updates and exploratory sampling of the points to query.

Reliable localization is an essential capability for marine robots navigating in GPS-denied environments. SLAM, commonly used to mitigate dead reckoning errors, still fails in feature-sparse environments or with limited-range sensors. Pose estimation can be improved by incorporating the uncertainty prediction of future poses into the planning process and choosing actions that reduce uncertainty. However, performing belief propagation is computationally costly, especially when operating in large-scale environments. This work proposes a computationally efficient planning under uncertainty frame-work suitable for large-scale, feature-sparse environments. Our strategy leverages SLAM graph and occupancy map data obtained from a prior exploration phase to create a virtual map, describing the uncertainty of each map cell using a multivariate Gaussian. The virtual map is then used as a cost map in the planning phase, and performing belief propagation at each step is avoided. A receding horizon planning strategy is implemented, managing a goal-reaching and uncertainty-reduction tradeoff. Simulation experiments in a realistic underwater environment validate this approach. Experimental comparisons against a full belief propagation approach and a standard shortest-distance approach are conducted.

Morden deep ensembles technique achieves strong uncertainty estimation performance by going through multiple forward passes with different models. This is at the price of a high storage space and a slow speed in the inference (test) time. To address this issue, we propose Density-Regression, a method that leverages the density function in uncertainty estimation and achieves fast inference by a single forward pass. We prove it is distance aware on the feature space, which is a necessary condition for a neural network to produce high-quality uncertainty estimation under distribution shifts. Empirically, we conduct experiments on regression tasks with the cubic toy dataset, benchmark UCI, weather forecast with time series, and depth estimation under real-world shifted applications. We show that Density-Regression has competitive uncertainty estimation performance under distribution shifts with modern deep regressors while using a lower model size and a faster inference speed.

Self-reflecting about our performance (e.g., how confident we are) before doing a task is essential for decision making, such as selecting the most suitable tool or choosing the best route to drive. While this form of awareness -- thinking about our performance or metacognitive performance -- is well-known in humans, robots still lack this cognitive ability. This reflective monitoring can enhance their embodied decision power, robustness and safety. Here, we take a step in this direction by introducing a mathematical framework that allows robots to use their control self-confidence to make better-informed decisions. We derive a mathematical closed-form expression for control confidence for dynamic systems (i.e., the posterior inverse covariance of the control action). This control confidence seamlessly integrates within an objective function for decision making, that balances the: i) performance for task completion, ii) control effort, and iii) self-confidence. To evaluate our theoretical account, we framed the decision-making within the tool selection problem, where the agent has to select the best robot arm for a particular control task. The statistical analysis of the numerical simulations with randomized 2DOF arms shows that using control confidence during tool selection improves both real task performance, and the reliability of the tool for performance under unmodelled perturbations (e.g., external forces). Furthermore, our results indicate that control confidence is an early indicator of performance and thus, it can be used as a heuristic for making decisions when computation power is restricted or decision-making is intractable. Overall, we show the advantages of using confidence-aware decision-making and control scheme for dynamic systems.

Abrupt maneuvers by surrounding vehicles (SVs) can typically lead to safety concerns and affect the task efficiency of the ego vehicle (EV), especially with model uncertainties stemming from environmental disturbances. This paper presents a real-time fail-operational controller that ensures the asymptotic convergence of an uncertain EV to a safe state, while preserving task efficiency in dynamic environments. An incremental Bayesian learning approach is developed to facilitate online learning and inference of changing environmental disturbances. Leveraging disturbance quantification and constraint transformation, we develop a stochastic fail-operational barrier based on the control barrier function (CBF). With this development, the uncertain EV is able to converge asymptotically from an unsafe state to a defined safe state with probabilistic stability. Subsequently, the stochastic fail-operational barrier is integrated into an efficient fail-operational controller based on quadratic programming (QP). This controller is tailored for the EV operating under control constraints in the presence of environmental disturbances, with both safety and efficiency objectives taken into consideration. We validate the proposed framework in connected cruise control (CCC) tasks, where SVs perform aggressive driving maneuvers. The simulation results demonstrate that our method empowers the EV to swiftly return to a safe state while upholding task efficiency in real time, even under time-varying environmental disturbances.

Given time series data, how can we answer questions like "what will happen in the future?" and "how did we get here?" These sorts of probabilistic inference questions are challenging when observations are high-dimensional. In this paper, we show how these questions can have compact, closed form solutions in terms of learned representations. The key idea is to apply a variant of contrastive learning to time series data. Prior work already shows that the representations learned by contrastive learning encode a probability ratio. By extending prior work to show that the marginal distribution over representations is Gaussian, we can then prove that joint distribution of representations is also Gaussian. Taken together, these results show that representations learned via temporal contrastive learning follow a Gauss-Markov chain, a graphical model where inference (e.g., prediction, planning) over representations corresponds to inverting a low-dimensional matrix. In one special case, inferring intermediate representations will be equivalent to interpolating between the learned representations. We validate our theory using numerical simulations on tasks up to 46-dimensions.

Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these contexts, with autoregressive models being especially prominent. This dissertation focuses on using autoregressive models to answer complex probabilistic queries that go beyond single-step prediction, such as the timing of future events or the likelihood of a specific event occurring before another. In particular, we develop a broad class of novel and efficient approximation techniques for marginalization in sequential models that are model-agnostic. These techniques rely solely on access to and sampling from next-step conditional distributions of a pre-trained autoregressive model, including both traditional parametric models as well as more recent neural autoregressive models. Specific approaches are presented for discrete sequential models, for marked temporal point processes, and for stochastic jump processes, each tailored to a well-defined class of informative, long-range probabilistic queries.

Existing causal discovery methods based on combinatorial optimization or search are slow, prohibiting their application on large-scale datasets. In response, more recent methods attempt to address this limitation by formulating causal discovery as structure learning with continuous optimization but such approaches thus far provide no statistical guarantees. In this paper, we show that by efficiently parallelizing existing causal discovery methods, we can in fact scale them to thousands of dimensions, making them practical for substantially larger-scale problems. In particular, we parallelize the LiNGAM method, which is quadratic in the number of variables, obtaining up to a 32-fold speed-up on benchmark datasets when compared with existing sequential implementations. Specifically, we focus on the causal ordering subprocedure in DirectLiNGAM and implement GPU kernels to accelerate it. This allows us to apply DirectLiNGAM to causal inference on large-scale gene expression data with genetic interventions yielding competitive results compared with specialized continuous optimization methods, and Var-LiNGAM for causal discovery on U.S. stock data.

In this paper we propose an efficient data-driven solution to self-localization within a floorplan. Floorplan data is readily available, long-term persistent and inherently robust to changes in the visual appearance. Our method does not require retraining per map and location or demand a large database of images of the area of interest. We propose a novel probabilistic model consisting of an observation and a novel temporal filtering module. Operating internally with an efficient ray-based representation, the observation module consists of a single and a multiview module to predict horizontal depth from images and fuses their results to benefit from advantages offered by either methodology. Our method operates on conventional consumer hardware and overcomes a common limitation of competing methods that often demand upright images. Our full system meets real-time requirements, while outperforming the state-of-the-art by a significant margin.

Recurrent Spiking Neural Networks (RSNNs) have emerged as a computationally efficient and brain-inspired learning model. The design of sparse RSNNs with fewer neurons and synapses helps reduce the computational complexity of RSNNs. Traditionally, sparse SNNs are obtained by first training a dense and complex SNN for a target task, and, then, pruning neurons with low activity (activity-based pruning) while maintaining task performance. In contrast, this paper presents a task-agnostic methodology for designing sparse RSNNs by pruning a large randomly initialized model. We introduce a novel Lyapunov Noise Pruning (LNP) algorithm that uses graph sparsification methods and utilizes Lyapunov exponents to design a stable sparse RSNN from a randomly initialized RSNN. We show that the LNP can leverage diversity in neuronal timescales to design a sparse Heterogeneous RSNN (HRSNN). Further, we show that the same sparse HRSNN model can be trained for different tasks, such as image classification and temporal prediction. We experimentally show that, in spite of being task-agnostic, LNP increases computational efficiency (fewer neurons and synapses) and prediction performance of RSNNs compared to traditional activity-based pruning of trained dense models.