The features in many prediction models naturally take the form of a hierarchy. The lower levels represent individuals or events. These units group naturally into locations and intervals or other aggregates, often at multiple levels. Levels of groupings may intersect and join, much as relational database tables do. Besides representing the structure of the data, predictive features in hierarchical models can be assigned to their proper levels. Such models lend themselves to hierarchical Bayes solution methods that ``share'' results of inference between groups by generalizing over the case of individual models for each group versus one model that aggregates all groups into one. In this paper we show our work-in-progress applying a hierarchical Bayesian model to forecast purchases throughout the day at store franchises, with groupings over locations and days of the week. We demonstrate using the \textsf{stan} package on individual sales transaction data collected over the course of a year. We show how this solves the dilemma of having limited data and hence modest accuracy for each day and location, while being able to scale to a large number of locations with improved accuracy.

Neuro-symbolic artificial intelligence is an emerging area that combines traditional symbolic techniques with neural networks. In this paper, we consider its application to sequential decision making under uncertainty. We introduce neuro-symbolic partially observable Markov decision processes (NS-POMDPs), which model an agent that perceives a continuous-state environment using a neural network and makes decisions symbolically, and study the problem of optimising discounted cumulative rewards. This requires functions over continuous-state beliefs, for which we propose a novel piecewise linear and convex representation (P-PWLC) in terms of polyhedra covering the continuous-state space and value vectors, and extend Bellman backups to this representation. We prove the convexity and continuity of value functions and present two value iteration algorithms that ensure finite representability by exploiting the underlying structure of the continuous-state model and the neural perception mechanism. The first is a classical (exact) value iteration algorithm extending $\alpha$-functions of Porta et al (2006) to the P-PWLC representation for continuous-state spaces. The second is a point-based (approximate) method called NS-HSVI, which uses the P-PWLC representation and belief-value induced functions to approximate value functions from below and above for two types of beliefs, particle-based and region-based. Using a prototype implementation, we show the practical applicability of our approach on two case studies that employ (trained) ReLU neural networks as perception functions, dynamic car parking and an aircraft collision avoidance system, by synthesising (approximately) optimal strategies. An experimental comparison with the finite-state POMDP solver SARSOP demonstrates that NS-HSVI is more robust to particle disturbances.

Reinforcement learning (RL) has achieved remarkable success in complex robotic systems (eg. quadruped locomotion). In previous works, the RL-based controller was typically implemented as a single neural network with concatenated observation input. However, the corresponding learned policy is highly task-specific. Since all motors are controlled in a centralized way, out-of-distribution local observations can impact global motors through the single coupled neural network policy. In contrast, animals and humans can control their limbs separately. Inspired by this biological phenomenon, we propose a Decentralized motor skill (DEMOS) learning algorithm to automatically discover motor groups that can be decoupled from each other while preserving essential connections and then learn a decentralized motor control policy. Our method improves the robustness and generalization of the policy without sacrificing performance. Experiments on quadruped and humanoid robots demonstrate that the learned policy is robust against local motor malfunctions and can be transferred to new tasks.

Reinforcement Learning (RL) algorithms have shown tremendous success in simulation environments, but their application to real-world problems faces significant challenges, with safety being a major concern. In particular, enforcing state-wise constraints is essential for many challenging tasks such as autonomous driving and robot manipulation. However, existing safe RL algorithms under the framework of Constrained Markov Decision Process (CMDP) do not consider state-wise constraints. To address this gap, we propose State-wise Constrained Policy Optimization (SCPO), the first general-purpose policy search algorithm for state-wise constrained reinforcement learning. SCPO provides guarantees for state-wise constraint satisfaction in expectation. In particular, we introduce the framework of Maximum Markov Decision Process, and prove that the worst-case safety violation is bounded under SCPO. We demonstrate the effectiveness of our approach on training neural network policies for extensive robot locomotion tasks, where the agent must satisfy a variety of state-wise safety constraints. Our results show that SCPO significantly outperforms existing methods and can handle state-wise constraints in high-dimensional robotics tasks.

We develop an algorithm for automatic differentiation of Metropolis-Hastings samplers, allowing us to differentiate through probabilistic inference, even if the model has discrete components within it. Our approach fuses recent advances in stochastic automatic differentiation with traditional Markov chain coupling schemes, providing an unbiased and low-variance gradient estimator. This allows us to apply gradient-based optimization to objectives expressed as expectations over intractable target densities. We demonstrate our approach by finding an ambiguous observation in a Gaussian mixture model and by maximizing the specific heat in an Ising model.

We study sampling problems associated with potentials that lack smoothness. The potentials can be either convex or non-convex. Departing from the standard smooth setting, the potentials are only assumed to be weakly smooth or non-smooth, or the summation of multiple such functions. We develop a sampling algorithm that resembles proximal algorithms in optimization for this challenging sampling task. Our algorithm is based on a special case of Gibbs sampling known as the alternating sampling framework (ASF). The key contribution of this work is a practical realization of the ASF based on rejection sampling for both non-convex and convex potentials that are not necessarily smooth. In almost all the cases of sampling considered in this work, our proximal sampling algorithm achieves better complexity than all existing methods.

Despite its importance in both industrial and service robotics, mobile manipulation remains a significant challenge as it requires a seamless integration of end-effector trajectory generation with navigation skills as well as reasoning over long-horizons. Existing methods struggle to control the large configuration space, and to navigate dynamic and unknown environments. In previous work, we proposed to decompose mobile manipulation tasks into a simplified motion generator for the end-effector in task space and a trained reinforcement learning agent for the mobile base to account for kinematic feasibility of the motion. In this work, we introduce Neural Navigation for Mobile Manipulation (N$^2$M$^2$) which extends this decomposition to complex obstacle environments and enables it to tackle a broad range of tasks in real world settings. The resulting approach can perform unseen, long-horizon tasks in unexplored environments while instantly reacting to dynamic obstacles and environmental changes. At the same time, it provides a simple way to define new mobile manipulation tasks. We demonstrate the capabilities of our proposed approach in extensive simulation and real-world experiments on multiple kinematically diverse mobile manipulators. Code and videos are publicly available at http://mobile-rl.cs.uni-freiburg.de.

Statistical machine learning methods often face the challenge of limited data available from the population of interest. One remedy is to leverage data from auxiliary source populations, which share some conditional distributions or are linked in other ways with the target domain. Techniques leveraging such \emph{dataset shift} conditions are known as \emph{domain adaptation} or \emph{transfer learning}. Despite extensive literature on dataset shift, limited works address how to efficiently use the auxiliary populations to improve the accuracy of risk evaluation for a given machine learning task in the target population. In this paper, we study the general problem of efficiently estimating target population risk under various dataset shift conditions, leveraging semiparametric efficiency theory. We consider a general class of dataset shift conditions, which includes three popular conditions -- covariate, label and concept shift -- as special cases. We allow for partially non-overlapping support between the source and target populations. We develop efficient and multiply robust estimators along with a straightforward specification test of these dataset shift conditions. We also derive efficiency bounds for two other dataset shift conditions, posterior drift and location-scale shift. Simulation studies support the efficiency gains due to leveraging plausible dataset shift conditions.

We focus on the problem of uncertainty informed allocation of medical resources (vaccines) to heterogeneous populations for managing epidemic spread. We tackle two related questions: (1) For a compartmental ordinary differential equation (ODE) model of epidemic spread, how can we estimate and integrate parameter uncertainty into resource allocation decisions? (2) How can we computationally handle both nonlinear ODE constraints and parameter uncertainties for a generic stochastic optimization problem for resource allocation? To the best of our knowledge current literature does not fully resolve these questions. Here, we develop a data-driven approach to represent parameter uncertainty accurately and tractably in a novel stochastic optimization problem formulation. We first generate a tractable scenario set by estimating the distribution on ODE model parameters using Bayesian inference with Gaussian processes. Next, we develop a parallelized solution algorithm that accounts for scenario-dependent nonlinear ODE constraints. Our scenario-set generation procedure and solution approach are flexible in that they can handle any compartmental epidemiological ODE model. Our computational experiments on two different non-linear ODE models (SEIR and SEPIHR) indicate that accounting for uncertainty in key epidemiological parameters can improve the efficacy of time-critical allocation decisions by 4-8%. This improvement can be attributed to data-driven and optimal (strategic) nature of vaccine allocations, especially in the early stages of the epidemic when the allocation strategy can crucially impact the long-term trajectory of the disease.

Recently, a new class of non-convex optimization problems motivated by the statistical problem of learning an acyclic directed graphical model from data has attracted significant interest. While existing work uses standard first-order optimization schemes to solve this problem, proving the global optimality of such approaches has proven elusive. The difficulty lies in the fact that unlike other non-convex problems in the literature, this problem is not "benign", and possesses multiple spurious solutions that standard approaches can easily get trapped in. In this paper, we prove that a simple path-following optimization scheme globally converges to the global minimum of the population loss in the bivariate setting.